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1 PRIMA 2013-Table of Contents

Table of Contents

Welcome………………………………………………………………………………………………………………….2

Organization ...... 3 Scientific Committee ...... 3 Local Organizing Committee ...... 3 Local Advisory Committee ...... 3 Public Lecturers ...... 3 Plenary Speakers ...... 4 Special Sessions & Organizers ...... 4 Sponsors ...... 6

Useful Information ...... 7 Congress Venues…………………………………………………………………………………………..…..7 Hotel…………………………………………………………………………………………………………………7 Transportation Directions ...... 7 Airports & Railway Stations ...... 7 Congress Bus ...... 9 Dining ...... 9 On-campus Dining ...... 9 Off-campus Dining……………………………………………………………………………………10 Standard Audio/Visual Set-up…………………………………………………………………………..10 Internet Access…………………………………………………………………………………………………10 Get-togethers……………………………………………………………………………………………………10 Book Display..……………………………………………………………………………………………………10

Program…………………………………………………………………………………………………………………13 Schedule-at-a-Glance……..………………………………………………………………………………..13 Monday, June 24………………..…………………………………………………………………………..14 Tuesday, June 25…….………………………………………………………………………………………23 Wednesday, June 26…...……………………………………………………………………………………32 Thursday, June 27...…..……………………………………………………………………………………33 Friday, June 28….………………………………………………………………………………………………42

Abstracts……………………………………………………………………………………………………Appendix 1 Map from Airports to Hua Ting Hotel & Towers…………………...... …Appendix 2 Map of SJTU Xuhui Campus ...... Appendix 3 Floor Plan of Engineering Hall ...... ………….Appendix 4

2 PRIMA 2013-Welcome

Welcome

Dear Colleagues,

It is a pleasure for me to write a few words of welcome on behalf of the scientific and organizing committees for the 2013 PRIMA Congress, which will take place at Jiao Tong University in the vibrant city of Shanghai, China on June 24- 28, 2013. PRIMA, the Pacific Rim Mathematical Association, was established in 2005 as an organization for promoting the development of mathematical sciences in the Pacific Rim region. Our most important activity is the PRIMA Congress, which is held every four years. Our inaugural event took place in Sydney, Australia in 2009.

The 2013 PRIMA Congress promises to be an exciting event, with world-class plenary lectures and public speakers. In addition there will be 23 special sessions or mini-symposia in a broad array of topics in the mathematical sciences, with participants from all over the Pacific Rim. Our host for this event is Shanghai Jiao Tong University, and they have done a wonderful job with the local arrangements. Aside from the excellent scientific program, the Congress will be a unique opportunity for participants to establish contacts throughout the Pacific Rim. We would like to invite the mathematical community to attend this meeting and join us in celebrating the incredible vitality and intellectual richness of our region.

We are looking forward to welcoming you to the 2013 PRIMA Congress in Shanghai!

With best regards,

Alejandro Adem Director of PRIMA University of British Columbia, Vancouver, Canada

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3 PRIMA 2013-Organization

Organization

Scientific Committee Local Organizing Committee at SJTU

Alejandro Adem, Shi Jin (Chair) The University of British Columbia, Canada David Cai Federico Ardila Dong Han San Francisco State University, USA Jianguo Huang Marston Conder Hongze Li University of Auckland, New Zealand Yachun Li David Eisenbud Lihe Wang UC Berkeley, USA Weike Wang Yakov Eliashberg Ya-Guang Wang Stanford University, USA Yaokun Wu Nassif Ghoussoub Dongmei Xiao The University of British Columbia, Canada Pu Zhang Tony Guttmann Xiao-Dong Zhang University of Melbourne, Australia Xiaoqun Zhang Le Minh Ha Vietnam National University, Vietnam Local Advisory Committee Shi Jin Shanghai Jiao Tong University, China and Kungching Chang, Peking University University of Wisconsin-Madison, USA Weinan E, Princeton University and Peking Alejandro Jofré University University of Chile, Chile Lei Guo, Chinese Academy of Sciences Yujiro Kawamata Jiaxing Hong, The University of Tokyo, Japan Peiwen Ji, National Natural Science Jong HaeKeum Foundation of China Korea Institute for Advanced Study, Korea Tatsien Li, Fudan University Doug Lind Yiming Long, Nankai University University of Washington, USA Zhongci Shi, Chinese Academy of Sciences KyewonKoh Park Jie Wang, National Natural Science Ajou University, Korea Foundation of China Shige Peng Jie Zhang, Shanghai Jiao Tong University Shandong University, China

Jose Seade Universidad Nacional Autónoma de México, Public Lecturers México Gang Tian , University of California, San Princeton University and Peking University, Diego, USA USA/China Cédric Villani, Université de Lyon and Institut Tatiana Toro Henri Poincaré, France University of Washington, USA 4 PRIMA 2013-Organization

Yuxin Dong (Fudan University, China) Plenary Lecturers Martin A. Guest (Waseda University, Japan) Martin Barlow, University of British Columbia, Wei Zhang (University of Science and Canada Technology of China, China) Andrea Bertozzi, University of California, Los 5. Combinatorics and Discrete Angeles, USA Andreas Dress (Chinese Academy of Sciences, Weinan E, Princeton University, USA and China) Peking University, China Jing Huang (University of Victoria, Canada) Jun-Muk Hwang, Korea Institute for Advanced Yaokun Wu (Shanghai Jiao Tong University, Study, Korea China) Vaughan Jones, University of California, 6. Geometric Analysis Berkeley, USA Jie Qing (University of California, Santa Cruz, Zhi-Ming Ma, Chinese Academy of Sciences, USA) China Gang Tian (Princeton University and Peking Matilde Marcolli, California Institute of University, USA/China) Technology, USA Xiaohua Zhu (Peking University, China) Arun Ram, University of Melbourne, Australia 7. Geometric Aspects of Semilinear Elliptic Yongbin Ruan, University of Michigan, USA Equations: Recent Advances & Future Shuji Saito, Tokyo Institute of Technology, Perspectives Japan Nassif Ghoussoub (The University of British Weiping Zhang, Nankai University, China Columbia, Canada) Manuel del Pino (University of Chile, Chile) Juncheng Wei (The Chinese University of Special Sessions & Organizers Hong Kong, Hong Kong) 1. A Glimpse of Stochastic Dynamics 8. Hyperbolic Conservation Laws and Related Jinqiao Duan (University of California, Los Applications Angeles & Illinois Institute of Technology, Feimin Huang (Chinese Academy of Sciences, USA) China) Hongjun Gao (Nanjing Normal University, Dehua Wang (University of Pittsburgh, USA) China) Ya-Guang Wang (Shanghai Jiao Tong 2. Algebraic and Complex Geometry University, China) Yujiro Kawamata (The University of Tokyo, 9. Inverse Problems Japan) Guillaume Bal (Columbia University, USA) JongHaeKeum (Korea Institute for Advanced Jin Cheng (Fudan University, China) Study, Korea) Gunther Uhlmann (University of Washington, 3. Algebraic Topology and Related Topics USA) Alejandro Adem (The University of British 10. Kinetic Equations Columbia, Canada) Radjesvarane Alexandre (Shanghai Jiao Tong Alan Jonathan Berrick (National University of University, China) Singapore, Singapore) Benoit Perthame (University of Pierre and Craig Westerland (University of Melbourne, Marie Curie, France) Australia) 11. Mathematical Dynamics and 4. Applications of Harmonic Maps and Related Topics Submanifold Theory Dongho Chae (Chung-Ang University, Korea) 5 PRIMA 2013-Organization

Yoshikazu Giga (The University of Tokyo, 18. Probability Japan) Shige Peng (Shandong University, China) Yasunori Maekawa (Kobe University, Japan) Martin Barlow (The University of British Tai-Peng Tsai (The University of British Columbia, Canada) Columbia, Canada) 19. Representation Theory and 12. Mathematics of String Theory Categorification Peter Bouwknegt (Australian National Xuhua He (Hong Kong University of Science University, Australia) and Technology, Hong Kong) Mathai Varghese (The University of Adelaide, Joel Kamnitzer (University of Toronto, Australia) Canada) Siye Wu (Hong Kong University, Hong Kong) Tony Licata (Australian National University, 13. Measurable and Topological Dynamics Australia) Alejandro Maass (University of Chile, Chile) James Parkinson (University of Sydney, Hitoshi Nakada (Keio University, Japan) Australia) KyewonKoh Park (Ajou University, Korea) Arun Ram (University of Melbourne, Xiangdong Ye (University of Science and Australia) Technology of China, China) 20. Singularities in Geometry and Topology 14. Multiscale Analysis and Algorithms Guangfeng Jiang (Peking University of Weinan E (Princeton University and Peking Chemical Technology, China) University, USA/China) Laurentiu Maxim (University of Carlos Garcia-Cervera (University of California, Wisconsin-Madison, USA) Santa Barbara, USA) Mutsuo Oka (Tokyo University of Science, Pingbing Ming (Chinese Academy of Sciences, Japan) China) Jose Seade (Universidad NacionalAutonoma 15. Number Theory and Representation de Mexico, Mexico) Theory 21. Symplectic Geometry and Hamiltonian Clifton Cunningham (University of Calgary, Dynamics Canada) YakovEliashberg (Stanford University, USA) Atsushi Ichino (Kyoto University, Japan) Yiming Long (Nankai University, China) Vinayak Vatsal (The University of British 22. Symplectic Geometry and Mathematical Columbia, Canada) Physics 16. Operator Algebras and Harmonic Analysis Xiaobo Liu (University of Notre Dame and Anthony Lau (University of Alberta, Canada) Peking University, USA/China) Zhong-Jin Ruan (University of Illinois at Huijun Fan (Peking University, China) Urbana-Champaign, USA) 23. Triangulated Categories in 17. Optimization Representation Theory of Algebras Regina Burachik (University of South Australia, Ragnar-Olaf Buchweitz (University of Toronto, Australia) Canada) Xiaojun Chen (Hong Kong Polytechnic Shiping Liu (University of Sherbrook, Canada) University, Hong Kong) Claus Michael Ringel (Universitaet Bielefeld, Alejandro Jofré (Center for Mathematical Germany) Modeling, Chile) Pu Zhang (Shanghai Jiao Tong University, Hector Ramirez (Center for Mathematical China) Modeling, Chile) 6 PRIMA 2013-Sponsors

Funding Agencies and Sponsors PRIMA and the organizing committee of the 2nd PRIMA Congress wish to extend their thanks and appreciation to the following agencies for their supports to this congress.

7 PRIMA 2013-Useful Information

Useful Information

Congress Venues

Opening Ceremony /Public & Plenary Lectures, Wen Zhi Hall, SJTU Xuhui Campus Special Sessions & Contributed Talks, Engineering Hall, SJTU Xuhui Campus Address: No. 1954, Hua Shan Road, , Shanghai, China (上海交通大学徐汇校区地址：上海市徐汇区华山路 1954 号)

The Second PRIMA Congress will be convened at the Xuhui Campus of Shanghai Jiao Tong University. SJTU, one of the top universities of China, boasts a long history of more than 117 years. Xuhui Campus is located in , a shopping paradise and gourmet destination. There are many large department stores within walking distance, such as Grand Gateway, Oriental Department Store, Pacific Plaza, Metro City and Huijin Department Store, etc. There are also some ancient buildings nearby, and many great cafes and restaurants are located in the neighborhood. Shanghai, as the largest city in China, has many tourist attractions, such as , , , Chenghuang Temple and etc.

Hotel

HUA TING HOTEL & TOWERS (华亭宾馆 ) 1200 North Cao Xi Road, Shanghai, China （上海市徐汇区漕溪北路 1200号） Telephone: +8621 64391000 Fax: +8621 6481 2070 Hotel website: http://www.huating.jinjianghotels.com

Transportation Directions

 From Shanghai Airport (PVG) to the Xuhui Campus of SJTU Metro: Take Metro Line 2 to East Station, then transfer to Metro Line 10 to Shanghai Jiao Tong University Station; after that, walk for around 10 minutes then you can arrive at the Xuhui Campus. The whole journey is around 47km and may take you about 1 hour. Taxi: The whole journey is around 47km, which will take you around 35 minutes with 150 Yuan. If you want to go directly from Pudong Airport to the Congress Venue, please give the following message to the taxi driver: ---请载我到徐汇区华山路 1954 号上海交通大学 (近广元西路 )。 ---Please take me to No. 1954, Hua Shan Road, Xuhui District, SJTU Xuhui Campus.

 From Shanghai Hongqiao Airport (SHA) to SJTU Xuhui Campus Metro: Take Metro Line 10 to Shanghai Jiao Tong University Station; after that, walk for 8 PRIMA 2013-Useful Information

around 10 minutes then you can arrive at the Xuhui Campus. The whole journey is around 10 km and may take you about 40 minutes. Taxi: The whole journey is around 12 km, which will take you around 30 minutes with 50 Yuan. If you want to go directly from Hongqiao Airport to the Congress Venue, please give the following message to the taxi driver: ---请载我到徐汇区华山路 1954 号上海交通大学。 ---Please take me to No. 1954, Hua Shan Road, Xuhui District, SJTU Xuhui Campus.

 From to the Xuhui Campus of SJTU Metro: Take Metro to ; after that, walk north along Huashan Road for around 10 minutes then you can arrive at the Xuhui Campus. The whole journey is around 10 km and may take you about 30 minutes. Taxi: The whole journey is around 10 km, which will take you around 30 minutes with 50 Yuan.

 From Hongqiao Railway Station to the Xuhui Campus of SJTU Metro: Take Metro Line 10 to Shanghai Jiao Tong University Station; after that, walk for around 10 minutes then you can arrive at Xuhui Campus. The whole journey is around 10 km and may take you about 40 minutes. Taxi: The whole journey is around 12 km, which will take you around 30 minutes with 50 Yuan.

 From Pudong International Airport (PVG) to Hua Ting Hotel & Towers Metro: 1. Take Metro Line 2 to People Square Station and change to Metro Line 1 and get off at Shanghai Indoor Stadium and get out from Exit 7. 2. Take the Metro Line 2 and change to Metro at the Century Avenue Station, and take Metro Line 4 heading for Xinzhuang and get off at Shanghai Indoor Stadium Station and get out from Exit 7. Bus: Take Airport Bus No. 7 and arrive at South Shanghai Railway Station and change to Metro Line 1 and get off at Shanghai Indoor Stadium Station, and get out from Exit 7. Taxi: Take taxi for about 50 minutes. Normal taxi charge is about RMB ¥ 175, plus 30% night extra charge after 11:00 PM. If you want to go directly from Pudong Airport to the Hotel, please give the following message to the taxi driver: ---请载我到徐汇区徐汇区漕溪北路1200号华亭宾馆。 宾馆前台电话：6439 1000 --- Please take me to 1200 North Cao Xi Road, Hua Ting Hotel & Towers. Reception phone: 6439 1000

 From Hongqiao Airport (SHA) to Hua Ting Hotel & Towers Metro: Take Metro Line 2 to People Square Station and change to Metro Line 1 and get off at Shanghai Indoor Stadium Station and get out from Exit 7. Bus: Take Airport Bus No. 938. Get in the bus at Hongqiao Airport Station and get off at the cross of Western Zhongshan Road and North Caoxi Road. 9 PRIMA 2013-Useful Information

Taxi: Normal taxi charge is about 60 RMB, plus 30% night extra charge if after 11:00 PM. If you want to go directly from Hongqiao Airport to the Hotel, please give the following message to the taxi driver: ---请载我到徐汇区徐汇区漕溪北路1200号华亭宾馆。 宾馆前台电话：6439 1000 ---Please take me to 1200 North Cao Xi Road, Hua Ting Hotel & Towers. Reception phone: 6439 1000

Way-finding & Shuttle Bus at Airports

The 2nd PRIMA local organizing committee has arranged shuttle bus to bring the attendees to the Hua Ting Hotel & Towers on June 23. The shuttle bus will be available during 9:00-21:00 in Pudong Airport (PVG), and it will leave PVG for Hua Ting Hotel & Towers every three hours (see the below form for more details); the shuttle bus will be available during 12:00-20:00 in Hongqiao Airport (SHA) and it will leave SHA for Hua Ting Hotel & Towers every two hours (see the below form for more details). The attendees may choose to take public transportations or take the shuttle bus based on their own arrival time and needs. Volunteers will be in both PVG and SHA to guide the attendees to the shuttle bus or help the attendees to find the taxi or the metro station. The volunteers will wear orange T-shirts with PRIMA and SJTU logos.

Shuttle Bus at Airports ( June 23, Sunday) Airport 1st 2nd 3rd 4th 5th

PVG 9:00 12:00 15:00 18:00 21:00 SHA 12:00 14:00 16:00 18:00 20:00

Congress Bus

There will be buses to pick up the attendees at Hua Ting Hotel & Towers and send them to the congress venue (the Xuhui Campus of SJTU) every morning from June 24 to June 28.

Since there will be the congress banquet on Monday (June 24) evening so that congress buses will bring the attendees back from SJTU Xuhui Campus to the Hua Ting Hotel & Towers. However, in the later days (June 25-June 28) there will be no buses to bring the attendees back to the hotel after the meeting and they need to go back to the hotel by themselves.

10 PRIMA 2013-Useful Information

Congress Bus Schedule Departure Date From To Time

8:00-8:30 Hua Ting Hotel & Towers SJTU Xuhui Campus 2013.06.24 17:45 SJTU Xuhui Campus Banquet

2013.06.25 7:30-8:00 Hua Ting Hotel & Towers SJTU Xuhui Campus

2013.06.26 7:30-8:00 Hua Ting Hotel & Towers SJTU Xuhui Campus

2013.06.27 7:30-8:00 Hua Ting Hotel & Towers SJTU Xuhui Campus

2013.06.28 7:30-8:00 Hua Ting Hotel & Towers SJTU Xuhui Campus

Dining

Lunch on Campus 1/F, 2/F, University Canteen (Xuhui Campus). The attendees can buy Lunch Tickets from the registration desk.

Off-campus Dining Outside the campus is the center of the Xuhui District, which is a certified food paradise. The street outside of the gate at Panyu Road is lined with small eateries offering traditional food and Yunnan rice noodle. Be ready to pay at least 25 yuan for a decent meal. Further down the road is a Sihaiyoulong (四海游龙), a Taiwanese Fried Dumpling chain restaurant, where meals cost 30 yuan or so. By the gate at West Guang Yuan Road are various chain restaurants such as Yonghe King, Sukiya, etc.. Be ready to shell out 15 to 25 yuan per meal. The Hunan and Northeastern restaurants on Panyu Road are good choices for get-togethers with friends and for a taste of Chinese food. Average expenditure per person is 40 to 60 yuan (excluding alcoholic drinks). You can also consider Ajisen Ramen on Huashan Road (40 yuan per person), sushi-go-round restaurant Sushi Express in MetroCity (6 yuan per plate), and Pizza Hut in MetroCity. If you are feeling a little ritzy, try Charme and South Memory. Your taste buds are sure to be satisfied, but be prepared to get out that hundred-yuan bill!

Standard Audio/Visual Set-up in Meeting Rooms

All meeting rooms for PRIMA 2013 will be equipped with one computer, one blackboard, and one overhead projector. Speakers should load their talks to the computer before their speaking sessions.

Internet Access

Wireless internet access is available in all meeting rooms. The user names are: math1; math2; math3; math4; math5; math6; math7; math8; math9; 11 PRIMA 2013-Useful Information

math10 The password is: PLMN3148 Attendees staying at the hotel will be able to use the cable line to access to the internet or be provided with a password upon check-in for using the wireless connection.

Registration Fee Includes

 Printed scientific program  Welcome reception  Coffee breaks daily

Get-togethers

 Welcome reception at the Hua Ting Hotel & Towers Sunday, June 23 18:00-19:30  Banquet (self-paid) at the Hua Ting Hotel & Towers Monday, June 24 18:00-20:00

Book Display

Six publishing houses will be present in the Second PRIMA Congress, and they are: Oxford University Press, Science Press, Springer, Advances in Mathematics (China), Acta Mathematica Sinica, and Higher Education Press. A large variety of books in mathematical science will be on display.

Medical Service

The University Campus Hospital will provide medical service to the congress attendees during June 24-28. Special Medical Service Room for PRIMA: Room 105, Campus Hospital, 8:30-17:30, June 24-28 Emergency Call: 13788942692 (Mr. Liu) If the attendees need medical assistance in any other time or need emergency service, directly dial the national ambulance number: 120

Please Note

PRIMA 2013 is not responsible for the safety and security of attendees’ computers. Do not leave your laptop computers unattended. Please remember to turn off your cell phones during all talks.

12 PRIMA 2013-Useful Information

Recording of Presentations

Audio and video recording of presentations at PRIMA 2013 meetings is prohibited without the written permission of the presenter and PRIMA.

Useful Links

 Shanghai Jiao Tong University http://en.sjtu.edu.cn/  Department of Mathematics, SJTU http://www.math.sjtu.edu.cn/  PRIMA 2013 Website http://meeting.healife.com/prima2013  Institute of Natural Sciences, SJTU http://ins.sjtu.edu.cn/  Pacific Rim Mathematical Association http://www.math.sjtu.edu.cn/Conference/prima/index.htm  Shanghai Today http://www.shanghai-today.com/  Shanghai Airline http://en.ceair.com/ 13 PRIMA 2013 Program-Schedule-at-a-Glance

Schedule-at-a-Glance

Schedule-at-a-Glance

On-site Registration: Sunday, June 23 13:00-21:00, Hua Ting Hotel & Towers (1/F) Monday-Friday (June 24-28), 8:00-16:30, Room 114, Engineering Hall, SJTU Xuhui Campus

Congress Venues: Opening Ceremony /Public & Plenary Lectures, Wen Zhi Hall, SJTU Xuhui Campus Special Sessions & Contributed Talks, Engineering Hall, SJTU Xuhui Campus

Sunday Monday Tuesday Wednesday Thursday Friday Time June 23 June 24 June 25 June 26 June 27 June 28 8:30 Plenary Lecture Public Lecture Plenary Lecture Plenary Lecture 9:00- Opening Yongbin Ruan Ronald Graham Martin Barlow Vaughan Jones 9:30 Ceremony 9:30- Public Lecture Plenary Lecture Plenary Lecture Plenary Lecture Plenary Lecture 10:20 Cédric Villani Shuji Saito Weinan E Arun Ram Matlide Marcolli 10:30- Coffee Break 11:00

11:00- Plenary Lecture Plenary Lecture Plenary Lecture Plenary Lecture Special Sessions & 11:50 Zhi-Ming Ma Andrea Bertozzi Weiping Zhang Jun-Muk Hwang Contributed Talks

12:00- Lunch 14:00 14:00- Special Sessions & Contributed Talks Special Sessions & Contributed Talks 16:00 16:00- Registration Coffee Break Coffee Break 16:30 Free Afternoon

Special Sessions 16:30- Special Sessions & Contributed Talks & Contributed 17:30 Talks

18:00- Welcome 19:30 Banquet Reception

Welcome Reception: Sunday, June 23, 18:00-19:30, Hua Ting Hotel & Towers Banquet: Monday, June 24, 18:00-20:00, Hua Ting Hotel & Towers Lunch: University Canteen/Faculty Club

14 PRIMA 2013 Program-Monday, June 24

Monday, June 24

Morning Lectures: at Wen Zhi Hall Xu Sun, Huazhong University of Science and Technology, China 9:00-9:30 Fokker-Planck Equations for Nonlinear Opening Ceremony Dynamical Systems Driven by Non-Gaussian Lévy Processes 9:30-10:20 15:00-15:30 Public Lecture, Cédric Villani, Université de Huijie Qiao, Southeast University, China Lyon and Institut Henri Poincaré, France Some Results for Discontinuous Random Of Triangles, Gas, Prices and Men Dynamical Systems Chair: Jie Zhang, Shanghai Jiao Tong University, 15:30-16:00 China Jinqiao Duan, Institute for Pure and Applied Mathematics, USA 10:30-11:00 Perspectives in Stochastic Dynamics—Modeling, Coffee Break Analysis and Computation

11:00-11:50 Session 2: Algebraic and Complex Geometry Plenary Lecture, Zhi-Ming Ma, Academy of (Room: 207) Mathematics and Systems Science, CAS, China Organizers: Yujiro Kawamata, JongHae Keum Web Markov Skeleton Processes and Their 14:00-14:50 Applications Jun Li, Stanford University, USA Chair: Alejandro Adem, University of British Categorification of Donaldson-Thomas Columbia, Canada Invariants and Gopakumar-Vafa Invariants 15:00-15:50 12:00-14:00 Colin Ingalls, University of New Brunswick, Lunch Canada Venue: University Canteen Division Algebras of Transcendence Degree Two Afternoon sessions: at Engineering Hall Session 3: Algebraic Topology and Related Topics (Room: 229) 14:00-16:00 Organizers: Alejandro Adem, Alan Jonathan Berrick, Craig Westerland Session 1: A Glimpse of Stochastic Dynamics 14:00-14:30 (Room: 208) Vigleik Angeltveit, Australian National Organizers: Jinqiao Duan, Hongjun Gao University, Australia 14:00-14:30 The Topological Hochschild Homology of Thom Samuel Kou, , USA Spectra as Cyclotomic Spectra Fast Analysis of Dynamic Systems via Gaussian 14:30-15:00 Emulator Ryan Budney, University of Victoria, Canada 14:30-15:00 Universal Constructions on Spaces of Knots

15 PRIMA 2013 Program-Monday, June 24

15:00-15:30 Session 6: Geometric Analysis (Room: 226) Haibao Duan, Institute of Mathematics, Chinese Organizers: Jie Qing, Gang Tian, Xiaohua Zhu Academy of Sciences, China 14:00-14:30 Circle Actions on 5-Manifolds Albert Chau, The University of British Columbia, Canada Session 4: Applications of Harmonic Maps and TBA Submanifold Theory (Room: 224) 14:30-15:00 Organizers: Yuxin Dong, Martin A. Guest, Wei Yalong Shi, Nanjing University, China Zhang Bergman Kernel of a Polarized Kähler ALE 14:00-14:40 Manifold Reiko Miyaoka, Tohoku University, Japan 15:00-15:30 TBA Yuji Odaka, Kyoto University, Japan 14:45-15:25 K-stability of Fano Varieties and Alpha Peng Wang, , China Invariant Willmore Surfaces by Using Geometric Methods 15:30-16:00 and Loop Group Theory Xi Zhang, University of Science and 15:30-16:10 Technology of China, China Erxiao Wang, Hong Kong University of The Limit of the Yang-Mills-Higgs Flow on Science and Technology, China Semi-stable Higgs Bundles Definite Affine Spheres by the DPW Method Session 7: Geometric Aspects of Semilinear Session 5: Combinatorics and Discrete Elliptic Equations: Recent Advances & Future Mathematics (Room: 202) Perspectives (Room: 218) Organizers: Andreas Dress, Jing Huang, Organizers: Nassif Ghoussoub, Manuel delPino, Yaokun Wu Juncheng Wei 14:00-14:30 14:00-14:30 Pavol Hell , Simon Fraser University, Canada Fang-Hua Lin, Courant Institute, NYU, USA Matrix Partitions TBA 14:30-15:00 14:30-15:00 Jan Kratochvil, Charles University in Prague, Zhi-Qiang Wang, Nankai University, China and Czech Republic Utah State University, USA Geometric Representations of Graphs Synchronized and Segregated Solutions for 15:00-15:30 Coupled Nonlinear Schrödinger Equations Moshe Rosenfeld, University of Washington, 15:00-15:30 Tacoma, USA J.-M. Roquejoffre, University Toulouse, France Hamiltonian Cycles in Prisms TBA 15:30-16:00 15:30-16:00 Jack Koolen, University of Science and Daomin Cao, Chinese Academy of Sciences, Technology of China, China and Pohang China University of Science and Technology, Korea Regularization of Point Vortex Solution for On m-Walk-regular Graphs, a Generalization of Euler Equation Distance-regular Graphs

16 PRIMA 2013 Program-Monday, June 24

Session 8: Hyperbolic Conservation Laws and Session 11: Mathematical and Related Applications (Room: 100) Related Topics (Room: 228) Organizers: Feimin Huang, Dehua Wang, Organizers: Dongho Chae, Yoshikazu Giga, Ya-Guang Wang Yasunori Maekawa Tai-Peng Tsai 14:00-14:30 14:00-14:50 Alberto Bressan, Pennsylvania State University, Chun Liu, Pennsylvania State University, USA USA Some New Advances on Modeling and Some Counterexamples in the Theory of Algorithms Development of Multiphase Complex Conservation Laws Fluid System Using the Phase Method 14:30-15:00 15:00-15:50 Shuxing Chen, Fudan University, China Maria Schonbek, University of California, Nonlinear Mixed Type Equations Arisen in Santa Cruz, USA Mach Reflection Asymptotic Stability of Mild Solutions to the 15:00-15:30 Navier-Stokes Equations John K. Hunter, University of California at Davis, USA Session 12: Mathematics of String Theory Normal Forms and a Burgers-Hilbert Equation (Room: 234) 15:30-16:00 Organizers: Peter Bouwknegt, Mathai Varghese, Eun Heui Kim, California State University Siye Wu Long Beach, USA 14:00-15:00 Global Solutions for Transonic Self-similar Ugo Bruzzo, International School for Advanced Two-dimensional Riemann Problems Studies (SISSA), Italy Stacky Resolutions of the Moduli Spaces of Session 10: Kinetic Equations (Room: 220) Instantons on ALE Spaces Organizers: Radjesvarane Alexandre, Benoit 15:00-15:30 Perthame Jarah Evslin, Institute of High Energy Physics, 14:00-14:30 CAS, China Kazuo Aoki, Kyoto University, Japan Topology Change from Heterotic Narain TBA T-Duality 14:30-15:00 15:30-16:00 Nicolas Vauchelet, University of Pierre and Hisham Sati , University of Pittsburgh, USA Marie Curie, France M-branes and Higher Bundles Kinetic Description of Bacterial Motion by Chemotaxis and Asymptotics Session 13: Measurable and Topological 15:00-15:30 Dynamics (Room: 104) Xuguang Lu, Tsinghua University, China Organizers: Alejandro Maass, Hitoshi Nakada, Condensation and Regularity for Boson KyewonKoh Park, Xiangdong Ye Boltzmann Equation 14:00-14:30 15:30-16:00 Anthony Dooley, University of Bath, UK Peter Markowich, King Abdullah University of Random Dynamical Systems Science and Technology, Kingdom of Saudi 14:30-15:00 Arabia Masato Tsujii, Kyushu University, Japan Hamiltonian Propagation of Mono-kinetic The Semi-classical Zeta Function for Contact Measures with Rough Initial Profiles Anosov Flow 17 PRIMA 2013 Program-Monday, June 24

15:00-15:30 Complex Geometry and Similarity of Uijin Jung, Ajou University, Korea Cowen-Douglas Operators Decomposition Problems in Symbolic Dynamics 15:30-16:00 15:30-16:00 Zhiguo Hu, University of Windsor, Canada Song Shao, University of Science and Convolution Algebras Associated with Locally Technology of China, China Compact Quantum Groups Higher Order Bohr Problem and Related Topics Session 17: Optimization (Room: 110) Session 15: Number Theory and Organizers: Regina Burachik, Xiaojun Chen, Representation Theory (Room: 105) Alejandro Jofré, Hector Ramirez Organizers: Clifton Cunningham, Atsushi 14:00-14:40 Ichino, Vinayak Vatsal Xiaojun Chen, The Hong Kong Polytechnic 14:00-14:30 University, Hong Kong, China Noriyuki Abe, Hokkaido University, Japan Expected Residual Minimization for Stochastic On a Classification of Irreducible Modulo p Variational Inequalities Representations of p-adic Groups 14:40-15:20 14:30-15:00 Gui-Hua Lin, , China Pramod N. Achar, Louisiana State University, Solving Mathematical Programs with USA Equilibrium Constraints as Constrained Parity Sheaves on the Affine Grassmannian and Equations the Mirkovic-Vilonen Conjecture 15:20-16:00 15:00-15:30 Rafael Correa, Universidad de Chile, Chile Julia Gordon, University of British Columbia, Existence of Minimizers on Drops Canada Uniform in p Estimates for Orbital Integrals Session 18: Probability (Room: 103) 15:30-16:00 Organizers: Shige Peng, Martin Barlow Masoud Kamgarpour, University of 14:00-14:30 Queensland, Australia Xin Guo, University of California, Berkeley, On the Center of Lie Algebras USA Martingale Problem under Non-linear Session 16: Operator Algebras and Harmonic Expectations Analysis (Room: 106) 14:30-15:00 Organizers: Anthony Lau, Zhong-Jin Ruan Rainer Buckdahn, Université de Bretagne 14:00-14:30 Occidentale, France Liming Ge, University of New Hampshire, USA TBA Uncertainty Principles for Infinite Abelian 15:00-15:30 Groups Feng-Yu Wang, Beijing Normal University, 14:30-15:00 China Narutaka Ozawa, Kyoto University, Japan Bismut Formula and Gradient Estimates for Quantum Correlations and Tsirelson's Problem SDEs Driven by Multiplicative Levy Noise 15:00-15:30 15:30-16:00 Chunlan Jiang, Hebei Normal University, Louis Chen, National University of Singapore, China Singapore Multivariate Normal Approximation by Stein's 18 PRIMA 2013 Program-Monday, June 24

Method: The Concentration Inequality Approach 15:25-15:55 Osamu Iyama, Nagoya University, Japan Session 19: Representation Theory and Geigle-Lenzing Spaces and Canonical Algebras Categorification (Room:107) in Dimension d (II) Organizers: Xuhua He, Joel Kamnitzer, Tony Licata, James Parkinson, Arun Ram Contributed Talks Group 3: Discrete 14:00-15:00 Mathematics (Room: 219) Anthony Henderson, University of Sydney, Chair: Eiichi Bannai, Shanghai Jiao Tong Australia University, China The Modular Generalized Springer 14:00-14:20 Correspondence Xiao-Dong Zhang, Shanghai Jiao Tong 15:00-15:30 University, China Haibao Duan, Institute of Mathematics, Chinese The Number of Subtrees of a Tree Academy of Sciences, China 14:20-14:40 Schubert Calculus and Cohomology of Lie Jiyou Li, Shanghai Jiao Tong University, China Groups The Subsets Counting Problems and Their 15:30-16:00 Applications Hiroyuki Ochiai, Kyushu University, Japan 14:40-15:00 On Orbits in Double Flag Varieties for Liangxia Wan, Beijing Jiaotong University, Symmetric Pairs China Unimodality of Genus Distribution of Ladders Session 21: Symplectic Geometry and 15:00-15:20 Hamiltonian Dynamics (Room: 216) Lemin Gu, Tongji University, China Organizers: Yakov Eliashberg, Yiming Long Generalization of Legendre Polynomials Theory 14:00-14:50 15:20-15:40 Yongbin Ruan, University of Michigan, Ann Peng Li, Shanghai Jiao Tong University, China Arbor, USA Paths and Cycles of Interval Graphs Witten Equation and the Geometry of LG-model 15:40-16:00 15:00-15:50 Ziqing Xiang, Shanghai Jiao Tong University, Sheila Sandon, Université de Nantes, France China Translated Points and Contact Rigidity The Lit-onlyσ-Game

Session 23: Triangulated Categories in Contributed Talks Group 4: Computational Representation Theory of Algebras (Room: 214) Mathematics & Optimization (Room: 221) Organizers: Ragnar-Olaf Buchweitz , Shiping Chair: Wenjun Ying, Shanghai Jiao Tong Liu, Claus Michael Ringel, Pu Zhang University, China 14:00-14:45 14:00-14:20 Idun Reiten, Norwegian University of Science Jianguo Huang, Shanghai Jiao Tong University, and Technology, Norway China Triangulated Categories and Tau-tilting Theory An Uzawa Method for Solving Steady 14:50 -15:20 Navier-Stokes Equations Discretized by Mixed Martin Herschend, Nagoya University, Japan Element Methods Geigle-Lenzing Spaces and Canonical Algebras 14:20-14:40 in Dimension d (I) Qin Li, University of Wisconsin-Madison, USA 19 PRIMA 2013 Program-Monday, June 24

Semi-classical Limit for the Schroedinger Elena Karachanskaya, Pacific National Equation with Lattice Potential, and University, Russia Band-crossing The Generalized Ito-Wentzell Formula for Ito's 14:40-15:00 Process and the Stochastic First Integral AbdurRashid, Gomal University, Pakistan Legendre Pseudospectral Method for Solving 16:00-16:30 Three-dimensional Non-Linear Hyperbolic Coffee Break Partial Differential Equations 15:00-15:20 16:30-17:30 Xingzhong Shi, Wenzhou-Kean University, China Session 1: A Glimpse of Stochastic Dynamics Math and Gaming (Room: 208) 15:20-15:40 Organizers: Jinqiao Duan, Hongjun Gao Congmin Wu, Xiamen University, China 16:30-17:00 MD Simulations for Motions of Evaporative Dong Zhao, Academy of Mathematics & Droplets Driven by Thermal Gradients Systems Science, CAS, China 15:40-16:00 Malliavin Matrix of Degenerate PDE and Hongyu Zhu, University of Texas at Austin, Gradient Estimates USA 17:00-17:30 Inversion of Geothermal Heat Flux in a Wei Wang, Nanjing University, China Thermomechanically Coupled Stokes Ice Sheet Self-similarity for Some SPDEs Model Session 2: Algebraic and Complex Geometry Contributed Talks Group 6: Probability and (Room: 207) Statistics (Room: 222) Organizers: Yujiro Kawamata, JongHae Keum Chair: Dong Han, Shanghai Jiao Tong 16:30-17:20 University, China Amnon Neeman, The Australian National 14:00-14:20 University, Australia Jielin Zhu, University of British Columbia, Compacts Canada Asymptotic Analysis for Tipping Points Problems Session 3: Algebraic Topology and Related 14:20-14:40 Topics (Room: 229) Yanyan He, Florida State University, USA Organizers: Alejandro Adem, Alan Jonathan Data Fusion Based on Evidence Theory Berrick, Craig Westerland 14:40-15:00 16:30-17:00 Xiang Zhou, City University of Hong Kong, Soren Galatius, Stanford University, USA Hong Kong, China Cohomology of Moduli Spaces of Manifolds Explicit Cross Entropy for Mixture 17:00-17:30 15:00-15:20 Daniel Juan Pineda, National Autonomous Xiaoming Fan, Southwest Jiao Tong University University of Mexico, Mexico and Beijing Normal University, China Braid Groups of Surfaces and Their Lower Estimates of Ito Integral and Applications to Algebraic K-theory Random Dynamical Systems 15:20-15:40 20 PRIMA 2013 Program-Monday, June 24

Session 4: Applications of Harmonic Maps 17:00-17:30 and Submanifold Theory (Room: 224) Masaharu Taniguchi, Okayama University, Organizers: Yuxin Dong, Martin A. Guest, Wei Japan Zhang Multi-dimensional Traveling Fronts in Bistable 16:40-17:20 Reaction-diffusion Equations Yoshihiro Ohnita, Osaka City University and OCAMI, Japan Session 8: Hyperbolic Conservation Laws and Geometry of Lagrangian Submanifolds Related Related Applications (Room: 100) to Isoparametric Hypersurfaces Organizers: Feimin Huang, Dehua Wang, Ya-Guang Wang Session 5: Combinatorics and Discrete 16:30-17:00 Mathematics (Room: 202) Zhouping Xin, The Chinese University of Hong Organizers: Andreas Dress, Jing Huang, Kong, Hong Kong, China Yaokun Wu On the Existence of Meyer Type Transonic 16:30-17:00 Flows and a Degenerate Change Type Equation Bruce Reed, McGill University, Canada 17:00-17:30 The Structure of a Typical H-free Graph Mikhail Feldman, University of 17:00-17:30 Wisconsin-Madison, USA Sang-il Oum, Korea Advanced Institute of Shock Reflection and Von Neumann Conjectures Science and Technology, Korea Unavoidable Vertex-minors in Large Prime Session 10: Kinetic Equations (Room: 220) Graphs Organizers: Radjesvarane Alexandre, Benoit Perthame Session 6: Geometric Analysis (Room: 226) 16:30-17:00 Organizers: Jie Qing, Gang Tian, Xiaohua Zhu Benoit Perthame, University of Pierre and 16:30-17:00 Marie Curie and Institut Universitaire de France, Bing Wang, University of Wisconsin-Madison, France USA Scalar Conservation Laws and Kinetic The Regularity of Limit Space Formulation 17:00-17:30 17:00-17:30 Jihun Park, Institute for Basic Science & Lingbing He, Tsinghua University, China Pohang University of Science and Technology, On the Spatially Homogeneous Boltzmann and Korea Landau Equations α-Functions of Smooth del Pezzo Surfaces Session 11: Mathematical Fluid Dynamics Session 7: Geometric Aspects of Semilinear and Related Topics (Room: 228) Elliptic Equations: Recent Advances & Future Organizers: Dongho Chae, Yoshikazu Giga, Perspectives (Room: 218) Yasunori Maekawa Tai-Peng Tsai Organizers: Nassif Ghoussoub, Manuel del 16:30-16:55 Pino, Juncheng Wei Tsuyoshi Yoneda, Hokkaido University, Japan 16:30-17:00 Topological Instability of Laminar Flows for the Monica Musso, Universidad Católica de Chile, Two-dimensional Navier-Stokes Equation with Chile Circular Arc No-slip Boundary Conditions Critical Trudinger Moser Equation in R2 17:00-17:25 21 PRIMA 2013 Program-Monday, June 24

Dong Li, University of British Columbia, Organizers: Anthony Lau, Zhong-Jin Ruan Canada 16:30-17:00 TBA Volker Runde, University of Alberta, Canada Ergodic Theory over Locally Compact Quantum Session 12: Mathematics of String Theory Groups (Room: 234) 17:00-17:30 Organizers: Peter Bouwknegt, Mathai Varghese, Yong Zhang, University of Manitoba, Canada Siye Wu Amenability Properties of Weighted Group 16:30-17:00 Algebras Mathai Varghese, The University of Adelaide, Australia Session 17: Optimization (Room: 110) T-Duality for Circle Bundles via Organizers: Regina Burachik, Xiaojun Chen, Noncommutative Geometry Alejandro Jofré, Hector Ramirez 17:00-17:30 16:30-17:00 Matilde Marcolli, California Institute of Juan Peypouquet, Universidad Tecnica Technology, USA Federico Santa Marıa, Chile A Motivic Approach to Potts Models A Dynamical Approach to an Inertial Forward-backward Algorithm for Convex Session 13: Measurable and Topological Minimization Dynamics (Room: 104) 17:00-17:30 Organizers: Alejandro Maass, Hitoshi Nakada, Felipe Alvarez, Universidad de Chile, Chile KyewonKoh Park, Xiangdong Ye Regularized Interior Proximal Alternating 16:30-17:00 Directions Method Hiroki Sumi , Osaka University, Japan Negativity of Lyapunov Exponents in Generic Session 18: Probability (Room: 103) Random Dynamical Systems of Complex Organizers: Shige Peng, Martin Barlow Polynomials 16:30-17:00 17:00-17:30 Yongsheng Song, Chinese Academy of Sciences, Ercai Chen, Nanjing Normal University, China China TBA Backward Stochastic Differential Equations Driven by G-Brownian Motion Session 15: Number Theory and 17:00-17:30 Representation Theory (Room: 105) Jianfeng Zhang, University of Southern Organizers: Clifton Cunningham, Atsushi California, USA Ichino, Vinayak Vatsal Solutions of Path Dependent PDEs 16:30-17:00 Syu Kato, Kyoto University, Japan Session 19: Representation Theory and A homological study of Green polynomials Categorification (Room: 107) 17:00-17:30 Organizers: Xuhua He, Joel Kamnitzer, Tony David Roe, University of Calgary, Canada Licata, James Parkinson, Arun Ram Geometrizing Characters of Tori 16:30-17:00 Hiraku Nakajima, Kyoto University, Japan Session 16: Operator Algebras and Harmonic Cluster Algebras and Singular Supports of Analysis (Room: 106) Perverse Sheaves 22 PRIMA 2013 Program-Monday, June 24

Lu Zong, Xi’an Jiaotong -Liverpool University, Session 21: Symplectic Geometry and China Hamiltonian Dynamics (Room: 216) Modelling of Temperature and Pricing Weather Organizers: Yakov Eliashberg, Yiming Long Derivatives: a Comparison for Mainland China 16:30-17:20 17:10-17:30 Mei-Lin Yau, National Central University, Cheng Wang, University of Massachusetts Taiwan Dartmouth, USA Isotopy of Lagrangian Tori Revisited Linear Numerical Schemes for Epitaxial Thin Film Growth Model with Energy Stability Contributed Talks Group 3: Discrete Mathematics (Room: 219) 18:00-20:00 Chair: Xiao-Dong Zhang, Shanghai Jiao Tong Banquet University, China Venue: Hua Ting Hotel & Towers 16:30-16:50 Aaron Dutle, University of South Carolina, USA Realizations of Joint Degree Matrices 16:50-17:10 Trent G. Marbach, The University Of Queensland, Australia The Spectrum of 3-Way k-Homogeneous Latin Trades 17:10-17:30 David Cariolaro, Xi'an Jiaotong-Liverpool University, China Edge Colouring Graphs with Bounded Colour Classes

Contributed Talks Group 4: Computational Mathematics & Optimization (Room: 221) Chair: Jinyan Fan, Shanghai Jiao Tong University, China 16:30-16:50 Julian Romero Barbosa, University of Los Andes, Colombia A Semidefinite Approximation for Symmetric Travelling Salesman Polytopes 16:50-17:10 23 PRIMA 2013 Program-Tuesday, June 25

Tuesday, June 25

Morning Lectures: at Wen Zhi Hall Shanjian Tang, Fudan University, China Path-Dependent Optimal Stochastic Control and 8:30-9:20 Viscosity Solution of Associated Bellman Plenary Lecture, Yongbin Ruan, University Equations of Michigan, USA 14:30-15:00 Searching the Quantum Symmetry Guangyue Han , University of Hong Kong, Chair: Gang Tian, Princeton University, USA Hong Kong, China and Peking University, China Refinements of the Shannon-McMillan-Breiman Theorem 9:30-10:20 15:00-15:30 Plenary Lecture, Shuji Saito, Tokyo Xiaoying Han, Auburn University, USA Institute of Technology, Japan Convergent Analysis of Methods for Non-linear Geometric Class Field Theory and Existence Filtering Problems Conjecture of Smooth l-adic Sheaves on 15:30-16:00 Varieties over Finite Fields Hongjun Gao, Nanjing Normal University, Chair: Gang Tian, Princeton University, USA China and Peking University, China Large Deviations for the Stochastic Two-component b-Family System 10:30-11:00 Coffee Break Session 2: Algebraic and Complex Geometry (Room: 207) 11:00-11:50 Organizers: Yujiro Kawamata, JongHae Keum Plenary Lecture, Andrea Bertozzi, 14:00-14:50 University of California, Los Angeles, USA Junkai Chen, National Taiwan University, The Mathematics of Crime Taiwan Chair: Weinan E, Princeton University, USA Pluricanonical Maps and Minimal Models of and Peking University, China Threefolds 15:00-15:50 12:00-14:00 De-Qi Zhang, National University of Singapore, Lunch Singapore Positivity of Log Canonical Divisors and Afternoon sessions: at Mori/Brody Hyperbolicity Engineering Hall Session 3: Algebraic Topology and Related 14:00-16:00 Topics (Room: 229) Organizers: Alejandro Adem, Alan Jonathan Session 1: A Glimpse of Stochastic Dynamics Berrick, Craig Westerland (Room: 208) 14:00-14:30 Organizers: Jinqiao Duan, Hongjun Gao Fengchun Lei, Dalian University of Technology, 14:00-14:30 China 24 PRIMA 2013 Program-Tuesday, June 25

TBA L. Sunil Chandran, Indian Institute of Science, 14:30-15:00 Bangalore, Zhi Lü, Fudan University, China Boxicity and Cubicity of Graphs Equivariant Chern Numbers and the Number of 15:00-15:30 Fixed Points for Unitary Torus Manifolds Andreas Brandstädt, University of Rostock, 15:00-15:30 Germany Ernesto Lupercio, Center for Research and On the Efficient Solution of Some Packing and Advanced Studies of the National Polytechnic Covering Problems in Graphs Institute, Mexico 15:30-16:00 Virtual Orbifold Cohomology Jayme Luiz Szwarcfiter, Federal University of 15:30-16:00 Rio de Janeiro, Brazil Alejandro Adem, University of British On the Computation of the Radon Number in Columbia, Canada Some Graph Convexities Homotopy Colimits and Commutative Elements in Lie Groups Session 6: Geometric Analysis (Room: 226) Organizers: Jie Qing, Gang Tian, Xiaohua Zhu Session 4: Applications of Harmonic Maps 14:00-14:30 and Submanifold Theory (Room: 224) Xiaodong Cao, Cornell University, USA Organizers: Yuxin Dong, Martin A. Guest, Wei Curvature Behavior at Singularity Time of Ricci Zhang Flow 14:00-14:40 14:30-15:00 Ting-Hui Chang, Academia Sinica, Taiwan Xiaoli Han, Tsinghua University, China The Liouville Property for Pseudoharmonic Symplectic Mean Curvature CP2 Maps with Finite Dirichlet Energy 15:00-15:30 14:45-15:25 Shucheng Chang, National Taiwan University, Hezi Lin, Fujian Normal University, China Taiwan A Rigidity Theorem for Self-shrinkers of the Complete Pseudohermitian Manifolds with Mean Curvature Flow Positive Spectrum 15:30-16:10 15:30-16:00 Chen-Yu Chi, National Taiwan University, Haozhao Li, University of Science and Taiwan Technology of China, China On the Toda Systems of VHS Type Convergence of Calabi Flow with Small Initial Data Session 5: Combinatorics and Discrete Mathematics (Room: 202) Session 7: Geometric Aspects of Semilinear Organizers: Andreas Dress, Jing Huang, Elliptic Equations: Recent Advances & Future Yaokun Wu Perspectives (Room: 218) 14:00-14:30 Organizers: Nassif Ghoussoub, Manuel delPino, Jaroslav Nešetřil, Charles University, Czech Juncheng Wei Republic 14:00-14:30 Structural Limits in Logical and Analytic Changfeng Gui, University of Connecticut, Context USA 14:30-15:00 TBA 14:30-15:00 25 PRIMA 2013 Program-Tuesday, June 25

Mike Kowalczyk, Universidad de Chile, Chile 15:00-15:30 TBA Michael Lamoureux, University of Calgary, 15:00-15:30 Canada Juan Davila, Universidad de Chile, Chile Multi-scale Full Waveform Inversion for Seismic Nonlocal Minimal Surfaces Imaging 15:30-16:00 15:30-16:00 Shusen Yan, The University of New England, Kui Ren, University of Texas at Austin, USA Australia Inverse Problems to Elliptic Systems in Bubbling Solutions for the Chern-Simons Model Quantitative (Fluorescence) Photoacoustic Tomography Session 8: Hyperbolic Conservation Laws and Related Applications (Room: 100) Session 10: Kinetic Equations (Room: 220) Organizers: Feimin Huang, Dehua Wang, Organizers: Radjesvarane Alexandre, Benoit Ya-Guang Wang Perthame 14:00-14:30 14:00-14:30 Song Jiang, Institute of Applied Physics and Cédric Villani, Université de Lyon and Institut Computational Mathematics, China Henri Poincaré, France Incompressible Limit of the Non-isentropic Ideal TBA Magnetohydrodynamic Equations 14:30-15:00 14:30-15:00 Irene Gamba, University of Texas-Austin, USA Volker Elling, University of Michigan, Ann Angular Averaging, Propagation of Exponential Arbor, USA Tails and Grazing Collisions for Solutions of the Self-similar Vortex Spiral Solutions of the 2d Boltzmann Equation Incompressible Euler Equations 15:00-15:30 15:00-15:30 Shih-Hsien Yu, National University of Yongqian Zhang, Fudan University, China Singapore, Singapore Weakly Nonlinear Geometric Optics for Viscous Wave Propagation at Interface Hyperbolic Systems of Conservation Laws 15:30-16:00 15:30-16:00 Giuseppe Toscani, University of Pavia, Italy Tong Li, University of Iowa, USA TBA Traveling Waves of Chemotaxis Models Session 11: Mathematical Fluid Dynamics Session 9: Inverse Problems (Room: 219) and Related Topics (Room: 228) Organizers: Guillaume Bal, Jin Cheng, Gunther Organizers: Dongho Chae, Yoshikazu Giga, Uhlmann Yasunori Maekawa Tai-Peng Tsai 14:00-14:30 14:00-14:50 Gang Bao, Zhejiang University, China and Zhouping Xin, The Chinese University of Hong Michigan State University, USA Kong, Hong Kong, China Inverse Scattering Problems in Wave On Vanishing Viscosity Limit for 3-Dimensional Propagation Incompressible Navier-Stokes Equations with a 14:30-15:00 Slip Boundary Condition Otmar Scherzer, University of Vienna, Austria 15:00-15:50 TBA Seung-Yeal Ha, Seoul National University, Korea 26 PRIMA 2013 Program-Tuesday, June 25

Well-posedness of Coupled Kinetic-fluid Models Pingbing Ming for Flocking 14:00-14:30 Christof Schutte, Max Planck Institute for Session 12: Mathematics of String Theory Molecular Genetics, Germany (Room:234) TBA Organizers: Peter Bouwknegt, Mathai Varghese, 14:30-15:00 Siye Wu Tiejun Li, Peking University，China 14:00-14:30 TBA Pedram Hekmati , University of Adelaide, 15:00-15:30 Australia Di Liu, Michigan State University, USA T-duality Commutes with Reduction Multiscale Modeling and Computation of Nano 14:30-15:00 Optical Responses Fei Han, National University of Singapore, 15:30-16:00 Singapore Zhijian Yang, Wuhan University, China Equivariant Cohomology and Bismut-Chern Generalized Irving-Kirkwood Formula for the Character in the Stolz-Teichner Program Calculation of Continuum Quantities in 15:00-15:30 Molecular Dynamics Models David Ridout, The Australian National University, Australia Session 15: Number Theory and The Wess-Zumino-Witten Model on SL (2;R) Representation Theory (Room: 105) Organizers: Clifton Cunningham, Atsushi Session 13: Measurable and Topological Ichino, Vinayak Vatsal Dynamics (Room: 104) 14:00-14:30 Organizers: Alejandro Maass, Hitoshi Nakada, Jianshu Li, Hong Kong University of Science KyewonKoh Park, Xiangdong Ye and Technology, Hong Kong, China 14:00-14:30 On the First Betti Number of Hyperbolic Shigeki Akiyama, University of Tsukuba, Japan Arithmetic Manifolds Height Reducing Problem 14:30-15:00 14:30-15:00 Wen-Wei Li, Chinese Academy of Sciences, Jeong-Yup Lee, Kwandong University, Korea China Overlap and Strong Coincidences on On the Elliptic Part of the Trace Formula for Substitution Tilings Sp(2n) 15:00-15:30 15:00-15:30 Juan Rivera-Letelier, Pontificia Catholic Paul Mezo, Carleton University, Canada University, Chile Twisted Spectral Transfer for Real Groups TBA 15:30-16:00 15:30-16:00 Yoichi Mieda, Kyoto University, Japan Dou Dou, Nanjing University, China Zelevinsky Involution and l-adic Cohomology of Local Entropy Dimension for a Measure and a Rapoport-Zink Spaces Variational Principle Session 16: Operator Algebras and Harmonic Session 14: Multiscale Analysis and Analysis (Room: 106) Algorithms (Room: 102) Organizers: Anthony Lau, Zhong-Jin Ruan Organizers: Weinan E, Carlos Garcia-Cervera, 14:00-14:30 27 PRIMA 2013 Program-Tuesday, June 25

Quanhua Xu, Wuhan University, China and 15:30-16:00 University of Franche-Comté, France Zhen-Qing Chen, University of Washington, Recent Development of Analysis on USA Noncommutative Tori Stable Processes with Drift 14:30-15:00 Kunyu Guo, Fudan University, China Session 19: Representation Theory and Operator Theoretic Analogue for Lehmer's Categorification (Room: 107) Problem Organizers: Xuhua He, Joel Kamnitzer, Tony 15:00-15:30 Licata, James Parkinson, Arun Ram Nico Spronk, University of Waterloo, Canada 14:00-15:00 p-Variations of Fourier Algebras on Compact Kari Vilonen, Northwestern University, USA Groups Hodge Theory and Representation Theory 15:00-15:30 Session 17: Optimization (Room: 110) Kai Meng Tan, National University of Organizers: Regina Burachik, Xiaojun Chen, Singapore, Singapore Alejandro Jofré, Hector Ramirez Decomposition Numbers for the Symmetric 14:00-14:40 Groups and Schur Algebras Yanqin Bai, Shanghai University, China 15:30-16:00 Linear Conic Programming and Interior-point Clifton Cunningham, University of Calgary, Algorithms Canada 14:40-15:20 Geometric Reciprocity for Algebraic Tori over Julio López, Universidad Diego Portales, Chile Non-Archimedean Local Fields A Feasible Direction Algorithm for Nonlinear Second-Order Cone Optimization Problems Session 20: Singularities in Geometry and 15:20-16:00 Topology (Room: 221) Hector Ramirez, Universidad de Chile, Chile Organizers: Guangfeng Jiang, Laurentiu Maxim, Second-order Analysis in Conic Programming: Mutsuo Oka, Jose Seade Applications to Stability 14:00-14:50 David Massey, Northeastern University, USA Session 18: Probability (Room: 103) Improved Bounds on the Ranks of the Milnor Organizers: Shige Peng, Martin Barlow Fiber Cohomology 14:00-14:30 15:00-15:25 Mark Holmes, The University of Auckland, Min Yan, Hong Kong University of Science and New Zealand Technology, Hong Kong Scaling Limits of Interacting Particle Systems in Topological Classification of Multiaxial High Dimensions U(n)-Actions 14:30-15:00 15:30 -16:00 Mingshang Hu, Shandong University, China Junda Chen, Fudan University, China TBA Orbit Configuration Spaces of Small Covers and 15:00-15:30 Quasitoric Manifolds Rongfeng Sun, National University of Singapore, Singapore Session 21: Symplectic Geometry and Symmetric Rearrangements around Infinity with Hamiltonian Dynamics (Room: 216) Applications to Levy Processes Organizers: Yakov Eliashberg, Yiming Long 28 PRIMA 2013 Program-Tuesday, June 25

14:00-14:50 Session 1: A Glimpse of Stochastic Dynamics Kaoru Ono, RIMS, Kyoto University, Japan (Room: 208) Anti-symplectic Involution and Floer Theory Organizers: Jinqiao Duan, Hongjun Gao 15:00-15:50 16:30-17:00 An-min Li, Sichuan University, China Yong Liu, Peking University, China The Extremal Kahler Metrics on Toric Manifolds On Time Regularity of SPDE Driven by Levy Noise in Hilbert Spaces Session 22: Symplectic Geometry and 17:00-17:30 Mathematical Physics (Room: 222) Qi Zhang, Fudan University, China Organizers: Xiaobo Liu, Huijun Fan Backward Stochastic Partial Differential 14:00-14:45 Equations and Their Application to Stochastic Ludmil Katzarkov, University of Miami, USA Black-Scholes Formula and University of Vienna, Austria Categories and Dynamical Systems Session 2: Algebraic and Complex Geometry 14:50-15:35 (Room: 207) Bohui Chen, Sichuan University, China Organizers: Yujiro Kawamata, JongHae Keum Virtual Neighborhood Techniques in 16:30-17:20 Gromov-Witten Theory Keiji Oguiso, Osaka University, Japan and 15:35-16:20 Korea Institute for Advanced Study, Korea Hiroshi Iritani, Kyoto University, Japan Smooth Quartic K3 Surfaces and Cremona Fock Sheaf of Givental Quantization Transformations

Session 23: Triangulated Categories in Session 3: Algebraic Topology and Related Representation Theory of Algebras Topics (Room: 229) (Room: 214) Organizers: Alejandro Adem, Alan Jonathan Organizers: Ragnar-Olaf Buchweitz, Shiping Berrick, Craig Westerland Liu, Claus Michael Ringel, Pu Zhang 16:30-17:00 14:00-14:45 Dev P. Sinha, University of Oregon, USA Luchezar L. Avramov, University of Cohomology of Symmetric and Nebraska-Lincoln, USA Alternating Groups TBA 17:00-17:30 14:50-15:20 Dong Youp Suh, Korea Advanced Institute of Ryo Takahashi, Nagoya University,Japan Science and Technology, Korea Exact Categories over Cohen-Macaulay Rings Classification of Complex Projective Towers Up 15:25-15:55 to Dimension 8 and Cohomological Rigidity Changchang Xi, Capital Normal University, China Session 4: Applications of Harmonic Maps Rigid Morphisms, Exact Pairs and Applications and Submanifold Theory (Room: 224) Organizers: Yuxin Dong, Martin A. Guest, Wei 16:00-16:30 Zhang Coffee Break 16:40-17:20 ShihShu Walter Wei, University of Oklahoma, 16:30-17:30 USA TBA 29 PRIMA 2013 Program-Tuesday, June 25

Session 5: Combinatorics and Discrete 16:30-17:00 Mathematics (Room: 202) Ronghua Pan, Georgia Institute of Technology, Organizers: Andreas Dress, Jing Huang, USA Yaokun Wu Compressible Navier-Stokes Equations with 16:30-17:00 Chapman Dissipation Xuding Zhu, Zhejiang Normal University, 17:00-17:30 China Daoyuan Fang, Zhejiang University, China On-line List Colouring of Graphs Some Results about Compressible Oldroyd-B 17:00-17:30 Pinar Heggernes, University of Bergen, Session 10: Kinetic Equations (Room: 220) Norway Organizers: Radjesvarane Alexandre, Benoit Enumeration in Graph Classes Perthame 16:30-17:00 Session 6: Geometric Analysis (Room: 226) Seung-Yeal Ha, Seoul National University, Organizers: Jie Qing, Gang Tian, Xiaohua Zhu Korea 16:30-17:00 Lp-scattering and Uniform Stability of Kinetic Ivan Cheltsov, University of Edinburgh, UK Equations Affine Cones over Smooth del Pezzo Surfaces 17:00-17:30 17:00-17:30 Pierre-Emmanuel Jabin, University of Hong Huang, Beijing Normal University, China Maryland, USA Ricci Flow and 4-Manifolds with Positive New Regularity Estimates for Transport Isotropic Curvature Equations 17:30-18:00 Session 7: Geometric Aspects of Semilinear Radjesvarane Alexandre, French Naval Elliptic Equations: Recent Advances & Future Academy, France and Shanghai Jiao Tong Perspectives (Room: 218) University, China Organizers: Nassif Ghoussoub, Manuel delPino, On Some Kinetic Models for Bose Einstein Juncheng Wei Condensation 16:30-17:00 Yong Liu, North China Electric Power Session 11: Mathematical Fluid Dynamics University, China and Related Topics (Room: 228) Singly Periodic Solutions to the Allen-Cahn Organizers: Dongho Chae, Yoshikazu Giga, Equation and the Toda Lattice Yasunori Maekawa, Tai-Peng Tsai 17:00-17:30 16:30-16:55 Kelei Wang, Wuhan Institute of Physics and Ting Zhang, Zhejiang University, China Mathematics, Chinese Academy of Sciences, Global Strong Solution for Equations Related to China the Incompressible Viscoelastic Monotonicity Formula and Liouville Theorems 17:00-17:25 for Stable Solutions of Some Elliptic Problems Xiangdi Huang, Academy of Mathematics and System Sciences, CAS, China Session 8: Hyperbolic Conservation Laws and Global Classical and Weak Solutions to the 3D Related Applications (Room: 100) Fully Compressible Navier-Stokes-Fourier Organizers: Feimin Huang, Dehua Wang, System Ya-Guang Wang 30 PRIMA 2013 Program-Tuesday, June 25

Session 13: Measurable and Topological Minimum Phase Operators and the Polya-Schur Dynamics (Room: 104) Problem Organizers: Alejandro Maass, Hitoshi Nakada, KyewonKoh Park, Xiangdong Ye Session 17: Optimization (Room: 110) 16:30-17:00 Organizers: Regina Burachik, Xiaojun Chen, Seonhee Lim, Seoul National University, Korea Alejandro Jofré, Hector Ramirez Subword Complexity and Sturmian Colorings of 16:30-17:00 Trees Huifu Xu, City University of London, UK 17:00-17:30 Asymptotic Convergence Analysis for Xiongping Dai, Nanjing University, China Distributional Robust Optimization and Chaotic Dynamics of Continuous-time Equilibrium Problems Topological Semiflow on Polish Space 17:00-17:30 Alejandro Jofré, Universidad de Chile, Chile Session 14: Multiscale Analysis and The Robust Stability of Every Equilibrium in Algorithms (Room: 102) Economic Models of Exchange Organizers: Weinan E, Carlos Garcia-Cervera, Pingbing Ming Session 18: Probability (Room: 103) 16:30-17:00 Organizer s : Shige Peng , Martin Barlow Mitchell Luskin, University of Minnesota, USA 16:30-17:00 TBA Takashi Kumagai, Kyoto University, Japan 17:00-17:30 Quenched Invariance Principles for Random Xiantao Li, Pennsylvania State University, USA Walks and Random Divergence Forms in Atomic Level Interpretation of Fracture Criteria Random Media with a Boundary 17:00-17:30 Session 15: Number Theory and Ryoki Fukushima, Kyoto University, Japan Representation Theory (Room: 105) Brownian Motion in a Heavy Tailed Poissonian Organizers: Clifton Cunningham, Atsushi Potential Ichino, Vinayak Vatsal 16:30-17:00 Session 19: Representation Theory and Moshe Adrian, University of Utah, USA Categorification (Room:107) Rectifiers and the Local Langlands Organizers: Xuhua He, Joel Kamnitzer, Tony Correspondence Licata, James Parkinson, Arun Ram 17:00-17:30 16:30-17:00 Chung Pang Mok, McMaster University, Julia Pevtsova, University of Washington, USA Canada Elementary Subalgebras of Modular Lie Endoscopic Classification of Automorphic Algebras Representations of Classical Groups 17:00-17:30 Stephen Griffeth, Universidad de Talca, Chile Session 16: Operator Algebras and Harmonic Vanishing Properties of Jack Polynomials Analysis (Room: 106) Organizers: Anthony Lau, Zhong-Jin Ruan Session 20: Singularities in Geometry and 16:30-17:00 Topology (Room: 221) Michael Lamoureux, University of Calgary, Organizers: Guangfeng Jiang, Laurentiu Maxim, Canada Mutsuo Oka, Jose Seade 31 PRIMA 2013 Program-Tuesday, June 25

16:30 -17:20 University, China Ricardo Uribe-Vargas, Université de 16:30-16:50 Bourgogne, France Ju Zhou, Kutztown University of Pennsylvania, Characteristic Points, Fundamental Cubic USA

Form and Euler Characteristic of Projective Pancyclicity of 4-Connected〔K1,3, Z8〕-free Surfaces Graphs 16:50-17:10 Session 21: Symplectic Geometry and Congpei An, Jinan University, China Hamiltonian Dynamics (Room: 216) Numerical Verification Method for Well Organizers: Yakov Eliashberg, Yiming Long Conditioned Spherical t-Designs 16:30-17:20 17:10-17:30 Yong-Geun Oh, University of Suhadi Wido Saputro, Institut Teknologi Wisconsin-Madison, USA & IBS-Center for Bandung, Indonesia Geometry and Physics, Korea On the Fractional Metric Dimension of Tree Canonical Connection and Analysis of Contact Graphs Cauchy-Riemann Equation Contributed Talks Group 5: Differential Session 22: Symplectic Geometry and Equations (Room: 229) Mathematical Physics (Room: 222) Chair: Lei Zhang, Shanghai Jiao Tong Organizers: Xiaobo Liu, Huijun Fan University, China 16:30-17:15 16:30-16:50 Yakov Eliashberg, Stanford University, USA Beixiang Fang, Shanghai Jiao Tong University, Algebra of Legendrian Surgery China Global Stability of E-H Type Regular Refraction Session 23: Triangulated Categories in of Shocks on the Interface between Two Media Representation Theory of Algebras 16:50-17:10 (Room: 214) Fang Yu, Shanghai Jiao Tong University, China Organizers: Ragnar-Olaf Buchweitz, Shiping Stability of Supersonic Contact Discontinuities Liu, Claus Michael Ringel, Pu Zhang for Three Dimensional Compressible Steady 16:30-17:15 Euler Flows Pierre-Guy Plamondon, University of 17:10-17:30 Paris-Sud, France Qin Wang, Shanghai Jiao Tong University, Cluster Categories and Independence Results for China Exchange Graphs The Regularity of Semi-hyperbolic Patches at 17:25-17:55 Sonic Lines for the Gradient Equation Claus Michael Ringel, Bielefeld University, in Gas Dynamics Germany and Shanghai Jiao Tong University, China From Submodule Categories to Preprojective Algebras

Contributed Talks Group 3: Discrete Mathematics (Room: 219) Chair: Xiao-Dong Zhang, Shanghai Jiao Tong 32 PRIMA 2013 Program-Wednesday, June 26

Wednesday, June 26

Morning Lectures: at Wen Zhi Hall

8:30-9:20 Public Lecture, Ronald Graham, University of California, San Diego, USA Computers and Mathematics: Problems and Prospects Chair: Shige Peng, Shandong University, China

9:30-10:20 Plenary Lecture, Weinan E, Peking University, China and Princeton University, USA The Exact Renormalization Group Flow Chair: Shige Peng, Shandong University, China

10:30-11:00 Coffee Break

11:00-11:50 Plenary Lecture, Weiping Zhang, Nankai University, China Geometric Quantization Formulas on Symplectic Manifolds Chair: Yakov Eliashberg, Stanford University, USA

12:00-14:00 Lunch

14:00-17:30 Free afternoon

33 PRIMA 2013 Program-Thursday, June 27

Thursday, June 27

Morning Lectures: at Wen Zhi Hall 14:00-14:30 Yong Xu 8:30-9:20 Northwestern Polytechnical University, China Plenary Lecture, Martin Barlow The Availability of Logical Operation Induced University of British Columbia, Canada by Dichotomous Noise for a Nonlinear Bistable Random Walks and Percolation System Chair: Doug Lind, University of Washington, 14:30-15:00 USA Guillaume Bal, Columbia University, USA TBA 9:30-10:20 15:00-15:30 Plenary Lecture, Arun Ram, University of Hassan Allouba, Kent State University, USA Melbourne, Australia TBA Combinatorics, Representations, 15:30-16:00 Homogeneous Spaces and Elliptic Mickael Chekroun, University of Hawaii, USA Cohomology TBA Chair: Doug Lind, University of Washington, USA Session 2: Algebraic and Complex Geometry (Room: 207) 10:30-11:00 Organizers: Yujiro Kawamata, JongHae Keum Coffee Break 14:00-14:50 Sijong Kwak, Korea Advanced Institute of 11:00-11:50 Science and Technology, Korea Plenary Lecture, Jun-Muk Hwang, Korea Geometry and Syzygies in the First Linear Institute for Advanced Study, Korea Strand Sphere Packings, Symplectic Lattices and 15:00-15:50 Riemann Surfaces Takehiko Yasuda, Osaka University, Japan Chair: JongHae Keum, Korea Institute for The Hilbert Scheme of Points and Extensions of Advanced Study, Korea Local Fields

12:00-14:00 Session 3: Algebraic Topology and Related Lunch Topics (Room: 229) Organizers: Alejandro Adem, Alan Jonathan Afternoon Sessions: at Berrick, Craig Westerland Engineering Hall 14:30-15:00 Jie Wu, National University of Singapore, 14:00-16:00 Singapore On Simplicial Resolutions of Framed Links Session 1: A Glimpse of Stochastic Dynamics 15:00-15:30 (Room: 208) Shengkui Ye, University of Oxford, UK Organizers: Jinqiao Duan, Hongjun Gao Rigidity of Matrix Groups 34 PRIMA 2013 Program- Thursday, June 27

15:30-16:00 Zhou Zhang, University of Sydney, Australia Craig Westerland, University of Melbourne, Ricci Curvature in Kahler-Ricci Flow Australia Homology of Hurwitz Spaces and the Session 7: Geometric Aspects of Semilinear Cohen-Lenstra Heuristics Elliptic Equations: Recent Advances & Future Perspectives (Room: 218) Session 5: Combinatorics and Discrete Organizers: Nassif Ghoussoub, Manuel delPino, Mathematics (Room: 202) Juncheng Wei Organizers: Andreas Dress, Jing Huang, 14:00-14:30 Yaokun Wu Yoshihiro Tonegawa, Hokkaido University, 14:00-14:30 Japan Brendan McKay, Australian National Existence and Regularity of Mean Curvature University, Australia Flow with Transport Term The Practice of Graph Isomorphism 14:30-15:00 14:30-15:00 Congming Li, Shanghai Jiao Tong University, Ryuhei Uehara, Japan Advanced Institute of China and University of Colorado at Boulder, Science and Technology, Japan USA The Graph Isomorphism Problem on Geometric Existence and Non-existence of Positive Graphs Solutions on the Hardy-Littlewood-Sobolev Type 15:00-15:30 Systems Nikolai Dolbilin, Steklov Mathematics Institute 15:00-15:30 of the Russian Academy of Sciences, Russia Yong Yu, The Chinese University of Hong Parallelohedra: From Minkowski and Voronoi to Kong, Hong Kong, China the Present Day Gamma Convergence for Maxwell-Chern- 15:30-16:00 Simons-Higgs Energy Eiichi Bannai, Shanghai Jiao Tong University, 15:30-16:00 China Yiming Long, Nankai University, China On Tight Relative t-Designs TBA

Session 6: Geometric Analysis (Room: 226) Session 8: Hyperbolic Conservation Laws and Organizers: Jie Qing, Gang Tian, Xiaohua Zhu Related Applications (Room: 100) 14:00-14:30 Organizers: Feimin Huang, Dehua Wang, Zizhou Tang, Beijing Normal University, China Ya-Guang Wang The First Eigenvalue of Minimal Submanifolds 14:00-14:30 in a Unit Sphere Hai-Liang Li, Capital Normal University, China 14:30-15:00 Long Time Behaviors of Sergio Almaraz, Universidade Federal Vlasov-Poisson-Boltzmann Equations Fluminense, Brazil 14:30-15:00 Convergence of Scalar-flat Metrics on Manifolds Yue-Jun Peng, Université Blaise with Boundary under the Yamabe Flow Pascal, Clermont-Ferrand, France 15:00-15:30 Stability of Steady State Solutions for Bin Zhou, Peking University, China Euler-Maxwell Equations A Class of Weingarten Curvature Measures 15:00-15:30 15:30-16:00 Yi Wang, Chinese Academy of Sciences, China 35 PRIMA 2013 Program- Thursday, June 27

TBA KyewonKoh Park, Xiangdong Ye 15:30-16:00 14:00-14:30 Ming Mei, Champlain College Saint-Lambert Piotr Oprocha, AGH University of Science and and McGill University, Canada Technology, Poland Asymptotic Behavior of Solutions to Shadowing Properties with Average Tracing of Euler-Poisson Equations for Bipolar Pseudo-orbits Hydrodynamic Model of Semiconductors 14:30-15:00 Yong Moo Chung, Hiroshima University, Japan Session 9: Inverse Problems (Room: 219) Large Deviation Principle for Chaotic Organizers: Guillaume Bal, Jin Cheng, Gunther Dynamical Systems Uhlmann 15:00-16:00 14:00-14:30 Guohua Zhang, Fudan University, China Matti Lassas, University of Helsinki, Finland Local Weak Mixing in Dynamical Systems TBA 14:30-15:00 Session 14: Multiscale Analysis and Axel Osses, University of Chile, Chile Algorithms (Room: 102) A Heat Source Reconstruction Formula from Organizers: Weinan E, Carlos Garcia-Cervera, Single Internal Measurements Using a Family of Pingbing Ming Null Controls 14:00-14:30 15:00-15:30 Claude Le Bris, École des Ponts ParisTech, Hongyu Liu, University of North Carolina, France USA TBA TBA 14:30-15:00 15:30-16:00 Xu Yang, University of California, Santa Ting Zhou, Massachusetts Institute of Barbara, USA Technology, USA A Path Way Based Mean Field Model for E. coli TBA Chemotaxis 15:00-15:30 Session 11: Mathematical Fluid Dynamics Olof Runborg, KTH Royal Institute of and Related Topics (Room: 228) Technology, Sweden Organizers: Dongho Chae, Yoshikazu Giga, Multiscale Methods for Wave Propagation Yasunori Maekawa Tai-Peng Tsai Problems 14:00-14:50 15:30-16:00 Tastuo Iguchi, Keio University, Japan Ruo Li, Peking Univeristy, China Solvability of the Initial Value Problem to a From Discrete Velocity Model to Moment Model System for Water Waves Method 15:00-15:50 Stephen Gustafson, University of British Session 15: Number Theory and Columbia, Canada Representation Theory (Room: 105) Global Solutions of the Equivariant Heat-flow Organizers: Clifton Cunningham, Atsushi Ichino, Vinayak Vatsal Session 13: Measurable and Topological 14:00-14:30 Dynamics (Room: 104) Shunsuke Yamana, Kyushu University, Japan Organizers: Alejandro Maass, Hitoshi Nakada, L-functions and Theta Correspondence 36 PRIMA 2013 Program- Thursday, June 27

14:30-15:00 Facially Exposed Cones Are Not Always Nice Loren Spice, Texas Christian University, USA 15:00-16:00 Stability and Sign Changes in p-adic Harmonic Miguel Carrasco, Universidad de los Andes, Analysis Chile 15:00-15:30 Design of Robust Truss Structures for Minimum Binyong Sun, Academy of Mathematics and Weight Using the Sequential Convex Systems Science, CAS, China Approximation Method Conservation Relations for Local Theta Correspondence Session 18: Probability (Room: 103) 15:30-16:00 Organizers: Shige Peng, Martin Barlow Masato Kurihara, Keio University, Japan 14:00-14:30 On the Structure of Selmer Groups Dayue Chen, Peking University, China The Motion of a Tagged Particle in the Simple Session 16: Operator Algebras and Harmonic Exclusion Process Analysis (Room: 106) 14:30-15:00 Organizers: Anthony Lau, Zhong-Jin Ruan Jaime San Martin, University of Chile, Chile 14:00-14:30 Ultrametric Potentials Huaxin Lin, University of Oregon, USA 15:00-15:30 Kishimoto's Conjugacy Theorems in Simple Qi-Man Shao, The Chinese University of Hong C*-algebras of Tracial Rank One Kong, Hong Kong, China 14:30-15:00 From Stein's Method to Self-normalized Ngai-Ching Wong, National Sun Yat-sen Moderate Deviations University, Taiwan 15:30-16:00 Zero Products and Norm Preserving Panki Kim, Seoul National University, Korea Orthogonally Additive Homogeneous Parabolic Littlewood-Paley Inequality for Polynomials on C*-algebras -type Operators and Applications to 15:00-15:30 Chi-Keung Ng, Nankai University, China Stochastic Integro-differential Equations Spectral Gap Actions and Invariant States 15:30-16:00 Session 19: Representation Theory and Ebrahim Samei, University of Saskatchewan, Categorification (Room:107) Canada Organizers: Xuhua He, Joel Kamnitzer, Tony Extending Derivations to Dual Banach Algebras Licata, James Parkinson, Arun Ram 14:00-15:00 Session 17: Optimization (Room: 110) Weiqiang Wang, University of Virginia, USA Organizers: Regina Burachik, Xiaojun Chen, Globalizing Crystal Basis for Quantum Alejandro Jofré, Hector Ramirez Superalgebras 14:00-14:40 15:00-15:30 Zhiping Chen, Xi'an Jiaotong University, China Alexander Molev, University of Sydney, Stability of Two-stage Stochastic Programs with Australia Quadratic Continuous Recourse Center at the Critical Level and Commutative 14:40-15:20 Subalgebras Vera Roshchina, University of Ballarat, 15:30-16:00 Australia Paul Sobaje, University of Melbourne, Australia 37 PRIMA 2013 Program- Thursday, June 27

Support Varieties for Reductive Groups Australia Orbifold Hurwitz Numbers and Eynard-Orantin Session 20: Singularities in Geometry and Invariants Topology (Room: 221) Organizers: Guangfeng Jiang, Laurentiu Maxim, Session 23: Triangulated Categories in Mutsuo Oka, Jose Seade Representation Theory of Algebras 14:00-14:25 (Room: 214) Osamu Saeki, Kyushu University, Japan Organizers: Ragnar-Olaf Buchweitz, Shiping Broken Lefschetz Fibrations and Their Moves Liu, Claus Michael Ringel, Pu Zhang 14:30-14:55 14:00-14:45 Masahiko Yoshinaga, Hokkaido University, Henning Krause, Bielefeld University, Japan Germany Milnor Fibers of Real Line Arrangements Cohomological Length Functions 15:00-15:25 14:50-15:20 Vu The Khoi, Hanoi Institute of Mathematics, Christof Geiss, Universidad Nacional Vietnam Autónoma de México, México TBA The Representation Type of Non-degenerate QPs 15:30-15:55 15:25-15:55 Kiyoshi Takeuchi, University of Tsukuba, Thomas Bruestle, Bishops’s University and Japan Université de Sherbrooke, Canada Geometry of Non-tame Polynomial Maps The Decorated Mapping Class Group of a Marked Surface Session 21: Symplectic Geometry and Hamiltonian Dynamics (Room: 216) Contributed Talks Group 1: Geometry and Organizers: Yakov Eliashberg, Yiming Long Analysis (Room:224) 14:00-14:50 Chair: Deliang Xu, Shanghai Jiao Tong ViktorGinzburg, University of California, University, China Santa Cruz, USA 14:00-14:20 Mean Euler Characteristic: the Degenerate Feng Rong, Shanghai Jiao Tong University, Case China 15:00-15:50 On Automorphism Groups of Hua Domains Xijun Hu, Shandong University, China 14:20-14:40 The Hill-type Formula and Krein-type Trace Peng Wu, Cornell University, USA Formula On the Potential Function of Gradient Steady Ricci Solitons Session 22: Symplectic Geometry and 14:40-15:00 Mathematical Physics (Room: 222) Paul Tupper, Simon Fraser University, Canada Organizers: Xiaobo Liu, Huijun Fan Diversities and the Geometry of Hypergraphs 14:00-14:45 15:00-15:20 Alejandro Adem, University of British Yuan-Jen Chiang, University of Mary Columbia, Canada Washington, USA A Classifying Space for Commutativity Developments of Harmonic Maps into 15:00-15:45 Biharmonic Maps Paul Norbury, University of Melbourne, 15:20-15:40 38 PRIMA 2013 Program- Thursday, June 27

Xiangjin Xu, Binghamton University, USA Min Ding, Shanghai Jiao Tong University, New Heat Kernel Estimates on Manifolds with China Negative Ricci Curvature Lower Bound Some Piston Problems in Fluid Dynamics 15:40-16:00 14:20-14:40 Rui Liu, Nankai University, China Cheng-Jie Liu, Shanghai Jiao Tong University, Cb-frames and the Completely Bounded China Approximation Property for Operator Spaces Stability of Boundary Layers for the Non-isentropic Compressible Circularly Contributed Talks Group 2: Algebra and Symmetric 2D Flow Number Theory (Room: 220) 14:40-15:00 Chair: Hongze Li, Shanghai Jiao Tong Wei Yan, Institute of Applied Physics and University, China Computational Mathematics, China 14:00-14:20 Blowup of Classical Solutions to the Yuehui Zhang, Shanghai Jiao Tong University, Compressible Navier-Stokes Equations China 15:00-15:20 Triangulated Categories from Categories of Fengquan Li, Dalian University of Technology, Special Exact Sequences China 14:20-14:40 Overdetermined Boundary Value Problems with Liping Li, University of California, Riverside, Strongly Nonlinear Elliptic PDE USA 15:20-15:40 A Generalized Koszul Theory Yun-Ho Kim, Sangmyung University, Korea 14:40-15:00 On Quasilinear Elliptic Equations with Variable Shuvra Gupta, University of Iowa, USA Exponents Realising Galois Groups via Galois 15:40-16:00 Representations Linglong Du, National University of Singapore, 15:00-15:20 Singapore Yeansu Kim, Purdue University, USA Over-compressive Shock Profile Associated with L-functions from Langlands-Shahidi Method for a Simplified System from MHD GSpin Groups and the Generic Arthur L-packet Conjecture 16:00-16:30 15:20-15:40 Coffee Break Igor Bakovic, University of Warsaw, Poland Categorification in Topology, Geometry and 16:30-17:30 Combinatorics 15:40-16:00 Session 2: Algebraic and Complex Geometry Hirotaka Koga, University of Tsukuba, Japan (Room: 207) Derived Equivalences and Gorenstein Organizers: Yujiro Kawamata, JongHae Keum Dimension 16:30-17:20 Meng Chen, Fudan University, China

Contributed Talks Group 5: Differential Some Birationality Criteria on 3-folds with pg>1 Equations (Room: 229) Chair: Chunjing Xie, Shanghai Jiao Tong University, China 14:00-14:20 39 PRIMA 2013 Program- Thursday, June 27

Session 5: Combinatorics and Discrete Lassi Paivarinta, University of Helsinki, Mathematics (Room: 202) Finland Organizers: Andreas Dress, Jing Huang, TBA Yaokun Wu 17:00-17:30 16:30-17:00 Jun Zou, The Chinese University of Hong Kong, Jing Huang, University of Victoria, Canada Hong Kong, China The Lexicographic Method Some Efficient Domain Decomposition Methods 17:00-17:30 for a Class of Inverse Problems Michel Habib, University Paris Diderot - Paris VII, France Session 11: Mathematical Fluid Dynamics New Trends for Graph Searches and Related Topics (Room: 228) Organizers: Dongho Chae, Yoshikazu Giga, Session 7: Geometric Aspects of Semilinear Yasunori Maekawa Tai-Peng Tsai Elliptic Equations: Recent Advances & Future 16:30-16:55 Perspectives (Room: 218) Satoshi Masaki, Hiroshima University, Japan Organizers: Nassif Ghoussoub, Manuel delPino, Classical Limit of Some Quantum Euler Juncheng Wei Equations 16:30-17:00 Hsin-Yuan Huang, National Sun Yat-sen Session 14: Multiscale Analysis and University, Taiwan Algorithms (Room: 102) On the Entire Radial Solutions Arising in Organizers: Weinan E, Carlos Garcia-Cervera, Chern-Simons Equations Pingbing Ming 17:00-17:30 16:30-17:00 Ignacio Guerra, Universidad de Santiago de Weiguo Gao, Fudan University, China Chile, Chile Solving Nonlinear Eigenvalue Problem in Solutions for a Semilinear Elliptic Equation in Resonant Tunneling Diodes Dimension Two with Supercritical Growth 17:00-17:30 Jianfeng Lu, Duke University, USA Session 8: Hyperbolic Conservation Laws and Convergence of Force-based Related Applications (Room: 100) Atomistic-to-continuum Methods Organizers: Feimin Huang, Dehua Wang, Ya-Guang Wang Session 15: Number Theory and 16:30-17:00 Representation Theory (Room: 105) Wen Shen, Pennsylvania State University, USA Organizers: Clifton Cunningham, Atsushi Traveling Waves for Slow Erosion Ichino, Vinayak Vatsal 17:00-17:30 16:30-17:00 Quansen Jiu, Capital Normal University, China Gordan Savin, University of Utah, USA The Cauchy Problem to the Kazhikhov-Vaigant Twisted Bhargava Cubes Model in Compressible Flow Session 19: Representation Theory and Session 9: Inverse Problems (Room: 219) Categorification (Room: 107) Organizers: Guillaume Bal, Jin Cheng, Gunther Organizers: Xuhua He, Joel Kamnitzer, Tony Uhlmann Licata, James Parkinson, Arun Ram 16:30-17:00 16:30-17:30 40 PRIMA 2013 Program- Thursday, June 27

Aaron Lauda, University of Southern Invariant Flags for Nilpotent Operators, and California, USA Weighted Projective Lines Knot Invariants and Their Categorifications via 17:20-17:50 Howe Duality Bin Zhu, Tsinghua University, China T-structures and Torsion Pairs in a Session 20: Singularities in Geometry and 2-Calabi-Yau Triangulated Category Topology (Room: 221) Organizers: Guangfeng Jiang, Laurentiu Maxim, Contributed Talks Group 1: Geometry and Mutsuo Oka, Jose Seade Analysis (Room: 224) 16:30-16:55 Chair: Lihe Wang, Shanghai Jiao Tong José Luis Cisneros-Molina, Universidad University, China Nacional Autónoma de México, México 16:30-16:50 On the Topology of Real Analytic Maps Ming Shen, Fuzhou University, China 17:00-17:25 Variable Equation of State for a Dark Energy Donghe Pei Model with Linearly Varying Deceleration Northeast Normal University, China Parameter Singularities of Several Geometric Objects 16:50-17:10 Related to Null Curves in Minkowski 3-space Shengda Hu, Wilfrid Laurier University, Canada Session 21: Symplectic Geometry and Hamiltonian Group of Self Product Hamiltonian Dynamics (Room: 216) 17:10-17:30 Organizers: Yakov Eliashberg, Yiming Long Yi Huang, The University of Melbourne, 16:30-17:20 Australia Urs Frauenfelder, Seoul National University, A McShane-type Identity for Closed Surfaces Korea Contacting the Moon Contributed Talks Group 2: Algebra and Number Theory (Room: 220)) Session 22: Symplectic Geometry and Chair: Mikhail Tyaglov, Shanghai Jiao Tong Mathematical Physics (Room: 222) University, China Organizers: Xiaobo Liu, Huijun Fan 16:30-16:50 16:30-17:15 Natella Antonyan, Techologico de Monterrey, Todor Milanov, Kavli Institute for the Physics CCM, Mexico and Mathematics of the Universe, Japan Universal Objects for Free G-spaces The Eynard-Orantin Recursion in Singularity 16:50-17:10 Theory Jongyook Park, University of Science and Technology of China, China

Session 23: Triangulated Categories in On Symmetric Association Scheme with k1=3

Representation Theory of Algebras and mi=3 (Room: 214) Organizers: Ragnar-Olaf Buchweitz, Shiping Contributed Talks Group 5: Differential Liu, Claus Michael Ringel, Pu Zhang Equations (Room 229) 16:30-17:15 Chair: Beixiang Fang, Shanghai Jiao Tong Helmut Lenzing, Paderborn University, University, China Germany 16:30-16:50 41 PRIMA 2013 Program- Thursday, June 27

Fang Wang, Princeton University, USA 17:10-17:30 On the Radiation Field for Wave Equations Lei Yu, SISSA, Italy 16:50-17:10 Global Structure of Admissible BV Solutions to Tsing-San Hsu, Chang Gung University, Strictly Hyperbolic Conservation Laws in One Taiwan Space Dimension Multiplicity of Positive Solutions for a p-q-Laplacian Equation with Critical Nonlinearities

42 PRIMA 2013 Program- Friday, June 28

Friday, June 28

Morning Lectures: at Wen Zhi Hall Pingbing Ming 11:00-11:30 8:30-9:20 Xiao-Ping Wang, Hong Kong University of Plenary Lecture, Vaughan Jones, Science and Technology, Hong Kong, China Vanderbilt University, USA Modeling and Simulation of Three-component The Classification of Subfactors of Small Flows on Solid Surface Index 11:30-12:00 Chair: Yujiro Kawamata, University of Tokyo, Weiqing Ren, National University of Singapore Japan and Institute of High Performance Computing, Singapore 9:30-10:20 The Growing String Method for Saddle Point Plenary Lecture, Matlide Marcolli, Search California Institute of Technology, USA Moduli Spaces and the Field with One Session 20: Singularities in Geometry and Element Topology (Room: 221) Chair: Yujiro Kawamata, University of Tokyo, Organizers: Guangfeng Jiang, Laurentiu Maxim, Japan Mutsuo Oka, Jose Seade 11:00-11:25 10:30-11:00 Laurentiu Paunescu, The University of Sydney, Coffee Break Australia Newton-Puiseux Analysis Friday Morning Talks: at 11:30-11:55 Engineering Hall Mutsuo Oka, Tokyo University of Science, Japan 11:00-12:00 Intersection Theory on Mixed Curves

Session 9: Inverse Problems (Room: 219) Session 22: Symplectic Geometry and Organizers: Guillaume Bal, Jin Cheng, Gunther Mathematical Physics (Room: 222) Uhlmann Organizers: Xiaobo Liu, Huijun Fan 11:00-11:30 11:00-12:00 Plamen Stefanov, Purdue University, USA Jian Zhou, Tsinghua University, China Local Lens Rigidity Gopakumar-Vafa Invariants of Local 11:30-12:00 Calabi-Yau 3-Folds Jin Kenn Seo, Yongsei University, Korea Recent Progress in Electrical Tissue Property Session 23: Triangulated Categories in MRI Representation Theory of Algebras (Room: 214) Session 14: Multiscale Analysis and Organizers: Ragnar-Olaf Buchweitz, Shiping Algorithms (Room: 102) Liu, Claus Michael Ringel, Pu Zhang Organizers: Weinan E, Carlos Garcia-Cervera, 11:00-11:30 43 PRIMA 2013 Program- Friday, June 28

Quanshui Wu, Fudan University, China Chair: Yachun Li, Shanghai Jiao Tong Some Results Related to Poisson (co)Homology University, China 11:30-12:00 11:00-11:20 Jiaqun Wei, Nanjing Normal University, China Jianzhong Su, University of Texas at Arlington, Toward Repetitive Equivalences USA Dynamics in Immune Reactions during Wound Contributed Talks Group 1: Geometry and Healing Processes Analysis (Room: 224) 11:20-11:40 Chair: Yihu Yang, Shanghai Jiao Tong Bin Cheng, University of Surrey, UK University, China Analysis of Some Nonlinear PDEs from 11:00-11:20 Multi-scale Geophysical Applications Jagjit Singh Matharu, Guru Nanak Dev 11:40-12:00 University, India Aimin Huang, Indiana University, USA Some Inequalities for Unitarily Invariant Norms The Linear Hyperbolic Initial Boundary Value 11:20 -11:40 Problems in a Domain with Corners Luis Manuel Tovar Sanchez, Instituto Politecnico Nacional, Mexico 12:00-14:00 Weighted Harmonic Spaces Lunch 11:40-12:00 Massoud Amini, Institute for Research in Afternoon Sessions: at Fundamental Sciences, Iran Engineering Hall Bounded Operators on Hilbert C*-modules 14:00-16:00 Contributed Talks Group 4: Computational Mathematics & Optimization (Room: 216) Session 5: Combinatorics and Discrete Chair: Xiaoqun Zhang, Shanghai Jiao Tong Mathematics (Room: 202) University, China Organizers: Andreas Dress, Jing Huang, 11:00-11:20 Yaokun Wu Wei Weng, Waseda University, Japan 14:00-14:30 Application of MILP to Solve Complex Mikhail Tyaglov, Shanghai Jiao Tong Scheduling Problems University, China 11:20-11:40 A Class of Periodic Continued Fractions and Pablo Zafra, Kean University, U.S.A. Factorization in Modular Group Calculating Areas and Volumes with Rotated 14:30-15:00 Axis David Bryant, University of Otago, New 11:40-12:00 Zealand and Simon Fraser University, Canada Chang Yang, Université Claude Bernard Lyon 1, From Metrics to Diversities France 15:00-15:30 Efficient Numerical Method for Boundary Stefan Grünewald, CAS-MPG Partner Institute Conditions of Kinetic Equations and Key Lab for Computational Biology (PICB), China Contributed Talks Group 5: Differential Slim Systems of Binary Phylogenetic Trees Equations (Room:229) 15:30-16:00 44 PRIMA 2013 Program- Friday, June 28

Andreas Dress, CAS-MPG Partner Institute and Organizers: Weinan E, Carlos Garcia-Cervera, Key Lab for Computational Biology (PICB), Pingbing Ming China 14:00-14:30 What is and to Which End Does One Study Pingbing Ming, Institute of Computational Phylogenetic Combinatorics? Mathematics, CAS, China Session 7: Geometric Aspects of Semilinear Ghost Forces for Multiscale Coupling Methods Elliptic Equations: Recent Advances & Future in Solids Perspectives (Room: 218) 14:30-15:00 Organizers: Nassif Ghoussoub, Manuel del Carlos J. García-Cervera, University of Pino, Juncheng Wei California, Santa Barbara, USA 14:00-14:30 Quantum, Kinetic and Hydrodynamic Shin-Hwa Wang, National Tsing Hua Descriptions on Spin Transfer Torque University, Taiwan 15:00-15:30 Global Bifurcation Diagrams and Exact Wei Cai, University of North Carolina at Multiplicity of Positive Solutions for a Charlotte, USA and Shanghai Jiao Tong One-dimensional Prescribed Mean Curvature University, China Problem Arising in MEMS A Hybrid Method for Solving Laplace Equations 14:30-15:00 with Dirichlet Data Using Local Boundary Qiuping Liu Integral Equations and Random Walks TBA Session 20: Singularities in Geometry and Session 9: Inverse Problems (Room: 219) Topology (Room: 221) Organizers: Guillaume Bal, Jin Cheng, Gunther Organizers: Guangfeng Jiang, Laurentiu Maxim, Uhlmann Mutsuo Oka, Jose Seade 14:00-14:30 14:00-14:25 Xu Zhang, Sichuan University, China Haydée AguilarCabrera, National Stochastic Controllability Aotonomous University of Mexico, Mexico 15:00-15:30 The Topology of Real Suspension Singularities Lingyun Qiu, Purdue University, USA of Type Inverse Boundary Value Problems for Time-harmonic Acoustic Waves: 14:30-14:55 Conditional Stability and Iterative Laurentiu Maxim, University of Reconstruction Wisconsin-Madison, USA 15:30-16:00 Characteristic Classes of Singular Toric Shuai Lu, Fudan University, China Varieties On the Inverse Problems for the Coupled 15:00-15:25 Continuum Pipe Flow Model for Flows in Karst Rong Du，East China Normal University, China Aquifers On Griffiths Numbers for Higher Dimensional 16:30-17:00 Isolated Singularities Jin Cheng, Fudan University, China 15:25 -15:55 TBA Terence Gaffney, Northeastern University, USA Session 14: Multiscale Analysis and Equisingularity and Integral Closure of Ideals Algorithms (Room: 102) and Modules: Two Partners in a Dance 45 PRIMA 2013 Program- Friday, June 28

Session 22: Symplectic Geometry and Contributed Talks Group 4: Computational Mathematical Physics (Room: 222) Mathematics & Optimization (Room: 216) Organizers: Xiaobo Liu, Huijun Fan Chair: Min Tang, Shanghai Jiao Tong 14:00-14:45 University, China Bumsig Kim, Korea Institute for Advanced 14:00-14:20 Study, Korea Pengtao Sun, University of Nevada Las Vegas, Quasimap Invariants and Mirror Maps USA 15:00-16:00 Full Eulerian Finite Element Methods for Youjin Zhang, Tsinghua University, China Fluid-structure Interaction Problem in Fictitious On a Certain Generalization of Virasoro Domain and Phase Field Approaches Constraints for Frobenius Manifolds 14:20-14:40 Jintao Cui, University of Arkansas at Little Session 23: Triangulated Categories in Rock, USA Representation Theory of Algebras An Analysis of HDG Methods for the Helmholtz (Room: 214) Equation Organizers: Ragnar-Olaf Buchweitz, Shiping 14:40-15:00 Liu, Claus Michael Ringel, Pu Zhang Ning Ruan, University of Ballarat, Australia 14:00-14:30 Efficient Duality Method to a Class of Global Lidia Angeleri Huegel, University of Verona, Optimizations Problems with Nonconvex Italy Objective Function Derived Simple Algebras 14:35-15:05 Contributed Talks Group 5: Differential Xiao-Wu Chen, University of Science and Equations (Room: 229) Technology of China, China Chair: Shijin Deng, Shanghai Jiao Tong Singular Equivalences with Examples University, China 15:10-15:55 14:00-14:20 Ragnar-Olaf Buchweitz, University of Toronto Ying Wang, University of Minnesota, USA Scarborough, Canada The Half Line versus Finite Domain Problems of Autoequi valences under Derived Equivalences the Modified Buckley-Leverett Equation 14:20-14:40 Contributed Talks Group 1: Geometry and XinAn Wang, Shanghai Jiao Tong University, Analysis (Room: 224) China Chair: Chunqin Zhou, Shanghai Jiao Tong Constructing Global Lyapunov Function for University, China Complex Systems 14:00-14:20 14:40-15:00 Xiaobin Li, Southwest Jiaotong University, Larry Wang, Southern Polytechnic State China University, USA A New Gluing Recursive Relation for Linear Relationship between Omega-limit Sets and Sigma Model of P1-orbifold Minimal Sets 14:20-14:40 15:20-15:40 Sergey Antonyan, National University of Baili Chen, Gustavus Adolphus College, USA Mexico, Mexico Nonlinear Impulsive Differential Equations Gromov-Hausdorff Hyperspaces of Rn Arising from Chemotherapeutic Treatment

1 PRIMA 2013 Abstracts

Contents 1 Public Lectures 2

2 Plenary Lectures 2

3 Special Sessions 4 Special Session 1 A Glimpse of Stochastic Dynamics ...... 4 Special Session 2 Algebraic and Complex Geometry ...... 5 Special Session 3 Algebraic Topology and Related Topics ...... 6 Special Session 4 Applications of Harmonic Maps and Submanifold Theory ...... 8 Special Session 5 Combinatorics and Discrete Mathematics ...... 9 Special Session 6 Geometric Analysis ...... 13 Special Session 7 Geometric Aspects of Semilinear Elliptic Equations: Recent Advances & Future Perspectives 15 Special Session 8 Hyperbolic Conservation Laws and Related Applications ...... 17 Special Session 9 Inverse Problems ...... 19 Special Session 10 Kinetic Equations ...... 21 Special Session 11 Mathematical Fluid Dynamics and Related Topics ...... 22 Special Session 12 Mathematics of String Theory ...... 24 Special Session 13 Measurable and Topological Dynamics ...... 25 Special Session 14 Multiscale Analysis and Algorithms ...... 27 Special Session 15 Number Theory and Representation Theory ...... 29 Special Session 16 Operator Algebras and Harmonic Analysis ...... 31 Special Session 17 Optimization ...... 33 Special Session 18 Probability ...... 36 Special Session 19 Representation Theory and Categorification ...... 38 Special Session 20 Singularities in Geometry and Topology ...... 39 Special Session 21 Symplectic Geometry and Hamiltonian Dynamics ...... 42 Special Session 22 Symplectic Geometry and Mathematical Physics ...... 43 Special Session 23 Triangulated Categories in Representation Theory of Algebras ...... 45

4 Contributed Talks 47 Contributed Talks Group 1 Geometry and Analysis ...... 47 Contributed Talks Group 2 Algebra and Number Theory ...... 49 Contributed Talks Group 3 Discrete Mathematics ...... 51 Contributed Talks Group 4 Computational Mathematics & Optimization ...... 53 Contributed Talks Group 5 Differential Equations ...... 55 Contributed Talks Group 6 Probability and Statistics ...... 58 2 PRIMA 2013 Abstracts

1 Public Lectures Andrea Bertozzi University of California, Los Angeles, USA Computers and mathematics: problems and [email protected] prospects There is an extensive applied mathematics literature de- veloped for problems in the biological and physical sci- Ron Graham ences. Our understanding of social science problems from University of California, San Diego, USA a mathematical standpoint is less developed, but also [email protected] presents some very interesting problems. This lecture uses crime as a case study for using applied mathemati- There is no question that the recent advent of the mod- cal techniques in a social science application and covers ern computer has had a dramatic impact on what mathe- a variety of mathematical methods that are applicable to maticians do and on how they do it. However, there is in- such problems. We will review recent work on agent based creasing evidence that many apparently simple problems models, methods in linear and nonlinear partial differen- may in fact be forever beyond any conceivable computer tial equations, variational methods for inverse problems attack. In this talk, I will describe a variety of mathemat- and statistical point process models. From an applica- ical problems in which computers have had, may have or tion standpoint we will look at problems in residential will probably never have a significant role in their solu- burglaries and gang crimes. Examples will consider both tions. bottom up and top down approaches to understanding the mathematics of crime, and how the two approaches could converge to a unifying theory. Of triangles, gas, prices and men The exact renormalization group flow Cédric Villani Université de Lyon and Institut Henri Poincaré, France [email protected] Weinan E Peking University, China and Princeton University, USA [email protected] The story of mathematical progress coming from the ac- cidental encounter of three different fields which seemed to have hardly anything in common. Renormalization and renormalization group is the most important theoretical advance in the second half of the last centrury in physics. At its heart is a mathemati- cal tool for handling singularities, infinities and complex systems involving multiple scales. Yet at the mathemat- 2 Plenary Lectures ical level, it still remains to be somewhat of a mysteri- ous, ad hoc and even dubious procedure. We will dis- Random walks and percolation cuss our effort to develop the mathematical foundation of the exact renormalization group flow. We will start with some simple examples (central limit theorem, ex- Martin Barlow treme statistics, homogenization) and then discuss ap- University of British Columbia, Canada [email protected] plications to stochastic PDEs, quantum field theory and turbulent transport. This is joint work with Hao Shen, Yajun Zhou and Qingyun Sun. Around 1960 de Giorgi, Moser and Nash proved regular- ity for the heat equation associated with divergence form PDE: Sphere packings, symplectic lattices and Rie- mann surfaces ∂u = Lu, u = u(x, t), x ∈ Rd, t > 0. (1) ∂t Jun-Muk Hwang Korea Institute for Advanced Study, Korea Here L = ∇a∇, where a = aij (x) is uniformly elliptic. In [email protected] the special case when a = ρ(x)I, (1) describes heat flow in a medium of varying conductivity ρ, and uniformly elliptic means that ρ is bounded away from 0. If on the Symplectic lattices are lattices in Euclidean space with other hand Z = {x : ρ(x) = 0} 6= ∅, then the zero regions certain extra-symmetries associated to Hermitian forms. can form barriers, and the behaviour of solutions to (1) They correspond to principally polarized abelian varieties in . Classical examples are given by pe- will depend on the detailed geometry of Z. riod lattices of compact Riemann surfaces. As an approach to problems of this kind, one can consider Our theme is the density of sphere packing for symplec- discrete approximations to (1). One such is percolation tic lattices. In their seminal work in 1994, Buser and on the Euclidean lattice Zd, which was introduced by Sarnak showed that peorid lattices of compact Riemann Broadbent and Hammersley in 1957. Let p be a fixed surfaces give remarkably poor sphere packing. Following probability between 0 and 1. Each bond in Zd is retained Buser-Sarnak’s work, many interesting relations between with probability p, and removed with probability 1 − p, the density of sphere packing for symplectic lattices and independently of all the others. If p is larger than some algebro-geometric properties of corresponding abelian va- critical value p = pc(d) then the resulting graph has a rieties have been discovered. We will give an overview of unique infinite connected component C. De Gennes in this subject with a report on a recent work on period lat- 1976 called the random walk on C the ‘the ant in the tices of Prym varieties, another important class of sym- labyrinth’. The problem is related to the heat equation, plectic lattices arising from algebraic geometry. since if p(n, x, y) is the probability that a random walker (‘the ant’), starting at x, is at y at time n, then p satisfies a discrete version of (1). The classification of subfactors of small index The PDE techniques of Nash and Moser have proved very useful in these contexts. I will discuss recent progress on Vaughan Jones these models, and in particular will discuss the proof of Vanderbilt University, USA Gaussian bounds for pn, and a central limit theorem for [email protected] the (rescaled) random walk. Starting with the definition of a von Neumann algebra I The Mathematics of Crime will survey old and new developments in the index theory 3 PRIMA 2013 Abstracts

of subfactors which suggest that a complete classification During last thirty years, there has been a great deal of of "nice" subfactors may be possible up to index 6. At interactions between mathematics and physics. During index 6 certain wild phenomena begin even for the nice these interactions, mathematician are often impressed by subfactors. the magic formula and conjectures physicists can come up. At the same time, it is frustrating that we can not come up the similar formula and conjecture by our own. Web Markov skeleton processes and their ap- In the talk, I will illustrate how to apply a simple physical plications principal (quantization principal) to discover several new area of mathematics. Zhi-Ming Ma Academy of Mathematics and Systems Science, CAS, Geometric class field theory and existence China [email protected] conjecture of smooth `-adic sheaves on vari- eties over finite fields Recently a new class of stochastic processes, Web Markov Skeleton Processes (WMSP), has been found to be very Shuji Saito useful in the study of information retrieval on the Web. Tokyo Institute of Technology, Japan In our research we found that the framework of WMSP [email protected] enjoys also many interesting theoretical properties by its own. In this talk I shall briefly review some of our work in this research direction. I shall introduce the notion of A main result of this talk is a proof of the rank one case WMSP, compare it with the previous notion of Markov of an existence conjecture for smooth `-adic sheaves on a skeleton processes introduced and studied by Hou el.al., smooth variety X over a finite field due to Deligne and discuss the relation between WMSP and multivariate Drinfeld. The conjecture says that a compatible system point processes, discuss in detail the properties of mir- of smooth `-adic sheaves on the curves on X, satisfying a ror semi-Markov processes, a new class of processes in certain boundedness condition for ramification at infinity, WMSP family. At the end of my talk I shall briefly ex- should arise from a smooth `-adic sheaf on X. It may be plore the applications of WMSP in modeling user brows- viewed as an arithmetic analogue of a well-known fact in ing behaviour on the web. topology that the fundamental group of a CW complex is determined by its 2-skeleton. The problem is translated into the language of geometric class field theory, which Moduli spaces and the field with one element describes the abelian fundamental group of X by Chow groups of zero cycles with modulus. Matilde Marcolli To give a more precise statement, let Sr(X) be the set of California Institute of Technology, USA smooth `-adic sheaves on X of rank r up to isomorphism [email protected] and up to semi-simplification. Let Cu(X) be the set of normalizations of integral curves on X. Let Skr(X) be This lecture is based on joint work with Yuri Manin the set of systems (VZ )Z∈Cu(X) with VZ ∈ Sr(Z) such (arXiv:1302.6526). Using a point of view on geometry that over the “field with one element" based on torifications, 0 developed by López-Peña and Lorscheid, we describe a (V ) 0 =(V 0 ) 0 for Z,Z ∈Cu(X). Z |Z×X Z Z |Z×X Z notion of constructible sets over F1, given in terms of suit- able differences of torifications with a positivity condition on the class in the Grothendieck . We then show that Such a system is called a skeleton sheaf on X (closed the operad of moduli spaces of genus zero curves with points and curves on X are viewed as 1-skeleton and 2- skeleton of X respectively). The question is how to de- marked points can be endowed with descent data to F1. We show that other moduli spaces generalizing the case termine the image of the restriction map of genus zero curves also give rise to operads defined over F1. Sr(X) → Skr(X),

Combinatorics, representations, homoge- i.e. when a skeleton sheaf on X glues to a smooth `- neous spaces and elliptic cohomology adic sheaf on X. We explain a conjecture of Deligne (motivated by work of Drinfeld) on the problem which describes the image in terms of a ramification condition Arun Ram at infinity and prove the conjecture in case r = 1 using University of Melbourne, Australia geometric class field theory. [email protected] Geometric quantization formulas on symplec- This talk will give an elementary survey of recent de- tic manifolds velopments in combinatorial representation theory, where input from stable homotopy theory and algebraic topol- ogy enters. The theory of p-compact groups founded by Weiping Zhang Dwyer and Wilkerson gives rise to homogeneous spaces Nankai University, China that generalize the combinatorics of Lie theory, and the [email protected] framework of generalized cohomology theories (elliptic co- homology and cobordism) provides new insight into clas- sical intersection theory computations for Grassmannians We describe the theme of “Quantization commutes with and flag varieties. In both cases, the study of possible gen- reduction" on symplectic manifolds admitting a Hamil- eralizations of the Weyl character formula, and their rela- tonnian action of a compact Lie group, which on com- tion to Atiyah-Bott localization formulas provides useful pact manifolds concerns the Guillemin-Sternberg conjec- motivation and insight. The combinatorial aspect pro- ture and on noncompact manifolds concerns a conjecture vides powerful elementary models for all of these objects. of Vergne.

Searching the quantum symmetry

Yongbin Ruan University of Michigan, Ann Arbor, USA [email protected] 4 PRIMA 2013 Abstracts

3 Special Sessions Auburn University, USA [email protected] Special Session 1 A Glimpse of Stochastic Dynamics Optimal filtering problems are important in signal pro- cessing and related fields. Most of the time the optimal Perspectives in stochastic dynamics — mod- filter does not admit a closed-form expression, and vari- ous numerical methods are developed to solve the filter- eling, analysis and computation ing problem. Among these methods, particle filter is a widely used tool for numerical prediction of complex sys- Jinqiao Duan tems when observation data are available. In this talk Institute for Pure and Applied Mathematics, USA I will first give a brief introduction on particle filtering [email protected] and present error analysis on the numerical formulation of particle filter. Then I will introduce an implicit filtering method, along with its convergence results. Dynamical systems arising in engineering and science are often subject to random influences. The noisy processes may be Gaussian or non-Gaussian, which are modeled Fast analysis of dynamic systems via Gaussian by Brownian motion or stable Levy motion, respectively. emulator Non-Gaussianity of the noise manifests as nonlocality at a "macroscopic" level. Stochastic partial/ordinary differ- Samuel Kou ential equations with Brownian motion or Levy motion Harvard University, USA are appropriate models for these systems. [email protected] To understand dynamics under uncertainty, topological, geometric and analytical approaches are taken to examine the quantities that carry dynamical information and the Dynamic systems are used in modeling diverse behaviors structures that act as dynamical skeletons. In particular, in a wide variety of scientific areas. Current methods within the analytical approaches, a quantity called scape for estimating parameters in dynamic systems from noisy probability is investigated and computed in order to de- data are computationally intensive (for example, relying scribe transitions between dynamical regimes. This leads heavily on the numerical solutions of underlying differen- to consideration of a deterministic nonlocal partial differ- ential equation. Moreover, the non-Gaussianity index in tial equations). We propose a new inference method by Levy motion is estimated by solving an inverse problem creating a system driven by a Gaussian process to mirror for this nonlocal partial differential equation, with the ob- the dynamic system. Auxiliary variables are introduced servation on escape probability. to connect this Gaussian system to the real dynamic sys- The speaker will fist present an overview of available theo- tem; and a sampling scheme is introduced to minimize retical and numerical techniques for investigating stochas- the "distance" between these two systems iteratively. The tic dynamical systems, highlighting some delicate and new inference method also covers the partially observed profound impact of noise on dynamics. Then, he will fo- case in which only certain components of the dynamic cus on understanding stochastic dynamics by examining system are observed. The method offers a drastic saving “escape probability in the context of prototypical exam- of computational time and fast convergence while still re- ples in biophysical and physical settings. taining high estimation accuracy. We will illustrate the method by numerical examples. Large deviations for the stochastic two- component b-family system On time regularity of SPDE driven by Levy noise in Hilbert spaces

Hongjun Gao Yong Liu Nanjing Normal University, China Peking University, China [email protected] [email protected]

A Wentzell-Freidlin type large deviation principle is es- In this talk, we will present some new progresses on tablished for the stochastic two-component b-family sys- the time regulaity of generalized Ornstein-Uhlenbeck pro- tem perturbed by a multiplicative noise. Firstly, the local cesses driven by Levy processes in Hilbert spaces. This well-posedness of the stochastic two-component b-family talk is based on the following articles: system is proved by regularization. Then, the large devi- 1. Brzezniak, Z., Goldys, B., Imkeller, P., Peszat, S., ation principle is obtained by weak convergence method. Priola, E., Zabczyk, J. Time irregularity of generalized Ornstein-Uhlenbeck processes, C. R. Acad. Sci. Paris, Ser. I 348(2010). Refinements of the Shannon-McMillan- 2. Liu, Y., Zhai, J.L. A note on time regularity of general- Breiman theorem ized Ornstein-Uhlenbeck processes with cylindrical stable noise, C. R. Acad. Sci. Paris, Ser. I 350(2012). Guangyue Han 3. Peszat, S., Zabczyk, J.Time regularity of solutions to University of Hong Kong, Hong Kong, China linear equations with Levy noise in infinite dimensions, [email protected] Stochastic Processes and their Applications, 123(3), 2013. 4. Liu, Y., Zhai, J.L. On time regularity of SPDE in Hilbert spaces, 2013. Preprint. In this talk, under mild assumptions, we derive a law of large numbers, a central limit theorem with an error estimate, an almost sure invariance principle and a vari- Some results for discontinuous random dy- ant of the Chernoff bound in finite-state hidden Markov namical systems models. These limit theorems, which can be refinements of the celebrated Shannon-McMillan-Breiman theorem, Huijie Qiao are of interest in certain areas of information theory and Southeast University, China statistics. Particularly, in information theory, these limit [email protected] theorems can be used to calculate the capacity of a class of finite-state channels, and in statistics, they can used to derive the rate of convergence of the maximum likelihood In the talk, first of all, discontinuous random dynam- ical systems are introduced. Next, escape probability, estimator in finite-state hidden Markov models. asymptotic methods, Lyapunov exponents and topologi- cal equivalence, which are related with discontinuous ran- Convergent analysis of methods for non-linear dom dynamical systems, are presented. filtering problems Fokker-Planck equations for nonlinear dy- Xiaoying Han namical systems driven by non-Gaussian Lévy 5 PRIMA 2013 Abstracts

processes Backward stochastic partial differential equa- tions and their application to stochastic Xu Sun Black-Scholes formula Huazhong University of Science and Technology, China [email protected]; [email protected] Qi Zhang Fudan University, China [email protected] The Fokker-Planck equations describe time evolution of probability densities of stochastic dynamical systems and are thus widely used to quantify random phenomena The backward SPDEs, originated from the study of op- such as uncertainty propagation. For dynamical systems timal control theory of SPDEs, can be applied to math- driven by non-Gaussian Lévy processes, however, it is dif- ematical finance problems. We demonstrate their appli- ficult to obtain explicit forms of Fokker-Planck equations. cation to stochastic Black-Scholes formula, in a general In the present paper, Fokker-Planck equations are de- setting to the parameters of the model. This application rived for nonlinear stochastic differential equations with is based on our recent studies of the solvability to degener- non-Gaussian Lévy processes. The stochastic differential ate backward SPDEs without technical assumptions and equations are considered in sense of both Ito and Marcus. their connection to forward-backward SDEs. The con- A few examples are presented to illustrate the method. nection between backward SPDEs and forward-backward SDEs can also be regarded as an extension of Feynman- Kac formula to non-Markovian framework. Path-dependent optimal stochastic control and viscosity solution of associated Bellman Malliavin matrix of degenerate PDE and gra- equations dient estimates

Shanjian Tang & Fu Zhang Dong Zhao Fudan University, China Academy of Mathematics and Systems Science, CAS, [email protected] China [email protected] Abstract In this paper we study the optimal stochastic control problem for a path-dependent stochastic system In this talk, we present the bounded of the inverse for under a recursive path-dependent cost functional, whose Malliavin Matrix of Degenerate PDE under a new condi- associated Bellman equation from dynamic programming tion, which is equivalent to the Hoermander condition as principle is a path-dependent fully nonlinear partial dif- the coefficients are smooth. Also, the gradient estimatats ferential equation of second order. A novel notion of vis- for the semigroup is given. cosity solutions is introduced by restricting the semi-jets α 1 on an α -Hölder space C for α ∈ (0, 2 ). Using Dupire’s functional Itô calculus, we prove that the value functional of the optimal stochastic control problem is a viscosity Special Session 2 solution to the associated path-dependent Bellman equa- tion. We expect that our viscosity solution is the value Algebraic and Complex Geometry functional in a fairly general situation. Pluricanonical maps and minimal models of threefolds Self-similarity for some SPDEs Junkai Chen Wei Wang National Taiwan University, Taiwan Nanjing University, China [email protected] [email protected] Given a smooth projective variety, there are natural maps This talk discusses self-similarity in distribution, which induced by the pluricanonical system. It is natural to ask is called stochastic self-similarity, for some SPDEs. Two when the pluricanonical maps stablized birationally. On types of noise are considered, one is additive noise and the the other hand, it is known that there exists a minimal other is of some multiplicative noise. The existence of a model with terminal singularities. This model play the self-similar solution is implied by the existence of a sta- key ingredient in the study of geometry of threefolds. In tionary solution under self-similar variables. We further show the attracting property of a self-similar solution. this talk, we are going to demonstrate some application For the case additive noise, different attraction is consid- of birational geometry that one can obtain by comparing ered by different approach. For the case of multiplicative above two structures. noise, a diffusion approximation approach is applied. Some birationality criteria on 3-folds with The availability of logical operation induced pg > 1 by dichotomous noise for a nonlinear bistable system Meng Chen Fudan University, China Yong Xu, Xiaoqin Jin, Huiqing Zhang & Tingting Yang [email protected] Northwestern Polytechnical University, China [email protected]ąą We give some birationality criteria for ϕm (m = 4, 5, 6, 7) on general type 3-folds with pg ≥ 2 by means of an Instead of a continuous system driven by Gaussian white intensive classification. noise, logical stochastic resonance will be investigated in a nonlinear bistable system with two thresholds driven by dichotomous noise, which shows a phenomenon dif- Division algebras of transcendence degree two ferent from Gaussian white noise. We can realize two parallel logical operations by simply adjusting the values of these two thresholds. Besides, to quantify the reliabil- Colin Ingalls ity of obtaining the correct logic output, we numerically University of New Brunswick, Canada calculate the success probability, and effects of dichoto- [email protected] mous noise on the success probability are observed, these observations show that the reliability of realizing logical operation in the bistable system can be improved through We study Artin’s conjecture that division algebras of frac- optimizing parameters of dichotomous noise. tions of domains of dimension two are either rational, 6 PRIMA 2013 Abstracts

ruled or finite over their centres. We have a proof of the We discuss about the following question of Gizatullin: conjecture that depends adds a few other conditions. We Question. Is an automorphism g of a smooth quartic show that such domains over finite fields are finite over K3 surface S ⊂ P3 derived from some birational automor- their centres. Then a deformation theory argument for phism, i.e., some Cremona transformation of the ambient orders over surfaces shows that we have Artin’s conjec- space P3? More precisely, first I explain the following tured classification. This is work in progress with Jason negative result: Theorem 1. There is a smooth K3 sur- Bell. face S of Picard number 2 such that (i) Aut (S) ' Z and (ii) No element Aut (S) other than idS is derived from Geometry and syzygies in the first linear Bir (P3) in any embedding of S into P3. Then, I ex- strand plain the following positive result: Theorem 2. There is a smooth K3 surface S of Picard number 2 such that Sijong Kwak (i) Aut (S) ' Z and (ii) Aut (S) is derived from Bir (P3) Korea Advanced Institute of Science and Technology, Ko- in any embedding of S into P3. As I will explain in rea my talk, examples in Theorem 2 are the ones found in a [email protected] completely different context. However, they turn out to be very closely related with old works of Cayley, Snyder Property Nd,p, d ≥ 2 for algebraic sets is defined (due and Sharpe, as it is discovered by Festi, Garbagnati, van to Eisenbud-Green-Hulek-Popescu) as follows: the j-th Geemen and vam Luijk quite recently. Being based on syzygies of the homogeneous coordinate ring are gener- all of their works, I describe the automorphism group of ated by elements of degree ≤ d−1+j for 1 ≤ j ≤ p. When these S both explicitly algebraically in terms of homoge- d = 2, linear syzygies of quadratic schemes have been fo- neous coordinates and explicitly geometrically in terms of cused for a long time. In this talk, we consider upper Sarkisov link. bounds and lower bounds of higher linear syzygies in the first linear strand of Betti tables for projective varieties The Hilbert scheme of points and extensions in arbitrary characteristic. For this purpose, we estab- of local fields lish fundamental inequalities which govern the relations between the graded Betti numbers of an algebraic set X and those of its inner projection Xq in the first linear Takehiko Yasuda strand. We obtain some natural sharp upper bounds and Osaka University, Japan lower bounds for linear syzygies of any non-degenerate [email protected] projective variety using these inequalities. We also clas- sify what the extremal case and next-to-extremal case are. From the viewpoint of ’syzygies’, this is a general- Two formulas very similar to each other appear in totally ization of Castelnuovo and Fano’s results on the number different contexts, the Hilbert scheme of points and Bhar- of quadrics containing a given variety. gava’s formula for extensions of local fields. In this talk, I will explain the similarity as a special case of the wild McKay correspondence. The talk is based on a joint work Categorification of Donaldson-Thomas invari- with Melanie Matchett Wood. ants and Gopakumar-Vafa invariants Positivity of log canonical divisors and Jun Li Mori/Brody hyperbolicity Stanford University, USA [email protected] De-Qi Zhang National University of Singapore, Singapore For a projective Calabi-Yau threefold, we can form the [email protected] moduli of stable sheaves with prescribed Chern classes. The Donaldson-Thomas invariants of this Calabi-Yau threefolds are virtual degrees of these moduli spaces. Let X be a complex projective variety of dimension n and In this talk, we will show that each of such moduli D a reduced divisor with a decomposition D = Pr D , spaces admits perverse sheaves whose Euler classes are i=1 i the Donaldson-Thomas invariants associated to the mod- where the Di’s are reduced Cartier but not necessarily uli spaces. Using such sheaves, we propose a new defini- irreducible. The pair (X,D) is called Brody hyperbolic, tion of Gopakumar-Vafa invariants of Calabi-Yau three- respectively Mori hyperbolic, with respect to the decom- folds. This is a joint work with Young-Hoon Kiem. position if neither X\D nor (∩i∈I Di)\(∪j∈J Dj ) contains a non-constant holomorphic image, respectively algebraic ` Compacts image, of C for every partition of {1, . . . , r} = I J. Assuming that the singularities of the pair (X,D) are sufficiently mild, we show that the log canonical divisor Amnon Neeman KX +D is numerically effective in the case of Mori hyper- The Australian National University, Australia bolicity and that KX + D is ample provided that either [email protected] n < 4 and D is non-empty or at least n−2 of the Di’s are ample in the case of Brody hyperbolicity. Our proof also For a flat map f : X −→ Y of noetherian schemes one gives simple geometric criteria for the log canonical divi- ∗ × ! sor KX + D to be numerically effective or to be ample in may define functors Lf , Rf∗, f and f on appropriate the above (respective) cases and, under weaker geometric derived categories of quasicoherent sheaves. In two re- conditions, for KX + D to be pseudo-effective. This is a cent papers, one by Avramov and Iyengar and the second joint work with Steven Lu. by Avramov, Iyengar, Lipman and Nayak, the authors proved some remarkable formulas relating f !, f × and cer- tain Hochschild homology objects. I will discuss a new approach to the results in terms of a map ψ : f × −→ f !. Special Session 3 Algebraic Topology and Related Topics Smooth quartic K3 surfaces and Cremona transformations Homotopy colimits and commutative ele- ments in Lie groups Keiji Oguiso Osaka University, Japan and Korea Institute for Ad- Alejandro Adem vanced Study, Korea University of British Columbia, Canada [email protected] [email protected] 7 PRIMA 2013 Abstracts

In this talk we describe homotopy invariants for a classi- I will review the theory of braid groups for surfaces, fying space assembled from the commuting elements in a some of their properties and will concentrate on the braid Lie group. This involves certain homotopy colimits over groups for the sphere and the proyective plane. I will also a topological poset and the resulting cohomology calcu- explain how the geometry of the braid groups determine lations for the unitary groups are expressed in terms of the lower algebraic K theory of their integral group rings. multisymmetric polynomials. This is joint work with Jose Gomez. Equivariant Chern numbers and the number The topological Hochschild homology of of fixed points for unitary torus manifolds Thom spectra as cyclotomic spectra Zhi Lü Vigleik Angeltveit Fudan University, China Australian National University, Australia [email protected] [email protected] Let M 2n be a unitary torus (2n)-manifold, i.e., a (2n)- One can construct a symmetric monoidal category of dimensional oriented stable complex connected closed spectra by finding a way to internalize the external smash T n-manifold having a nonempty fixed set. We show product. There is a corresponding category of "spaces", that M bounds equivariantly if and only if the equivariant n n Quillen equivalent to the usual category of spaces but Chern numbers h(cT )i(cT )j , [M]i = 0 for all i, j ∈ , with a more interesting symmetric monoidal structure 1 2 N T n that mirrors the smash product of spectra. In this setting where cl denotes the lth equivariant Chern class of M. many constructions commute with passing to spectra. As a consequence, we also show that if M does not For example, taking the cyclic bar construction (in spec- bound equivariantly then the number of fixed points is n n tra) of a Thom spectrum is the same as taking the Thom at least d 2 e + 1, where d 2 e denotes the minimal integer n spectrum of the cyclic bar construction (in "spaces"). no less than 2 . What’s new is that we can exploit an equivariant ver- sion of this to construct topological Hochschild homology of Thom spectra as genuine equivariant spectra with cer- Virtual orbifold cohomology tain extra structure. This is part of work in progress with Blumberg, Gerhardt, Hill and Lawson. Ernesto Lupercio Center for Research and Advanced Studies of the National Universal constructions on spaces of knots Polytechnic Institute, Mexico [email protected] Ryan Budney University of Victoria, Canada In this talk I will introduce Virtual Orbifold Cohomology [email protected] as an open-closed nearly orbifold TQFT and explain its relation to Chen-Ruan cohomology and to String Topol- ogy. This is joint work with Ana Gonzalez, Bernardo A basic unresolved question in traditional knot theory is Uribe and Carlos Segovia. ’what precisely does the Vassiliev spectral sequence tell us about the topology of the space of knots’? I will describe a current approach to this question, which takes as its Cohomology fo symmetric and alternating input a fairly detailed understanding of the homotopy- groups type of the space of knots in S3 coming from 3-manifold theory and the theory of operads. Dev P. Sinha University of Oregon, USA Circle actions on 5-manifolds [email protected]

Haibao Duan Institute of Mathematics, Chinese Academy of Sciences, The homology and cohomology of symmetric groups has China a long history. Recently we have found that a Hopf ring [email protected] structure first discovered by Strickland and Turner helps to give a description of the mod-two ring structure which gives rise to a new additive basis with explicit multipli- A circle action S1 × M → M on a manifold M is called cation rules, as well as clarifies and illuminates previous regular if the quotient space N = M/S1 is a manifold approaches. I will describe this structure, and then ad- with dim N = dim M − 1. We classify all the 1-connected dress other coefficients for symmetric groups as well as 5-manifolds that admit regular circle actions. the mod-two cohomology of alternating groups.

Cohomology of moduli spaces of manifolds Classification of complex projective towers up to dimension 8 and cohomological rigidity Soren Galatius Stanford University, USA Dong Youp Suh [email protected] Korea Advanced Institute of Science and Technology, Ko- rea I will discuss recent joint work with Oscar Randal- [email protected] Williams on the cohomology of BDiff(M) when M is a smooth even-dimensional manifold. A complex projective tower or simply a CP -tower is an it- erated complex projective fibrations starting from a point. Braid groups of surfaces and their lower alge- In this paper we classify all 6-dimensional CP -towers up braic K-theory to diffeomorphism, and as a consequence, we show that all such manifolds are cohomologically rigid, i.e., they are completely determined up to diffeomorphism by their co- Daniel Juan Pineda homology rings. We also show that cohomological rigid- National Autonomous University of Mexico, Mexico ity is not valid for 8-dimensional CP -towers by classifying 1 3 [email protected] some CP -fibrations over CP up to diffeomorphism. As 8 PRIMA 2013 Abstracts

a corollary we show that such CP -towers are diffeomor- Chen-Yu Chi phic if they are homotopy equivalent. National Taiwan University, Taiwan [email protected] Homology of Hurwitz spaces and the Cohen- Lenstra heuristics We consider the Toda systems of VHS type with singu- lar sources and provide a criterion for the existence of solutions with prescribed asymptotic behaviour near sin- Craig Westerland gularities. We also prove the uniqueness of solution. Our University of Melbourne, Australia approach uses Simpson’s theory of constructing Higgs- [email protected] Hermitian-Yang-Mills metrics from stability.

We will examine Hurwitz moduli spaces of branched cov- A rigidity theorem for self-shrinkers of the ers of Riemann surfaces, and study their stable homology mean curvature flow (as the number of branch points tends to infinity). The results may be used to prove a function field analogue of the Cohen-Lenstra heuristics on the distribution of class Hezi Lin groups of imaginary quadratic number fields. The main Fujian Normal University, China tools are a homological stability theorem for these spaces, [email protected] as well as an identification of their limit as a space of func- tions into a target which supports a certain “universal” branched cover. In this talk, by using a Simons’ type inequality and an im- proved Sobolev inequality of submanifolds, we can prove a global rigidity theorem for self-shrinkers as hypersur- On simplicial resolutions of framed links faces whose mean curvature and total curvature satisfy some appropriate conditions. Jie Wu National University of Singapore, Singapore Geometry of Lagrangian submanifolds related matwujnus.edu.sg to isoparametric hypersurfaces

In this paper, we investigate the simplicial groups ob- Yoshihiro Ohnita tained from the link groups of naive cablings on any Osaka City University & OCAMI, Japan given framed link. Our main result states that the re- [email protected] sulting simplicial groups have the homotopy type of the loop space of a wedge of 3-spheres. This gives simplicial group models for some loop spaces using link groups. In this talk I shall provide a survey of my recent works and Joint with Fengchun Lei and Fengling Li their environs on differential geometry of Lagrangian sub- manifolds in specific Kähler manifolds, such as complex projective spaces, complex space forms, Hermitian sym- Rigidity of matrix groups metric spaces and so on. I shall emphasis on the relation- ship between certain minimal Lagrangian submanifold in complex hyperquadrics and isoparametric hypersurfaces Shengkui Ye in spheres. This talk is mainly based on my joint work University of Oxford, UK with Associate Professor Hui Ma (Tsinghua University, [email protected] Beijing).

Let R be a general ring and En(R) the subgroup of Definite affine spheres by the DPW method general linear group generated by elementary matrices. Is there a nontrivial group homomorphism En+1(R) → Erxiao Wang En(R)? I will talk about how to consider such a problem by group actions on CAT(0) spaces, spheres and acyclic Hong Kong University of Science and Technology, Hong manifolds. Kong, China [email protected]

We will first clarify the loop group formulations for both Special Session 4 hyperbolic and elliptic proper definite affine spheres in 3 Applications of Harmonic Maps and Subman- R , relating them to primitive harmonic maps from a ifold Theory Riemann surface to 6-symmetric spaces SL3(R)/SO2(R). Then we will apply Dorfmeister-Pedit-Wu’s method to The Liouville property for pseudoharmonic give Weierstrass type representation of such surfaces us- maps with finite Dirichlet energy ing holomorphic/meromorphic potentials. New examples and pictures constructed from special type of potentials will be presented in the end, including equivariant ones. Ting-Hui Chang This is a joint work with Professor Josef Dorfmeister. Academia Sinica, Taiwan, R.O.C. [email protected] Willmore surfaces by using geometric meth- In this talk, we first derive the CR Bochner formula and ods and loop group theory the CR Kato’s inequality for pseudoharmonic maps. Sec- ondly, by applying the CR Bochner formula and the CR Peng Wang Kato’s inequality we are able to prove the Liouville prop- Tongji University, China erty for pseudoharmonic maps with finite Dirichlet energy [email protected] in a complete (2n + 1)-pseudohermitian manifold. This is served as an analogue to the Liouville theorem for har- monic maps in Riemannian Geometry. In this talk we will first introduce the notion of adjoint transforms of Willmore surfaces in Sn. The relations be- tween adjoint transforms of Willmore surfaces and the On the Toda systems of VHS type other harmonic maps associated with Willmore surfaced 9 PRIMA 2013 Abstracts

independently by Hélein and Xiang Ma, are also dis- Let G be a finite undirected and simple graph whose set of cussed briefly. Applying the DPW methods and the the- edges represents the “conflicts” of some objects. A pack- ory of Burstall-Guest for harmonic maps of finite uniton, ing problem asks for a largest set of vertices which are we obtained some descriptions of adjoint transforms and pairwise conflict-free, and a covering problem asks for a Hélein-Ma’s harmonic maps as well as some interesting smallest set of vertices which “cover” some objects. Typ- examples of Willmore surfaces together with their adjoint ical examples are Maximum Independent Set as packing surfaces. Some of these results is an adjoint work with problem and Minimum Vertex Cover as covering prob- Prof. Josef Dorfmeister. lem, however, there are many other variants such as dom- ination problems. In many cases, the problems are also weighted, and sometimes covering and packing conditions are combined. It is well known that such problems are Special Session 5 typically NP-complete, and most of them are hard to ap- Combinatorics and Discrete Mathematics proximate. We look at some examples such as Efficient Domination, On tight relative t-designs Efficient Edge Domination (which is sometimes called Dominating Induced Matching), and Maximum Induced Eiichi Bannai Matching and restrict them to inputs from structured Shanghai Jiao Tong University, China graph classes. If the graph class has certain kinds of [email protected] tree structure, most of the problems become efficiently solvable. This holds for tree decomposition by clique sep- arators and modular decomposition into “simple” parts The purpose of design theory is to study good subsets as well as width restrictions such as treewidth and clique- which approximate the whole space. This is the case for width. Moreover, there are some useful closure properties spherical t-designs (i.e. finite subsets of spheres) or for of squares of graphs and line graphs. combinatorial t-designs, here a combinatorial t-(v, k, λ) design means a good subset which approximates the space of all k element subsets of a v set. Euclidean t-designs From metrics to diversities are certain generalizations of spherical designs. Rela- tive t-designs (defined by Delsarte) are certain general- David Bryant & Paul Tupper izations of combinatorial t-designs. Note that t-designs University of Otago, New Zealand and Simon Fraser Uni- and relative t-designs are defined for any Q-polynomial versity, Canada association schemes. In particular, for the binary Ham- [email protected] ming association scheme H(n, 2) (i.e. the n-dimensional over the binary field) the concept of rela- tive t-design is equivalent to the concept called regular t- A diversity is a generalisation of metric spaces to beyond wise balanced design in combinatorial design theory. Our pairwise comparisons. Formally, it is a pair (X, δ) where main purpose is to study (and classify if possible) the X is a set and δ is a non-negative function defined on objects called tight design, i.e. those t-designs or rela- finite subsets of X satisfying the two axioms tive t-designs whose cardinalities attain the natural lower bounds called Fisher type lower bounds, in various situ- 1. δ(A) = 0 if and only if |A| ≤ 1; ations. Usually, these tight designs are expected to have good algebraic structures, such as association schemes, or 2. δ(A ∪ C) ≤ δ(A ∪ B) + δ(B ∪ C) whenever B 6= ∅. coherent configurations. It is known that there are close similarities between "the- Note that δ restricted to pairs gives a metric. Examples ory of spherical t-designs vs. theory of Euclidean t- of diversities include the diameter, the mean width, the designs" and "theory of combinatorial t-designs vs. the- length of the minimum tour, and the length of an optimal ory of relative t-designs in binary Hamming schemes." Steiner tree. Diversities were introduced in a recent paper The former theories have been studied more extensively of Bryant and Tupper, and generate a rich theory which than the latter ones, since spherical harmonics is more we are only just beginning to explore. We survey some of transparent than the theory of harmonic analysis on finite the main results and then speculate wildly on applications homogeneous spaces, i.e. on certain association schemes. and future developments. We will discuss how much we can imitate the former the- ories to get similar results in the latter case. For example, we obtain the following explicit results on tight relative Boxicity and cubicity of graphs t-designs in binary Hamming association schemes. (i) For tight relative 2e-designs in binary Hamming asso- ciation schemes, the weight function must be constant on Leela Sunil Chandran each shell. Indian Institute of Science, India (ii) For tight relative 2-designs on two shells in binary [email protected] Hamming association schemes H(n, 2), we can have the structure of coherent configurations. (iii) We can classify tight relative 2-designs on two shells A graph is said to have a d-dimensional box represen- tation (respectively cube representation-we consider d- in binary Hamming association schemes H(n, 2) for small n, say n ≤ 30. dimensional cubes of unit volume) if the vertices of G can be assigned axis parallel d-dimensional boxes (resp. We will also study more general results for more general association schemes. The contents of this talk are based cubes) in such a way that two vertices are adjacent if and on the following two joint papers with other authors. only i the corresponding boxes (resp. cubes) intersect. (1) Eiichi Bannai, Etsuko Bannai, Sho Suda and Hajime The smallest non-negative integer d for which this is pos- Tanaka: On relative t-designs in polynomial association sible, is the boxicity (resp. cubicity) of the graph G. In schemes, arXiv:1303.7163 this talk we will present an overview of the results we (2) Eiichi Bannai, Etsuko Bannai and Hideo Bannai: On obtained on boxicity and cubicity of graphs over the last the existence of tight relative 2-designs on binary Ham- few years. For example, we will discuss the relation of ming association schemes, arXiv:1304.5760 boxicity and cubicity with the width parameters such as treewidth and bandwidth, the connection between boxi- city and the partial order dimension and upper bounds On the efficient solution of some packing and for cubicity in terms of boxicity, and some interesting re- covering problems in graphs sults regarding the boxicity and cubicity of certain special classes of graphs. Andreas Brandstädt University of Rostock, Germany Parallelohedra: from Minkowski and Voronoi [email protected] to the present day 10 PRIMA 2013 Abstracts

Nikolai Dolbilin China Steklov Institute of Mathematics, Russia [email protected] [email protected] A phylogenetic tree is a tree where the leaves are labeled A parallelohedron is a convex polyhedron which tiles the by taxonomic units, e.g. species. Such trees are used in Euclidean space by parallel copies in face-to face way. The systematic biology to visualize the evolutionary history of concept of parallelohedron was introduced by E. Fedorov, those taxa. A common problem in phylogenetics is that the Russian crystallographer. He found all the five combi- we observe several small trees with overlapping but non- natorial types of 3-dimensional parallelohedra which are identical taxa sets and we would like to construct a tree of great importance in crystallography. High-dimensional on the union of the taxa that displays all the information parallelohedra have many applications in geometry of of the input trees. In general, it is NP-complete to de- numbers and some other other fields of mathematics. In cide whether such a "supertree" exists and whether it is addition, high-dimensional parallelohedra present an ex- unique. On the other hand, there is a lower bound on the tremely interesting class of polyhedra in itself. An ob- total number of interior edges in order to have a unique vious example of a parallelohedron of any dimension is supertree. If this bound is exactly attained, then the the parallelepiped. Much more interesting type of a par- uniqueness question can be decided in polynomial time allelohedron is presented by the permutahedron of any and the supertree can be constructed by gluing them to- dimension. gether in a pairwise fashion. This surprising result was First fundamental theorems on parallelohedra were been first established in the PhD thesis by Sebastian Böcker in found by H. Minkowski. G. Voronoi developed the the- 1999 and was referred to as “one of the most mysterious ory of a special type of a parallelohedra that are Voronoi and apparently difficult results in phylogeny". In my talk regions for lattices and now called the Voronoi parallelo- I will sketch a simplified proof that I published in 2012 hedra. Voronoi showed their importance for the study and some further improvement made by Andreas Dress. of arbitrary parallelohedra. Further important steps in the field have been done by B. Delone, A. Alexandrov, O. Zhitomirski, B. Venkov, S.Ryshkov, P. McMullen, R. New trends for graph searches Erdahl, and others. At the same time, despite the considerable efforts, the central problem - a proof of the Voronoi conjecture on Michel Habib the affine equivalence of an arbitrary parallelohedron to University Paris Diderot - Paris VII, France some Voronoi parallelohedron - remains unresolved. In [email protected] the talk we are going to present an overview of classical results of the theory of parallelohedra as well as some re- cent results obtained by the author and his students A. Since the 1950s, search, a mechanism for visiting the ver- Garber, A. Magazinov, and A.Gavrilyuk. tices and edges of a graph, has been a fundamental tech- nique in the design of graph algorithms. In this talk I will survey some new results of computation of graph pa- What is and to which end does one study phy- rameters using graph searches, but also how to discover logenetic combinatorics? graph structure using a series of graph searches. In fact using the seminal work [2], many graph searches can be Andreas Dress characterized by conditions on the visiting order of the CAS-MPG Partner Institute for Computational Biology, vertices. These conditions are very useful for algorithm China design. [email protected] First I will describe how to evaluate the diameter of a graph using only 4 successive BFS (Breadth First When Friedrich Schiller gave his inaugural lecture as a searches). This heuristic is very acurate and can be ap- Professor of History in Jena on May 26, 1789, he entitled plied on huge graphs. Furthermore it can be completed it "Was heißt und zu welchem Ende studiert man Uni- by an exact algorithm which seems to be very efficient versalgeschichte?", that is, "What is and to which end (much more that its worst case complexity indicates). does one study world history?". In this lecture, he dis- Then I will focuse on cocomparability graphs showing tinguished two kinds of scholars, the bread scholar who that first LDFS (Lexicographic Depth First Search) can just works for the money and with neither interest nor be used to compute a minimum path cover. A compa- ability to recognize the "big picture" (Gesamtzusammen- rability graph is a graph that admits a transitive orien- hänge) and who is frightened of any innovation because it tation, and a cocomparability graph is simply the com- shatters the old traditional system that he so laboriously plement of a comparability graph. Both classes compa- adopted, and the philosophical mind whose efforts are rability and cocomparability graphs are well studied sub- directed toward the perfection of his knowledge, who is de- classes of perfect graphs [3]. Cocomparability graphs gen- lighted by new discoveries in the sphere of his activities, eralize interval graphs, and we generalize for cocompara- who has always loved the truth more than his system, and bility graphs some algorithmic results already obtained who will gladly be the first to abandon to re-establish a for interval graphs [1]. more perfect view. I will finish by describing some fixed point properties of Similarly, one studies phylogenetic combinatorics to elu- graph search acting on a cocomparability graph, describ- cidate the rules and patterns of species evolution and ing many open problems. population genetics under the influence of the four main evolutionary processes: natural selection, genetic drift, mutation and gene flow (Wikipedia) and needs to com- [1] Corneil D.G., Dalton B., Habib M.: LDFS-based cer- bine modern biological knowledge and insight with in- tifying algorithm for the Minimum Path Cover problem novative mathematical conceptualization, modelling and on cocomparability graphs, to appear SIAM J. Comput. algorithm design supported by computer-science based IT [2] Corneil D.G., Krueger R.: A Unified View of Graph architectures and strategies. Searching, SIAM J. Discrete Math. 22(4): 1259-1276 In the lecture, I will particularly stress the impor- (2008). tance of phylogenetic networks and the mathematical [3] M. C. Golumbic Algorithmic Graph Theory and Per- concepts that support phylogenetic-network construc- fect Graphs, Volume 57, Second Edition, Annals of Dis- tion, the tight-span concept, the method of split- crete Mathematics, 2004. decomposition, and the quartet-analysis based ap- proach. Enumeration in graph classes Slim systems of binary phylogenetic trees Pinar Heggernes Stefan Grünewald University of Bergen, Norway CAS-MPG Partner Institute for Computational Biology, [email protected] 11 PRIMA 2013 Abstracts

Enumerating, counting, and determining the maximum The lexicographic method number of various objects in graphs have long been estab- lished as important areas within graph theory and graph algorithms. As the number of enumerated objects is very Jing Huang often exponential in the size of the input graph, enumera- University of Victoria, Canada tion algorithms fall into two categories depending on their [email protected] running time: those whose running time is measured in the size of the input, and those whose running time is measured in the size of the output. Based on this, we Lexicographic techniques have been identified as an im- concentrate on the following two types of algorithms. portant tool in the design of graph algorithms. In this 1. Exact exponential time algorithms. The design of talk I will give a short survey of how the techniques are these algorithms is mainly based on recursive branching. used for solving graph problems such as recognitions, ori- The running time is a function of the size of the input entations, representations, and homomorphisms. graph, and very often it also gives an upper bound on the number of enumerated objects any graph can have. On m-walk-regular graphs, a generalization of 2. Output polynomial algorithms. The running time of distance-regular graphs these algorithms is polynomial in the number of the enu- merated objects that the input graph actually contains. Some of these algorithms have even better running times Jack Koolen in form of incremental polynomial or polynomial delay, depending on the time the algorithm spends between each University of Science and Technology of China, China and consecutive object that is output. Pohang University of Science and Technology, Korea [email protected] The methods for designing the two types of algorithms are usually quite different. Common to both approaches is that efforts have traditionally mainly been concentrated In this talk I will discuss m-walk-regular graphs. These on arbitray graphs, whereas graphs with particular struc- graphs were introduced by Fiol and Garriga in 1999 as a ture have largely been left unattended. In this talk we generalization of distance-regular graphs. 0-Walk-regular look at enumeration of objects in graphs with special graphs were earlier introduced by Godsil and McKay as structure. In particular, we focus on enumerating min- walk-regular graphs. They showed that a graph G is walk- imal dominating sets in various graph classes. regular if and only if the spectrum of G where I delete a Algorithms of type 1: The number of minimal dominat- vertex x does not depend on the vertex x. ing sets that any graph on n vertices can have is known Our main motivation to study m-walk-regular graphs is to to be at most 1.7159n. This upper bound might not be understand the difference between m-walk-regular graphs tight, since no examples of graphs with 1.5705n or more and distance-regular graphs. We will show that many minimal dominating sets are known. For several classes results on distance-regular graphs can be generalized to of graphs, like chordal, split, and proper interval graphs, 2-walk-regular graphs. We also give many examples of m- we substantially improve the upper bound on the num- walk-regular graphs which are not distance-regular. But ber of minimal dominating sets. At the same time, we we also show that some results on distance-regular graphs give algorithms for enumerating all minimal dominating are not true for 2-walk-regular graphs. sets, where the running time of each algorithm is within a polynomial factor of the proved upper bound for the graph class in question. In some cases, we provide ex- Geometric representations of graphs amples of graphs containing the maximum possible num- ber of minimal dominating sets for graphs in that class, thereby showing the corresponding upper bounds to be Jan Kratochvil tight. Charles University in Prague, Czech Republic Algorithms of type 2: Enumeration of minimal dominat- [email protected]ff.cuni.cz ing sets in graphs has very recently been shown to be equivalent to enumeration of minimal transversals in hy- pergraphs. The question whether the minimal transver- Geometric representations of graphs are intensively stud- sals of a hypergraph can be enumerated in output poly- ied both for their practical motivation and interesting nomial time is a fundamental and challenging question; combinatorial properties. We will survey recent develop- it has been open for several decades and has triggered ment in this area, including recent results on coloring geo- extensive research. We show that all minimal dominat- metric intersection graphs and computational complexity ing sets of a line graph can be generated in incremental of extending partial geometric representations. polynomial, and consequently output polynomial, time. We are able to improve the delay further on line graphs of bipartite graphs. Finally we show that our method The practice of graph isomorphism is also efficient on graphs of large girth, resulting in an incremental polynomial time algorithm to enumerate the minimal dominating sets of graphs of girth at least 7. Brendan D. McKay The presentation is based on joint works with following Australian National University, Australia co-authors: Jean-Francois Couturier, Petr Golovach, Pim [email protected] van ’t Hof, Dieter Kratsch, and Yngve Villanger. We are concerned with the practical aspects of comput- ing the automorphism groups of graphs, and determining Matrix partitions canonical labellings of graphs. The speaker’s program nauty has been around since 1976, though it wasn’t called that until about 1983. Until a few years ago, there wasn’t Pavol Hell very much competition, but then came saucy, Bliss, Simon Fraser University, Canada conauto, and some other programs that could outperform [email protected] nauty in many cases. Our aim in the talk is to describe our response to the challenge. In particular, nauty is now bundled with a I will survey recent work on vertex partitions of graphs highly innovative program called Traces. We contend with certain internal and certain external constraints. (These constraints are conveniently encoded in a matrix.) that the present edition of Traces is now the performance Many well studied examples, especially from the study of champion. The talk will describe how these programs perfect graphs, fit into this model. The results discussed work and give a comparison between them. will include both algorithms and characterizations. Many This is joint work with Adolfo Piperno (University of open problem will be posed. Rome). 12 PRIMA 2013 Abstracts

Structural limits in logical and analytic con- A graph convexity is a pair (G, C), where G is a finite text graph with vertex V (G) and C a family of subsets of V (G) satisfying ∅,V (G) ∈ C and being closed under in- Jaroslav Nešetřil tersections. The sets C ∈ C are called convex sets. The most common graph convexities are those whose con- Charles University in Prague, Czech Republic vex sets are defined through special paths of the graph. [email protected]ff.cuni.cz Among them the most prominent are the geodesic con- vexity, where C is closed under taking shortest paths, the We survey recent development of limits of graphs (and monophonic convexity, where C is closed under induced other structures) in the unifying context of model theory. subgraphs and the P3 convexity, whose convex sets are Particularly, this leads to the analysis of limits of sparse closed under pairs of common neighbors. In special, the graphs (with unbounded degrees). This is joint work with latter is closely related to some well studied graph pro- cesses, as percolation and conversion processes. We exam- Patrice Ossona de Mendez (EHESS, Paris). ine some common parameters of graph convexities, as the geodetic number, convexity number, hull number, Helly Unavoidable vertex-minors in large , Carathéodory number and Radon number. In particular, we describe complexity results related to the graphs computation of the Radon number. These include hard- ness results, polynomial-time algorithms and bounds. Sang-il Oum Korea Advanced Institute of Science and Technology, Ko- rea A class of periodic continued fractions and [email protected] factorization in modular group

A graph is prime (with respect to the split decomposi- Mikhail Tyaglov tion) if its vertex set does not admit a partition (A, B) Shanghai Jiao Tong University, China (called a split) with |A|, |B| ≥ 2 such that if a pair of ver- [email protected] tices in A have neighbors in B, then they have the same set of neighbors in B. We prove that for each t, every suf- ficiently large prime graph must contain a vertex-minor In this talk we introduce some properties of periodic isomorphic to either a cycle of length t or a graph consist- continued fractions of the form ing of two vertices joined by t 3-edge paths and no other edges. This is a joint work with O-joung Kwon (KAIST). −1 −1 −1 −1 −1 −1 ··· , (1) b1 + b2 +···+ bn + b1 + b2 +···+ bn + | {z } | {z } The structure of a typical H-free graph n n

Bruce Reed where bk are (positive) integers. Such continued frac- McGill University, Canada tions are called periodic negative-regular continued [email protected] fraction. By Tietze’s theorem [1], the fraction (1) converges to an irrational number if |bk| > 2 (except We discuss the structure of a typical graph which does not for the case |bk| = 2 for all k). contain H as an induced subgraph and prove a weakening We have proved that without the requirement |b | of the Erdos-Hajnal conjecture. The talk presents joint k > work with F. Havet, R. Kang, P. Keevash, M. Loebl, C. 2 the fraction (1) may converge to rational numbers McDiarmid, J. Noel, A. Scott, and A. Thomason. or diverge. This is the difference between negative- regular continued fractions and classical regular con- tinued fractions. The last one always converge to Hamiltonian cycles in prisms irrational numbers. Several algorithms for construction of periods Moshe Rosenfeld {b1, . . . , bn} of periodic negative-regular continued University of Washington, Tacoma, USA fractions converging to rational numbers are given. [email protected] The periods of a given length can be obtained by Fer- mat’s infinite descent method applied to some Dio- The prism over a graph G is the Cartesian product of phantine equations. An explicit simple formula for G with K2. My interest in prisms began in 1973 when the minimal period for x is presented. A construction I tried to tackle Dave Barnette’s conjecture (1970) that using the Calkin-Wilf tree and Stern’s diatomic series all simple 4-polytopes are Hamiltonian (still open). Sub- is described. Arbitrary primitive periods are in one- sequently, we merged the study of Hamiltonian cycles in to-one correspondence with elements of the modular prisms with other refinements of Hamiltonian cycles. We group Γ. Explicit formulas converting products of observed that if G has a Hamiltonian prism then G has the standard generators S and ST in Γ into primitive a spanning closed 2-walk but the opposite is not true, periods are obtained. The periods of elliptic elements that is having a Hamiltonian prism is "closer" to being of Γ are completely described. This description re- Hamiltonian than having a spanning, closed 2-walk. This observation created many opportunities to study various sults in a parametric formula for primitive periods of classical problems on Hamiltonicity of graphs. rational numbers. A periodic negative-regular con- tinued fraction diverges if and only if either its period In this talk I will discuss some results on prism Hamil- tonicity, further refinements of Hamiltonicity and related or its double or its triple represents the identity in open problems. Γ.

On the computation of the Radon number in [1] H. Tietze, "Uber Kriterien für Konvergenz und some graph convexities Irrationalität unendlicher Ketenbrüche”, Math. Ann. 70 (1911). Jayme L Szwarcfiter Federal University of Rio de Janeiro, Brazil The graph isomorphism problem on geomet- [email protected] ric graphs 13 PRIMA 2013 Abstracts

Ryuhei Uehara Special Session 6 Japan Advanced Institute of Science and Technology, Geometric Analysis Japan [email protected] Convergence of scalar-flat metrics on mani- folds with boundary under the Yamabe flow

The graph isomorphism (GI) problem asks whether two Sérgio Almaraz given graphs are isomorphic or not. That is, it asks Universidade Federal Fluminense, Brazil whether there exists a one-to-one mapping between two [email protected]ff.br given graphs. The GI problem is quite basic and sim- ple, however, it’s time complexity is a long standing open problem. The problem is clearly in NP, but it is not In this talk I will discuss a convergence theorem for a known to be NP-complete or not. The GI problem is one Yamabe-type flow on manifolds with boundary. This is a flow that evolves conformal scalar-flat metrics accord- of candidates between the classes NP and P. The problem ing to equations envolving the boundary mean curvature. has four aspects from the viewpoints of theoretical com- Convergence to a scalar-flat metric with constant bound- puter science. (1) What the computational complexity ary mean curvature is established assuming either a pos- class that captures the GI problem? (2) How fast can we itive mass theorem or a genetric condition. solve the problem (in exponential time)? (3) What the graph classes such that the GI problem is still as hard as general graphs? (4) What the graph classes such that Curvature behavior at singularity time of the GI problem can be solved in polynomial time. In this Ricci flow talk, I focus on (3) and (4). If we can clarify this gap, it indicates the essential difficulty of the GI problem. Last Xiaodong Cao few decades, many graph classes are proposed and inves- Cornell University, USA tigated. Among them, we focus on some graph classes [email protected] that have geometric characterization. Typical examples are interval graphs, that are intersection graphs of inter- vals, and chordal graphs, that are intersection graphs of In this talk, we will first survey some known result about subtrees of a tree. The GI problem can be solved in lin- curvature behavior at the first finite-singularity time un- ear time for interval graphs, while the GI problem for der the Ricci flow. Then we will discuss some recent de- chordal graphs is as hard as general graphs. Some ba- velopment in this direction and their applications. sic techniques to show these results are presented, and I present some graph classes such that the complexity of Complete pseudohermitian manifolds with the GI problem are not known. positive spectrum

1 2 3 On-line list colouring of graphs Shu-Cheng Chang , Jui-Tang Chen & Ting-Jung Kuo 1National Taiwan University, Taiwan, R.O.C. [email protected] 2National Taiwan Normal University, Taiwan, R.O.C. Xuding Zhu [email protected] Zhejiang Normal University, China 3National Taiwan University, Taiwan [email protected] [email protected]

In this paper, we study complete noncompact pseudo- The on-line choice number of a graph is a variation of the hermitian manifolds with positive spectrum of the sub- choice number defined through a two person game. Given Laplacian. We proved splitting- type theorems for a class a finite graph G and a mapping f : V (G) → N, two play- of complete noncompact pseudohermitian manifolds with ers, the Lister and the Painter, play the on-line (G, f)-list vanishing torsion whose spectrum of the sub-Laplacian colouring game defined as follows: In the i-th step, the has an optimal positive lower bound. These can be viewed i−1 Lister presents a non-empty subset Vi of V (G) \ ∪j=1Xj , as the CR analogue of theorems of Li-Wang and the equal- ity case of a theorem of Cheng. and the Painter chooses an independent set Xi contained in Vi. If v ∈ Vi, then we say colour i is a permissible colour of vertex v. If v ∈ Xi, then we say v is coloured Affine cones over smooth del Pezzo surfaces by colour i. If at the end of a certain step, a vertex v is given f(v) permissible colours but remains uncoloured, then the game ends and the Lister wins the game. Oth- Ivan Cheltsov erwise, at some step, all vertices are coloured, the game The University of Edinburgh, UK ends and the Painter wins the game. We say G is on-line [email protected] f-choosable if the Painter has a winning strategy in the on-line (G, f)-list colouring game, and we say G is on-line We answer negatively the old question of Misha Zaiden- k-choosable if G is on-line f-choosable for the constant berg and Hubert Flenner by proving that affine cones over function f ≡ k. The on-line choice number of G, de- smooth cubic surfaces do not admit non-trivial actions of noted by χP (G), is the minimum k for which G is on-line the additive group. Our proof uses the alpha-functions k-choosable. It follows from the definition that for any of smooth del Pezzo surfaces and classical birational con- graph χP (G) ≥ ch(G), where ch(G) is the choice num- structions that go back to Manin and Serge. ber of G. There are graphs G for which χP (G) is strictly larger than ch(G). In particular, there are graphs G with 2 Symplectic mean curvature flow in CP |V (G)| = 2χ(G) + 1 with χP (G) > χ(G), in contrast to a recently confirmed conjecture of Ohba that every such graph has χ(G) = ch(G). It was conjectured by Huang, Xiaoli Han Wong and Zhu that every graph G with |V (G)| ≤ 2χ(G) Tsinghua University, China [email protected] has χP (G) = χ(G). This talk presents some progress on the study of the conjecture, and some results on the upper bounds for the on-line choice number of classes of I will give a talk about the symplectic mean curvature graphs. 2 flow in CP . Under some pinching conditions, the sym- plectic mean curvature flow exists for long time and con- verges to a holomorphic curve. 14 PRIMA 2013 Abstracts

Ricci flow and 4-manifolds with positive Yalong Shi isotropic curvature Nanjing University, China [email protected] Hong Huang Beijing Normal University, China I shall report some recent joint work with Claudio Arezzo [email protected] and Alberto Della Vedova on the Bergman kernel of Käh- ler ALE manifolds.

We’ll survey the work by Hamilton, Chen, Tang, Zhu and The first eigenvalue of minimal submanifolds the speaker on the classification of complete 4-manifolds (or orbifolds) with positive isotropic curvature. The main in an unit sphere tool used here is the Hamilton-Perelman theory on Ricci flow with surgery. When we consider noncompact mani- Zizhou Tang folds or orbifolds we need to adapt the original Hamilton- Beijing Normal University, China Perelman theory. We’ll indicate the necessary modifica- tions in these cases. We will talk about the first eigenvalue of a minimal isoparametric hypersurface in a unit spheres, as well as Convergence of Calabi flow with small initial that of their focal submanifolds. For the special case, we data verify Yau’s conjecture.

Haozhao Li The regularity of limit space University of Science and Technology of China, China [email protected] Bing Wang University of Wisconsin-Madison, USA We will discuss the long time existence and convergence of [email protected] the Calabi flow under some small initial conditions with- out assuming the existence of constant scalar curvature Kähler metrics. This is joint work with Kai Zheng. This is a joint work with Tian. We study the structure of the limit space of a sequence of almost Einstein manifolds, which are generalizations of Einstein manifolds.Roughly K-stability of Fano varieties and Alpha invari- speaking, such manifolds are the initial manifolds of some ant normalized Ricci flows whose scalar curvatures are almost constants over space-time in the L1-sense, Ricci curva- tures are bounded from below at the initial time. Un- Yuji Odaka der the non-collapsed condition, we show that the limit Kyoto university, Japan space of a sequence of almost Einstein manifolds has most [email protected] properties which is known for the limit space of Einstein manifolds. As applications, we can apply our structure results to study the properties of Kähler manifolds. The K-stability is first defined by Tian and later general- ized by Donaldson formally as a positivity of generalized Futaki invariants. This talk will focus on the case of Fano The limit of the Yang-Mills-Higgs flow on varieties. semi-stable Higgs bundles Thanks to the recent celebrated works of the proof of existence of Kähler-Einstein metrics on K-stable Fano manifolds due to Chen-Donaldson-Sun and Tian, the K- Jiayu Li & Xi Zhang stability has been finally proved to be equivalent to the University of Science and Technology of China, China existence of Kähler-Einstein metrics i.e. we can in prin- [email protected] ciple study the existence problem algebro-geometrically. However it is in general hard, at the moment, to test K-stability. In this talk, we consider the gradient flow of the Yang- The speaker will review the basic structure of the gen- Mills-Higgs functional for Higgs pairs on a Hermitian eralized Futaki invariants from algebro-geometric view- vector bundle (E,H0) over a compact Kähler manifold point and gives relation with (the Minimal model (M, ω). We study the asymptotic behavior of the Yang- program-based) birational geometry, in particular intro- Mills-Higgs flow for Higgs pairs at infinity, and show that ducing the notion of “destabilizing subschemes" after the limiting Higgs sheaf is isomorphic to the double dual the wake of Ross-Thomas. This analysis in particular of the graded Higgs sheaves associated to the Harder- will give a proof of K-stability of Fano n-fold X with Narasimhan-Seshadri filtration of the initial Higgs bun- n dle. α(X) > n+1 which corresponds to the theorem of Tian in 80s where the alpha invariant α(X) was introduced. This talk will be based on a joint work with Yuji Sano. Ricci curvature in Kahler-Ricci flow

Zhou Zhang α-functions of smooth del Pezzo surfaces University of Sydney, Australia [email protected] Jihun Park Institute for Basic Science & Pohang University of Science Ricci curvature is a geometric quantity naturally related and Technology, Korea to the behaviour of Ricci flow. In this talk, we discuss [email protected] some recent results on the relations between the various bounds of Ricci curvature and the Kähler-Ricci flow ex- isting for either finite or infinite time. We define α-functions of Fano varieties by considering the α-invariants of G. Tian locally. We demonstrate how to obtain the α-functions of smooth del Pezzo surfaces. In A class of Weingarten curvature measures addition, their applications are briefly introduced. Bin Zhou Bergman kernel of a polarized Kähler ALE Peking University, China manifold [email protected] 15 PRIMA 2013 Abstracts

In this talk, we study the weak continuity of k-curvature Hsin-Yuan Huang measures of locally bounded, upper semicontinous func- National Sun Yat-sen University, Taiwan, R.O.C tions which are subharmonic with respect to k-curvature [email protected] operators. The the proof uses the monotonicity integral inequality. This is a joint work with Qiuyi Dai and Xu-jia Wang. In this paper, we study the the entire radial solutions of (∗):

∆u = − (1 + a)(eu − (1 + a)e2u + aeu+v) Special Session 7 v 2v u+v Geometric Aspects of Semilinear Elliptic + a(e − (1 + b)e + be ) Equations: Recent Advances & Future Per- + 4πN1δ0 spectives

Regularization of point vortex solution for ∆v = − (1 + b)(ev − (1 + b)e2v + beu+v) Euler equation + b(eu − (1 + a)e2u + aeu+v) Daomin Cao + 4πN2δ0. Chinese Academy of Sciences, China [email protected] Here, a > 0, b > 0, N1 ≥ 0, and N2 ≥ 0. This sys- tem is motivated by studying the equations of relativistic non-Abelian Chern-Simons model proposed by by Kao- In this talk the speaker will talk about the regularization Lee and Dunne and Gudnason model of N =2 super- of point vortex solution for Euler equation of 2 dimen- symmetric Yang-Mills-Cherns-Simons-Higgs theory. Un- sion. The existence of point vortex solutions is closely derstanding the structure of entire radial solutions is one related to the so called Kirchhoff Routh function. The of fundamental issues for the system of nonlinear equa- critical points of Kirchhoff Routh function can deduce a tions. Under certain technical conditions for a and b, steady point vortex solution. For a given critical point of we prove that any entire radial solutions of (∗) must be Kirchhoff Routh function, can one establish the existence one of topological, non-topological and mixed type solu- of smooth steady solutions approximating the point vor- tions, and completely classify the asymptotic behaviors tex solution deduced by the point? He will talk about the at infinity of these solutions. As an application of this previous study concerning this respect. A newly obtained classification, we prove that the two components u and v results by the speaker and his collaborators, Liu Zhong have intersection at most finite times. Yuan and Wei Juncheng, will be introduced. Existence and non-existence of positive solu- Nonlocal minimal surfaces tions on the Hardy-Littlewood-Sobolev type systems Juan Dávila Universidad de Chile, Chile [email protected] Congming Li Shanghai Jiao Tong University, China and University of Colorado at Boulder, USA Caffarelli, Roquejoffre and Savin (2010) introduced a no- [email protected] tion of nonlocal minimal surface, which is a boundary of a set that is minimal with respect to an s-perimeter func- In this presentation, we provide some existence, nonexis- tional, where 0 < s < 1. It is natural to consider critical tence, and classification of positive solutions for Hardy- points of the s-perimeter, which we call s-minimal sur- Littlewood-Sobolev type systems. In deriving these re- faces. Up to now there are very few examples of such sets. sults, some useful methods are created. We will briefly Starting from the property that as s → 1, the s-minimal introduce some of the involved methods. equation approaches the classical minimal surface equa- tion, we construct new examples of s-minimal surfaces for s close to 1. Singly periodic solutions of the Allen-Cahn This is joint work with Manuel del Pino (Universidad de equation and the Toda lattice Chile) and Juncheng Wei (Chinese University Of Hong Kong and University of British Columbia). Yong Liu North China Electric Power University, China Solutions for a semilinear elliptic equation in [email protected] dimension two with supercritical growth We study the Allen-Cahn equation in the plane: Ignacio Guerra Universidad de Santiago de Chile, Chile −∆u = u − u3, in R2. [email protected] Of interest are bounded entire solutions whose behav- ior at infinity is in some sense simple. Examples are We consider the problem those with finite Morse index, which have been exten- sively studied in the past. Here we will construct solu- p −∆u = λueu , u > 0, in Ω, tions which are periodic in one direction in the plane, but are not doubly periodic. The core of the construction is u = 0 on ∂Ω, the one-soliton solution of the Toda lattice, which is a 2 classical integrable system. This is joint work with M. where Ω ⊂ R and p > 2. Let λ1 be the first eigenvalue Kowalczyk, F. Pacard and J. Wei. of the Laplacian. For each λ ∈ (0, λ1), we prove the exis- tence of solutions for p sufficiently close to 2. In the case 2 of Ω a ball, we also describe numerically the bifurcation Critical Trudinger Moser equation in R diagram (λ, u) for p > 2. Monica Musso On the entire radial solutions arising in Universidad Católica de Chile, Chile Chern-Simons equations [email protected] 16 PRIMA 2013 Abstracts

We review some new results on construction of single where λ > 0 is a bifurcation parameter, and p, L > 0 are and multiple bubbling solutions for variational prob- two evolution parameters. We are able to determine the lems leading to semlinear equations with nonlinearities exact number of positive solutions by the positive values of Trudinger Moser type. of p, L and λ. Moreover, for p ≥ 1, the bifurcation di- agram undergoes fold and splitting bifurcations. While for 0 < p < 1, the bifurcation diagram undergoes fold, Multi-dimensional traveling fronts in bistable splitting and segment-shrinking bifurcations. Our results reaction-diffusion equations extend and improve those of Brubaker and Pelesko (Non- linear Anal. 75 (2012) 5086–5102) and Pan and Xing Masaharu Taniguchi (Nonlinear Anal. Real World Appl. 13 (2012) 2432–2445) Okayama University, Japan by generalizing the nonlinearity (1 − u)−2 to (1 − u)−p [email protected] with general p ∈ [1, ∞). We also answer an open ques- tion raised by Brubaker and Pelesko on the extension of (global) bifurcation diagrams results to general p > 0. Multi-dimensional traveling fronts have been studied by mathematicians for bistable reaction-diffusion equations Concerning this open question, we find and prove that in the whole space. Especially, cylindrically symmetric global bifurcation diagrams for 0 < p < 1 are different to traveling fronts have been studied by Hamel, Monneau and more complicated than those for p ≥ 1. This is joint work with Yan-Hsiou Cheng and Kuo-Chih Hung. and Roquejoffre (2005). We study traveling fronts of cylindrically non-symmetric shapes in bistable reaction- diffusion equations. Synchronized and segregated solutions for coupled nonlinear Schrödinger equations Existence and regularity of mean curvature flow with transport term Zhi-Qiang Wang Yoshihiro Tonegawa Nankai University, China and Utah State University, USA Hokkaido University, Japan [email protected] [email protected]

Given a compact C1 hypersurface in Rn (n ≥ 2) and In this talk we report recent work on new type of so- a vector field u : Rn × [0, ∞) → Rn which belongs to lutions for the coupled nonlinear Schrodinger equations. q 1,p n n q Depending upon the system being attractive or repul- Lloc([0, ∞); Wloc (R )), p > 2 · q−1 , p ≥ 2, q > 2, sive multiple (infinitely many) synchronized or segregated we prove some existence result for evolving hypersurfaces type solutions can be constructed, further making corre- whose velocity is given by its mean curvature plus u. For lation between the coupling constants and the existence the existence, we take the singular perturbation limit of of different type of solutions. the Allen-Cahn equation with additional transport term. The regularity issue is also discussed. This is a joint work with K. Takasao. Bubbling solutions for the Chern-Simons model Monotonicity formula and Liouville theorems for stable solutions of some elliptic problems Shusen Yan Kelei Wang The University of New England Wuhan Institute of Physics and Mathematics, CAS, [email protected] China [email protected] We study the following Chern-Simons-Higgs equation: I will report some recent progress on the understanding  of stable solutions to a class of second and fourth order ∆u + 1 eu(1 − eu) = 8πδ , in Ω, nonlinear elliptic equations, such as the Liouvile theorems ε2 p for stable and finite Morse index solutions and the par- u is doubly periodic in ∂Ω, tial regularity problems. In particular, I will discuss the application of monotonocity formula and the method of where Ω is a rectangle. We show that the above problem tangent cone analysis in these problems, which goes back has exactly two solutions if ε > 0 is small. This is a joint to W. H. Fleiming. The talk is based on joint work with work with Chang-Shou Lin. Juan Davila, Louis Dupaigne and Juncheng Wei.

Global bifurcation diagrams and exact mul- Gamma convergence for Maxwell-Chern- tiplicity of positive solutions for a one- Simons-Higgs energy dimensional prescribed mean curvature prob- lem arising in MEMS Yong Yu Shin-Hwa Wang The Chinese University of Hong Kong, Hong Kong, China National Tsing Hua University Hsinchu, Taiwan [email protected] [email protected]

We study global bifurcation diagrams and exact multi- A gamma convergence result associated with the plicity of positive solutions for the one-dimensional pre- Maxwell-Chern-Simons-Higgs energy will be presented. scribed mean curvature problem arising in MEMS As a consequence, we obtain a non-local free boundary problem, which describes the condensation of vortices in   0 the MCSH theory. This result generalize the classical result on the mean field limit of the magnetic Ginzburg-  u0(x) λ  −  = , u<1, Landau theory. q  p −L

Special Session 8 tends to zero, the global solution converges to the solu- Hyperbolic Conservation Laws and Related tion to the corresponding incompressible model in some Applications function spaces,and obtained a kind of the converge rates. Some counterexamples in the theory of con- Shock reflection and von Neumann conjec- servation laws tures

Alberto Bressan Mikhail Feldman Pennsylvania State University, USA University of Wisconsin-Madison, USA [email protected] [email protected]

The first part of the talk is concerned with sticky parti- We discuss shock reflection problem for compressible gas cle models in two space dimensions. Examples of Cauchy dynamics, and von Neumann conjectures on transition problems can be constructed with two and with zero so- between regular and Mach reflections. Then we describe lutions, respectively. Similar ideas apply to the equations recent results on existence of regular reflection solutions of pressureless gases in two space dimensions, with L∞ for potential flow equation up to the detachment angle, initial data. and discuss some techniques. The approach is to reduce The second set of examples concern the p-system of isen- the shock reflection problem to a free boundary problem tropic gas dynamics. For initial data with large total for a nonlinear equation of mixed elliptic-hyperbolic type. variation, one can arrange repeated wave-front interac- Open problems will also be discussed. The talk will be tions in such a way that the total strength of all wave based on the joint work with Gui-Qiang Chen. fronts becomes arbitrarily large. Normal forms and a Burgers-Hilbert equation Nonlinear mixed type equations arisen in Mach reflection John K. Hunter University of California, Davis, USA Shuxing Chen [email protected] Fudan University, China [email protected] The Burgers-Hilbert equation arises as a model equation for the motion of a vortex patch or discontinuity In the study of Mach reflection we find a kind of nonlinear in a two-dimensional, inviscid, incompressible fluid flow, mixed type equations. The solvability of the generalized and describes the effect of nonlinear steepening on an in- Tricomi problem of the mixed type equation leads the terface or wave that oscillates at a constant background stability of corresponding Mach configuration. frequency. For small amplitudes, these oscillations de- lay wave breaking. We will explain how non-standard normal form methods can be used to prove an enhanced Self-similar vortex spiral solutions of the 2d life-span of small smooth solutions of the Burgers-Hilbert incompressible Euler Equations equation in comparison with the inviscid Burgers equa- tion. These normal form methods can be applied to other quasilinear wave equations, for which the Burgers-Hilbert Volker Elling equation provides a useful test case. This is joint work University of Michigan, Ann Arbor, USA with M. Ifrim, D. Tataru, and D. Wong. [email protected] Incompressible limit of the non-isentropic Vortex spirals are ubiquitous in fluid flow, for example as ideal magnetohydrodynamic equations turbulent eddies or as trailing vortices at aircraft wings. However, there are few proofs of existence for any of the Song Jiang common fluid models. We consider solutions of the in- compressible Euler equations that have vorticity stratify- Institute of Applied Physics and Computational Mathe- ing into algebraic spirals. The solutions are selfsimilar: matics, China velocity v(t, x) = tm−1v(t−mx), for similarity exponent [email protected] 1 2 < m < ∞. Selfsimilar flows are special solutions of the full initial-value problem, but obtained by solving more We first give a short review of results on the low Mach tractable boundary value problems. The key to the ex- number limit for the compressible magnetohydrodynamic istence proof is an coordinate change which is implicit, equations. Then, we study the incompressible limit of the depending on the a priori unknown solution. We will compressible non-isentropic ideal magnetohydrodynamic also discuss the importance of the program for showing equations with general initial data in the whole space IRd non-uniqueness in the initial-value problem for the 2d in- (d = 2, 3), and establish the existence of classic solutions compressible Euler solutions. on a time interval independent of the Mach number. Fi- nally, by deriving uniform a priori estimates, we obtain the convergence of the solution to that of the incompress- Some results about compressible Oldroyd-B ible magnetohydrodynamic equations as the Mach num- ber tends to zero. Daoyuan Fang (joint-work with Q.C. Ju and F.C. Li) Zhejiang University, China [email protected] The Cauchy problem to the Kazhikhov- Vaigant model in compressible flow In this talk, I will show some results about the com- pressible Oldroyd-B model, which is the joint work with Quansen Jiu Ruizhao Zi. For such medel, we proved that the system Capital Normal University, China admits a unique local strong solution with initial den- [email protected] sity vanishes from below, and give a blow-up criterion; In the framework of critical spaces, we establish the global solutions if the initial data and coupling constant are suf- In this talk, we will present some recent progresses of ficiently small. We also proved that as the Mach number the global well-posedness of the Cauchy problem to the 18 PRIMA 2013 Abstracts

Kazhikhov-Vaigant model which is a kind of compressible stationary solutions. The optimal algebraic convergence Navier-Stokes equations with the shear viscosity µ a posi- rates are obtained. tive constant and the bulk viscosity λ is a power function This is a joint work with D. Donatelli, B. Rubino and R. of the density.The initial data can be arbitrarily large to Sampalmieri contain vacuum states. This is joint with Yi Wang and Zhouping Xin. Compressible Navier-Stokes equations with Chapman dissipation Global solutions for transonic self-similar two- dimensional Riemann problems Ronghua Pan Georgia Institute of Technology, USA Eun Heui Kim [email protected] California State University, Long Beach, USA [email protected] From its physical origin, the viscosity and heat conduc- tivity in compressible fluids depend on absolute temper- We discuss the recent development of multi-dimensional ature through power laws. The mathematical theory on transonic Riemann problems. More precisely we discuss the well-posedness and regularity on this setting is widely analytical results and numerical results on a simplified open. I will report some recent progress made on this model system – the nonlinear wave system. direction, with emphasis on the lower bound of tempera- ture, and global existence of solutions in one or multiple Long Time behaviors of the Vlasov-Poisson- dimensions. The relation between thermodynamics laws and Navier-Stokes equations will also be discussed. This Boltzmann Equations talk is based on joint works with Weizhe Zhang.

Hai-Liang Li Stability of steady state solutions for Euler- Capital Normal University, China [email protected] Maxwell equations

This talk is concerned with the long time behaviors of Yue-Jun Peng global solution to the Vlasov-Poisson-Boltzmann (VPB) Blaise Pascal University, France equations with binary elastic collision of hard sphere as [email protected] the initial data is a small perturbation of the global Maxwellian. In terms of the spectrum analysis of lin- We consider Euler-Maxwell equations arising in the mod- earized system and energy estimates, the optimal time eling of magnetized plasmas. For such equations steady decay rates of global solution is established, and the influ- equilibrium states with zero velocity exist. For small ini- ence of electric filed governed by the self-consistent Pois- tial data, we show global existence of smooth solutions son equation on the distribution of the spectra and the with convergence toward the steady states as the time time-asymptotical behaviors are justified. goes to infinity. In this problem, the main ingredient is an induction argument on the order of the derivatives of Traveling waves of chemotaxis models solutions in energy estimates. It is also efficient to obtain the global stability of solutions with exponential decay near steady states for Euler-Poisson equations. Tong Li University of Iowa, USA [email protected] Traveling waves for slow erosion

We study global existence and long time behavior of clas- Wen Shen sical solutions for a hyperbolic-parabolic system derived Pennsylvania State University, USA from the Keller-Segel model describing chemotaxis. We [email protected] establish the existence and the nonlinear stability of large- amplitude traveling wave solutions to the system of non- linear conservation laws derived from Keller-Segel model. We consider an integro-differential equation that de- scribes the slow erosion of granular flow in one space di- mension, Asymptotic behavior of solutions to Euler- Poisson equations for bipolar hydrodynamic (  R +∞  ut + exp f(ux(t, y)) dy =0, model of semiconductors x x (1) u(x, 0) =u ¯(x). Ming Mei Here u(x, t) denotes the height of the standing profile Champlain College Saint-Lambert and McGill University, Canada at the point (x, t), and the time variable t denotes the [email protected], [email protected] amount of mass that passes through. The function f(ux) is the erosion function, which denotes the rate of ero- sion (or deposition if negative) per unit mass per distance In this talk, we study the Cauchy problem for 1-D Euler- travelled. In a normalized model, f(1) = 0, indicating a Poisson system, which represents a physically relevant critical slope ux = 1 where no erosions or depositions hydrodynamic model but also a challenging case for a occur. bipolar semiconductor device by considering two different Due to the nonlinearity of the function f, various types pressure functions and a non-flat doping profile. Different of singularities will form in the solution u(x, t), including from the previous studies for the case with two identical kinks (jumps in u ) and shocks (jumps in u). Existence pressure functions and zero doping profile, we realize that x the asymptotic profiles of this more physical model are of BV solutions is proved in [4], and semi-group solutions their corresponding stationary waves (steady-state solu- are established in [2], using a modified form of wave front tions) rather than the diffusion waves. Furthermore, we tracking approximation. In the simpler case where ux prove that, when the flow is fully subsonic, by means of does not blow up, uniqueness of solutions is also achieved a technical energy method with some new development, [1]. the smooth solutions of the system are unique, exist glob- In this talk we construct particular forms of traveling ally and time-algebraically converge to the corresponding wave solutions for (1), which connect to x = ±∞ with 19 PRIMA 2013 Abstracts

critical slope ux = 1. We show that, for a fixed relation Special Session 9 of the asymptote at x = ±∞, there exists a unique trav- Inverse Problems eling wave solution. Furthermore, such traveling wave solutions are local attractors. Nearby solutions approach Inverse scattering problems in wave propaga- the traveling wave asymptotically as t → ∞. This is a tion joint work with Graziano Guerra, see [3]. Gang Bao Zhejiang University, China and Michigan State Univer- [1] D. Amadori and W. Shen, Front tracking approxima- sity, USA tions for slow erosion, Discrete Contin. Dyn. Syst., 32 [email protected] (2012), no. 5, 1481–1502. [2] R. M. Colombo, G. Guerra, and W. Shen, Lipschitz semigroup for an integro–differential equation for slow Recent progress of our research group on inverse scatter- erosion, Quart. Appl. Math., 70 (2012), 539–578. ing problems in wave propagation will be reported. Issues [3] G. Guerra, and W. Shen, Existence and Stability of on uniqueness/stability and numerical solution for the in- Traveling Waves for an Integro-differential Equation for verse problems will be discussed. Slow Erosion Preprint, 2013. [4] W. Shen and T.Y. Zhang, Erosion profile by a global model for granular flow, Arch. Ration. Mech. Anal., 204 Multi-scale full waveform inversion for seismic (2012), no. 3, 837–879. imaging

Michael P. Lamoureux On the existence of Meyer type transonic University of Calgary, Canada flows and a degenerate change type equation [email protected]

The seismic imaging problem entails recovering an image Zhouping Xin of the earth’s subsurface from data that is recorded on the surface of the earth, determined by the propagation of The Chinese University of Hong Kong, Hong Kong, China [email protected] seismic (vibrational) waves through the body of the earth. The 2D or 3D acoustic wave equation is commonly used as a simplified mathematical model for this seismic wave propagation. The full waveform inverse problem aims to Historically, two types of smooth steady compress- deduce the physical parameters of the (acoustic) medium ible irrotational transonic flows were conjectured for 2- of propagation from recorded data of impulsive waves that dimensional de Laval nozzles: Taylor type and Meyer are transmitted or reflected through the medium, and type. However, it has known since that Tay- thus form an image of the subsurface. lor type transonic flows may not exist in general, while In this study, we demonstrate a numerical algorithm the existence of Meyer type transonic flows with suit- that uses factorization in the PDE solver of the 2D acous- able physical boundary condition has been a long stand- tic wave model, a multi-scale approach to the inverse so- ing open problem. Such a flow is governed by a quasi- lution, and a projection-based linearization search for the linear equation which changes type and becomes degen- solution to the inverse problem. The multi-scale approach erate upon crossing sonic state where the flow may have is used to decrease the rank of the inverse problem, thus singularities. In this talk, I will report some progress on decreasing the ill-posedness and under-determinedness of the solution. With a few examples, we show the robust studies of such problems. First, by investigating the prop- properties of the inversion algorithm, a fast numerical erties structure of the sonic curve, in particular its excep- 2 convergence rate, and the advantages of multi-scaling. tional points, for C -smooth transonic flows in a gen- Joint with Gary F. Margrave, Vladimir Zubov eral nozzle, we show the instability of Taylor type flows and Meyer type flows with non-empty exceptional points. Then we identify a class of de Laval nozzles and suitable On the inverse problems for the coupled con- physical boundary conditions such that Meyer type tran- tinuum pipe flow model for flows in karst sonic flow exists with sonic curve everywhere exceptional. Some global properties of such a solution and related open aquifers problems will be discussed. Shuai Lu Fudan University, China Weakly nonlinear geometric optics for hyper- [email protected] bolic systems of conservation laws In this talk, we investigate a coupled continuum pipe flow (CCPF) model which describes the fluid flows in karst Yongqian Zhang aquifers. After generalizing the well-posedness of the for- Fudan University, China ward problem to the anisotropic exchange rate case which [email protected] is a space-dependent variable, we present the uniqueness of this parameter by measuring the Cauchy data. Fi- nally, some regularization schemes are provided to solve In this talk I will present a new approach to analyze the one proposed inverse problem. validation of weakly nonlinear geometric optics for en- tropy solutions of nonlinear hyperbolic systems of con- servation laws whose eigenvalues are allowed to have con- A heat source reconstruction formula from stant multiplicity and corresponding characteristic fields single internal measurements using a family to be linearly degenerate. The approach is based on our of null controls careful construction of more accurate auxiliary approxi- mation to weakly nonlinear geometric optics, the proper- Axel Osses ties of wave front-tracking approximate solutions, the be- Universidad de Chile, Chile havior of solutions to the approximate asymptotic equa- [email protected] tions, and the standard semigroup estimates. This is a joint work with Guiqiang Chen and Wei Xiang of Univer- sity of Oxford. We consider the inverse problem of determining the spa- tial dependence f(x) of the source term in a heat equation ut − γ∆u = f(x)σ(t) in Ω × (0,T ) assuming σ(t) known, 20 PRIMA 2013 Abstracts

from a single partial internal measurement of the solu- can noninvasively measure magnetic fields inside the hu- tion in O × (0,T ), O ⊂ Ω. The purpose of this paper is man body, electrical tissue property imaging methods us- to establish a reconstruction formula for f(x) using ex- ing MRI have lately been proposed. Magnetic resonance act controls, and that could be generalized for general EIT (MREIT) performs conductivity imaging at dc or parabolic equations. The reconstruction formula is as- below 1 kHz by externally injecting current into the hu- sociated to a family of exact controls v(τ) indexed by man body and measuring induced internal magnetic flux τ ∈ (0,T ). We perform numerical simulations in order density data using an MRI scanner. Magnetic resonance to illustrate the feasibility, accuracy and stability of the electrical property tomography (MREPT) produces both proposed reconstruction formula. conductivity and permittivity images at the Larmor fre- quency of an MRI scanner based on B1-mapping tech- niques. Since internal data are only available in MREIT Inverse boundary value problems for time- and MREPT, we may formulate well-posed inverse prob- harmonic acoustic waves: conditional stabil- lems for image reconstructions. To develop related imag- ity and iterative reconstruction ing techniques, we should clearly understand the basic principles of MREIT and MREPT, which are based on coupled physics of bioelectromagnetism and MRI as well Lingyun Qiu as associated mathematical methods. In this talk, we de- Purdue University, USA scribe the physical principles of MREIT and MREPT in [email protected] a unified way and associate measurable quantities with the conductivity and permittivity. Clarifying the key re- lations among them, we examine existing image recon- The inverse boundary value problem for time-harmonic struction algorithms to reveal their capabilities and limi- acoustic waves is to determine the property of the medium tations. This talk is based on our recent book " Electro- inside a domain from the measurements of the displace- Magnetic tissue property MRI" by JK Seo, EJ Woo, K ment and normal stress on its boundary. The governing Ulrich, and Y Wang. equation is the Helmholtz equation. In the partial data case, the measurements are gathered over a subset of the boundary. Local lens rigidity In this work, we first prove a Lipschitz type stabil- ity estimate for the inverse problem assuming that the wavespeed is piecewise constant with discontinuities on a finite number of known interfaces. Then, a hierarchy Plamen Stefanov algorithm is proposed and analysed for the iterative re- Purdue University, USA construction with multi-frequency data. The algorithm is [email protected] based on a projected steepest descent iteration with sta- bility constraints. The numerical results demonstrate the proposed methodology has good performance in stability We show that we can recover locally a sounds speed near and accuracy. a boundary point p from the lens relation (travel times) assuming that the boundary is strictly convex near p. This is a recent result with Gunther Uhlmann and Andras Inverse problems to elliptic systems in quanti- Vasy. tative (fluorescence) photoacoustic tomogra- phy Stochastic controllability Kui Ren University of Texas at Austin, USA [email protected] Xu Zhang Sichuan University, China We study inverse problems to two systems of elliptic equa- [email protected] tions that arise from quantitative (fluorescence) photoa- coustic tomography. We present some general uniqueness and stability results following the general theory devel- Controllability for dynamical systems is a typical ill-posed oped in [Bal, arXiv:1210.0265], as well as some explicit problem. In this talk, I will explain why the formula- reconstruction strategies in simplified settings. tion of stochastic controllability problems and the tools to solve them may differ considerably from their deter- ministic counterpart. Recent progress in electrical tissue property MRI Some efficient domain decomposition meth- Jin Keun Seo ods for a Class of inverse problems Yonsei University, Korea seojyonsei.ac.kr Jun Zou Recently, imaging techniques in science, engineering, and Chinese University of Hong Kong, Hong Kong, China medicine have evolved to expand our ability to visualize [email protected] internal information of an object such as the human body. In particular, there has been marked progress in MR- based electromagnetic property imaging techniques which In this talk we shall present several new domain decom- use MRI to provide cross-sectional images of conductiv- position methods for solving some linear and nonlinear ity, permittivity, and susceptibility distributions inside inverse problems. The motivations and derivations of the the human body. These electromagnetic material prop- methods will be discussed, and numerical experiments erties of biological tissues are important biomarkers since will be demonstrated. This is a joint work with Xiao- they reveal physiological and pathological conditions of Chuan Cai (University of Colorado at Boulder) and Hui body tissues and organs. Since the conductivity and per- Feng (Wuhan University) and Daijun Jiang (Huazhong mittivity values exhibit frequency-dependent changes, it Normal University). The work was supported by Hong is worthwhile to perform spectroscopic imaging from al- most dc to hundreds of MHz. To probe the human body, Kong RGC grants (projects 405110 and 404611). we may inject current using surface electrodes or induce current using external coils. Noting that an MRI scanner 21 PRIMA 2013 Abstracts

Special Session 10 It is shown that when almost all collisions are grazing, Kinetic Equations that is, the deviation angle θ of the collision is limited near zero (i.e., θ ≤ ), the solution f  of the Boltzmann On some kinetic models for Bose Einstein con- equation with initial data f0 can be globally or locally densation expanded as f  = f + O(), Radjesvarane Alexandre for non Coulomb potential, or French Naval Academy, France and Shanghai Jiao Tong University, China [email protected] f  = f + O(| log |−1),

We present some models based on kinetic equations for for Coulomb potential, where the function f is the solu- describing Bose Einstein condensation. We will discuss tion of Landau equation, which is associated to the graz- about possible blow up or not of some of the partial dif- ing collisions limit of Boltzmann equation, with the same ferential equations. This is a joint work with Jie LIAO initial data f0. These give the rigorous justification of the Landau approximation in the spatially homogeneous and Chunjin LIN. case.

Angular averaging, propagation of exponen- New regularity estimates for transport equa- tial tails and grazing collisions for solutions of tions the Boltzmann equation Pierre-Emmanuel Jabin Irene Gamba University of Maryland, USA University of Texas at Austin, USA [email protected] [email protected] We present new regularity estimates which are prop- We will discuss the interplay on the collision kernels prop- agated by transport equations with rough coefficients. erties of the Boltzmann equation and the generation and Those estimates provides compactness on the density, propagation of summability of moments of the solution which is a key ingredient to obtain existence of solu- for the homogeneous initial value problem. Such summa- tions for models from fluid mechanics (of the compressible bility yields global bounds for the solution of the Boltz- Navier-Stokes type) to chemotaxis. The corresponding 1 mann equation by exponentially weighted norms in L spaces are defined at a logarithmic scale in terms of num- and pointwise, where the exponent depend on the initial ber of derivatives and can thus be seen as intermediary state norms, the rate of the intra-molecular potentials as between the usual Lp and Sobolev spaces. well as the integrability properties on the sphere (angular averaging) for the scattering angle cross-section. We will also discuss the impact of these estimates in open prob- Condensation and regularity for Boson Boltz- lems, such as the grazing collision limits to the Landau mann equation equation for Coulombic interactions. We will also show numerical simulations of these limits for different cross sections. Xuguang Lu Tsinghua University, China Lp-scattering and uniform stability of kinetic [email protected] equations We study the spatially homogeneous Boltzmann equation Seung-Yeal Ha for Bose-Einstein particles for the hard sphere model. We consider the case where the initial datum of a solution of Seoul National University, Korea the equation is a function so that there is no condensation [email protected] (Dirac mass) at the initial state. We show that if the initial datum is not very singular near the origin (the zero- In this talk, we will review recent progress on the Lp- point of particle energy) and if the kinetic temperature scattering and uniform stability of several kinetic equa- is sufficiently high, then the solution is also a function tions with self-consistent forces. For the Vlasov equa- for all time, and it is a unique classical mild solution tion with a self-consistent force, we will show that the of the equation; whereas if the initial datum is singular Coulomb’s potential in three dimensions is critical in the enough near the origin but still Lebesgue integrable, then sense that if spatial dimension is larger than three, there the condensation of a corresponding solution continuously exists a L1-scattering, whereas for low dimensions less starts to occur from the initial time to every later time. than equal to three, there is no L1-scattering. We also present a framework for the Lp-stability of kinetic equa- tions. This is a joint work with Sun-Ho Choi (NUS) and Hamiltonian propagation of mono-kinetic Qinghua Xiao (SNU). measures with rough initial profiles

On the spatially homogeneous Boltzmann and Peter Markowich Landau equations King Abdullah University of Science and Technology, Kingdom of Saudi Arabia [email protected] Lingbing He Tsinghua University, China [email protected] Consider in the phase space of classical mechanics a Radon measure which is a probability density carried by the graph of a Lipschitz continuous (or even less regular) In this talk, I will present some recent progress on the vector field. We study the structure of the push-forward lower and upper bounds for the Boltzmann collision op- of such a measure by a Hamiltonian flow. In particu- erator. As one application, we can build a unified frame- lar, we provide an estimate on the number of folds in the work to establish the well-posedness results for both support of the transported measure that is the image of Boltzmann and Landau equations. As another applica- the initial graph by the flow. We also study in detail the tion, we will revisit the so-called "grazing collisions limit". type of singularities in the projection of the transported 22 PRIMA 2013 Abstracts

measure in configuration space (averaging out the mo- of traveling pulse of bacteria in micro-channel. The above mentum variable). We study the conditions under which mathematical modeling allows to recover this behaviour, this projected measure can have atoms, and give an ex- which motivates the interest on such system. ample in which the projected measure is singular with respect to the Lebesgue measure and diffuse. Finally, we discuss applications of our results to the classical limit of Viscous wave propagation at interface the SchrŽdinger equation. Shih-Hsien Yu Scalar conservation laws and kinetic formula- National University of Singapore, Singapore tion [email protected]

Benoît Perthame In this talk we implement the LY algorithm to derive a Pierre-and-Marie-Curie University, CNRS/INRIA and two-sided master relationship. This gives rise the opera- Institut Universitaire de France, France tor to construct the surface wave at the interface and the [email protected] construction of the Green’s function of a simple variable coefficient problem for viscous conservation laws.

We present a theory of Scalar Conservation Laws with rough fluxes. The difficulty is that, even with BV esti- mates, the equations does not make sense in disctribu- Special Session 11 tional sense. Our approach is based on the kinetic formu- Mathematical Fluid Dynamics and Related lation of conservations laws. Topics This theory leads naturally to consider Kinetic Avergaing Lemmas with random fluxes. On simple situations we Global solutions of the equivariant heat-flow will show the differences int he gain of regularity. This talk is based on works with P.-L. Lions and P. E. Souganidis. Stephen Gustafson University of British Columbia, Canada Kinetic description of bacterial motion by [email protected] chemotaxis and asymptotics The harmonic map heat-flow is a canonical, parabolic, geometric evolution equation, which is (energy) critical Nicolas Vauchelet in two dimensions. I will present a global regularity re- Pierre-and-Marie-Curie University, France sult for the equivariant, higher-degree, above-threshold [email protected] heat-flow into the sphere, which extends to higher en- ergies earlier work with Nakanishi and Tsai on the heat Chemotaxis is the phenomenon in which cells direct their and Schroedinger flows. This is joint work with Dimitrios motion according to a chemical present in their environ- Roxanas. ment. Since experimental observations have shown that the motion of bacteria (e.g. Escherichia Coli) is due to Well-posedness of coupled kinetic-fluid mod- the alternation of ‘runs and tumbles’, mathematical mod- els for flocking elling thanks to a kinetic description has been proposed. The starting point of the study is the so-called Othmer- Dunbar-Alt model governing the dynamics of the distri- Seung-Yeal Ha bution function f of cells at time t, position x and veloc- Seoul National University, Korea ity v, assumed to have a constant modulus c > 0, as well [email protected] as the concentration S(t, x) of the involved chemical. A general formulation for this model can be written as In this talk, I will present several kinetic-fluid models for  ∂tf + v · ∇xf = Q(f), flocking. More precisely, I will discuss the dynamics of  Cucker-Smale flocking particles interacting with neigh-  Q(f) = R T [S](v0, v)f(v0)  |v0|=c boring compressible and incompressible fluid. For such −T [S](v, v0)f(v) dv0, coupled kinetic-fluid models, we will show global exis-  Z tence of weak and strong solutions and asymptotic flock-   −∆S + S = ρ(t, x) := f(t, x, v) dv. ing estimates for small initial data and large . |v|=c This is a joint work with H.O.Bae (Ajou Univ), Young-Pil Choi (Imperial College of London) and Moon-Jin Kang The third equation describes the dynamics of the chem- (SNU). ical agent which diffuses in the domain. It is produced by the cells themselves with a rate proportional to the density of cells ρ and disappears with a rate proportional Global classical and weak solutions to the 3D to S. The transport operator on the left-hand side of the fully compressible Navier-Stokes-Fourier sys- first equation stands for the unbiased movement of cells tem (‘runs’), while the right-hand side governs ‘tumbles’, that is chemotactic orientation, or taxis, through the turning kernel T [S](v0, v), which is the rate of cells changing their Xiangdi Huang velocity from v0 to v. Academy of Mathematics and System Sciences, CAS, China In this work, we focus on positive chemotaxis which [email protected] means that the involved chemical S is attracting cells, called chemoattractant. Existence results for this system has been obtained for various assumptions on the turn- We establish the global existence and uniqueness of clas- ing kernel. Macroscopic model can be derived from this sical solutions to the three-dimensional fully compressible system of equations after a rescaling. When the taxis is Navier-Stokes-Fourier system with smooth initial data small compared to the unbiased movement of cells, the which are of small energy but possibly large oscillations scaling must be of diffusive type, so that the limit equa- where the initial density is allowed to vanish. Moreover, tions are of diffusion or drift-diffusion type. When taxis for the initial data, which may be discontinuous and con- dominates the unbiased movements, a hyperbolic limit tain vacuum states, we also obtain the global existence can be derived, leading to aggregation equations. More- of weak solutions. These results generalize previous ones over, experimental observations have shown the formation on classical and weak solutions for initial density being 23 PRIMA 2013 Abstracts

strictly away from vacuum, and are the first for global In this talk, we consider classical limit problem of a class classical and weak solutions which may have large oscil- of quantum Euler equation. The classical limit describes lations and can allow vacuum states. the transition between quantum mechanics and classical mechanics (Newtonian mechanics). More specifically, we Solvability of the initial value problem to a consider the compressible Euler equation with a quantum model system for water waves pressure, that is,  ∂ ρ + divρv = 0,  t Tatsuo Iguchi   √   2 ∆ ρ Keio University, Japan ∂t(ρv)+div(ρv⊗v)+ρ∇P (ρ)=~ ρ∇ √ , (2) [email protected]  ρ   ρ(0, x) = ρ0(x), v(0, x) = v0(x), The water wave problem is mathematically formulated N as a free boundary problem for an irrotational flow of for (t, x) ∈ R+ × R , where ρ = ρ(t, x) and v = v(t, x) an inviscid and incompressible fluid under the gravita- denote the mass density and the velocity vector, respec- tional field. The basic equations for water waves are tively. (ρ0, v0) is a given initial data independent of complicated due to the nonlinearity of the equations to- ~. P stands for the pressure. In this talk, we mainly gether with the presence of an unknown free surface. consider the pressure given by the Poisson equation; Therefore, until now many approximate equations have P (ρ) = c(−∆)−1ρ with some constant c. In this case, (2) been proposed and analyzed to understand natural phe- is often referred to as an Euler-Poisson equations. The nomena for water waves. Famous examples of such ap- right hand side of the second line of (2) is the quantum proximate equations are the shallow water equations, the pressure. ~ is a positive parameter which corresponds to Green–Nagdhi equations, Boussinesq type equations, the the scaled Planck constant. Our problem is analysis of Korteweg–de Vries equation, the Kadomtsev–Petviashvili the limit → 0 (the classical limit). At least formally, a equation, the Benjamin–Bona–Mahony equation, the ~ Camassa–Holm equation, the Benjamin–Ono equations, solution (ρ, v) of (2) tends to a solution of the usual Euler and so on. All of them are derived from the water wave equation problem under the shallowness assumption of the water waves, which means that the mean depth of the water is  ∂tn + divnw = 0,  sufficiently small compared to the typical wavelength of ∂t(nw)+div(nw⊗w)+n∇P (n)=0, (3) the water surface.  On the other hand, it is well-known that the water wave n(0, x) = ρ0(x), w(0, x) = v0(x). problem has a variational structure. In fact, J. C. Luke N (1967) gave a Lagrangian in terms of the velocity poten- for (t, x) ∈ R+×R . Our purpose is to establish sufficient tial and the surface variation, and showed that the cor- existence results for (2) and (3) and to justify this limit. responding Euler–Lagrange equations are the basic equa- The difficulty of (2) lies in the treatment of the quantum tions for water waves. M. Isobe (1994) and T. Kakinuma pressure term. Since this pressure contains the density ρ (2000) derived model equations for water waves without as a denominator, we have to care about the existence of any shallowness assumption. The model equations are vacuum (zero points of ρ). the Euler–Lagrange equations to an approximated La- In this talk, we restrict our attention to the irrotational grangian, which is obtained by approximating the veloc- flow case, in which case (2) is an alternative formulation ity potential in Luke’s Lagrangian. of Schrödinger equation (the Madelung equation), and In this talk, we consider one of the model equations and analyze (2) by using a complex square root of the density. report the solvability of the initial value problem. The This method is introduced by Grenier in 1998 in order model are nonlinear dispersive equations and the hyper- to justify the semiclassical limit of the cubic nonlinear surface t = 0 is characteristic for the model equations. Schrödinger equation. Let a(t, x) be a C-valued function Therefore, the initial data have to be restricted in an in- N finite dimensional manifold in order to the existence of and u(t, x) be an R -valued function. We work with the the solution, and we show that the manifold is invariant following system. under the time evolution. This talk is based on the joint research with my former  1 i~  ∂ta + u · ∇a + a∇ · u = ∆a, student Yuuta Murakami.  2 2 2 (4) ∂tu + (u · ∇)u + ∇P (|a| ) = 0, Some new advances on modeling and algo-   p rithms development of multiphase complex a(0, x) = ρ0(x), u(0, x) = v0(x). fluid system using the phase field method N for (t, x) ∈ R+ × R . The heart of matter is that if (a, u) solves this system then (ρ, ρv) = (|a|2, |a|2u + Im(a∇a)) Chun Liu, Xiaofeng Yang & Jie Shen ~ becomes a solution to (2) (at (t, x) 6∈ {a(t, x) = 0}). Pennsylvania State University, USA [email protected] By this method, besides the justification of the limit (ρ, ρv) → (n, nw) as ~ → 0, we obtain an asymptotic expansion of (ρ, ρv) in the classical limit. We remark We present some efficient modeling approach for the two that the presence of vacuum makes no trouble when we phase fluid system with the variable densities and viscosi- solve (4) since the quantum pressure now changes into a ties. The model, derived by employing an energetic vari- dispersion term. ational approach, is thermodynamically consistent that admits an energy law. Some decoupled, energy stable schemes are developed to solve the model efficiently. Sim- Asymptotic stability of mild solutions to the ilar approach has been applied to the two phase complex Navier-Stokes equations fluid system, where one phase is considered to be the nematic liquid crystal. Qualitative agreements with ex- perimental results are observed. Maria Schonbek University of California, Santa Cruz, USA [email protected] Classical limit of some quantum Euler equa- tions We consider the initial value problem for the Navier- Stokes equations modeling an incompressible fluid in Satoshi Masaki three dimensions: Hiroshima University, Japan 3 [email protected] ut + u · ∇u + ∇p = ∆u + f, (x, t) ∈ R × (0, ∞), 24 PRIMA 2013 Abstracts

N N −1 div u = 0, ˙ 2 ˙ 2 B2,1) × B2,1 , while E0N and v0N are large, where ¯ > u(x, 0) = u0(x) E0 = [E0,ij ]i=1,...,N−1;j=1,...,N , v¯0 = [v01, . . . , v0,N−1] and E = [E ,...,E ]. It is well-known that this problem has a unique global- 0N 0,N1 0,NN in-time mild solution for a sufficiently small initial condi- tion u0 and for a small external force F in suitable scal- ing invariant spaces. We show that these global-in-time mild solutions are asymptotically stable under every (ar- Special Session 12 bitrary large) l2-perturbation of their initial conditions. Mathematics of String Theory The work is joint with Grsegorz Karch and Dominika Pi- larczyk. Stacky resolutions of the moduli spaces of in- stantons on ALE spaces On vanishing viscosity limit for 3-Dimensional incompressible Navier-Stokes equations with Ugo Bruzzo a slip boundary condition International School for Advanced Studies, Italy [email protected] Zhouping Xin The Chinese University of Hong Kong, Hong Kong, China Moduli spaces of framed sheaves on the complex projec- [email protected] tive plane are a of singularities of the mod- uli space of ideal instantons on the 4-sphere. Another instance of this phenomenon is provided by the moduli In this talk, we will discuss the problem of vanishing space of framed sheaves on the blowup of the projective viscosity limit for 3-dimensional incompressible Navier- plane, which resolves the singularities of the moduli space Stokes equations in a general bounded smooth domain of ideal instantons on the orientation-reversed projective with general Navier-Slip boundary conditions. The focus plane. This fact is used extensively in super Yang-Mills will be on the convergence of viscous solutions to the in- topological quantum field theories, where the instanton viscid ones in the space C([0,T ],H1(Ω)). Some uniform moduli spaces classify the classical vacua, in particular to estimates on the rate of convergence will be presented. compute Nekrasov partition functions and other invari- ants. A natural question arises whether similar constructions Topological instability of laminar flows for the can be made in the case of other spaces. I will consider two-dimensional Navier-Stokes equation with instantons on the ALE spaces X of type Ak. Here the circular arc no-slip boundary conditions nontrivial behaviour of the instantons at infinity makes it necessary to consider moduli spaces of framed sheaves on a DM projective stack whose coarse moduli space is Tsuyoshi Yoneda a toric compactification of X. In particular one needs to Hokkaido University, Japan introduce a so-called root stack which has a gerby be- [email protected] haviour over the compactifying divisor.

In this talk we show that a diffuser-shaped boundary in- Topology change from heterotic Narain T- duces the reverse flow even near the entrance of the dif- fuser. Let us be more precise. We consider the two- duality dimensional Navier-Stokes equation in Ω ⊂ R2 (define Ω later) with no-slip and inflow-outflow conditions on Jarah Evslin ∂Ω. We need to handle a shape of the boundary ∂Ω Institute of High Energy Physics, CAS, China precisely, thus we set a parametrized smooth boundary [email protected] 2 2 ϕ : (0,S) → R as |∂sϕ(s)| = 1, |∂s ϕ(s)| = κ (curva- 2 ture), ϕ(0) = (0, 0), ∂sϕ(0) = (1, 0), ∂s ϕ(0) = (0, −κ). We choose S later (should be sufficiently small). We de- I will describe topology changing Narain T-dualities on fine n = n(s) := (∂ ϕ(s))⊥ as a unit normal vector and torus-fibered compactifications with H flux in type II and s heterotic string theories. In heterotic string theories, such τ = τ(s) = ∂sϕ(s) as a unit tangent vector, where ⊥ T-dualities mix the topology of the gauge bundle with represents upward direction. that of spacetime consistently with the supersymmetry conditions. More precisely, T-duality mixes half of the Global strong solution for equations related field strength of an unbroken U(1) gauge symmetry with to the incompressible viscoelastic fluids the antiselfdual part of the curvature of the fibration of compactified circle.

Ting Zhang Zhejiang University, China Equivariant Cohomology and Bismut-Chern [email protected] Character in the Stolz-Teichner Program

Considering a system related to the incompressible vis- Fei Han coelastic fluids of Oldroyd–B type, National University of Singapore, Singapore [email protected] ∇ · v = 0, (t, x) ∈ R+ × RN ,N ≥ 2, vit +v · ∇vi +∂iΠ=µ∆vi +Ejk∂j Eik +∂j Eij , Abstract: The Stolz-Teichner program aims to relate su- Et + v · ∇E = ∇vE + ∇v, persymmetric field theories to generalized cohomology theories. In this talk, we will describe our joint projects (v, E)(0, x) = (v0,E0)(x), with Chris Schommer-Pries, Stephan Stolz and Peter Te- ichner, relating 0|1-dimensional gauged field theories to we investigate the global existence of the strong so- the equivariant cohomology of manifolds with Lie group lutions with some classes of large initial data E0 = actions and realizing the Bismut-Chern character as di- > [E0,ij ]i=1,...,N;j=1,...,N , v0 = [v01, . . . , v0N ] . We ob- mension reduction functor. tain the global existence and uniqueness of solution pro- N −1 ¯ ˙ 2 vided that (E0, v¯0) are sufficient small in (B2,1 ∩ T-duality commutes with reduction 25 PRIMA 2013 Abstracts

Pedram Hekmati It is known that topological T-duality can be extended University of Adelaide, Australia to apply not only to principal circle bundles, but also to [email protected] non-principal circle bundles. We show that this result can also be recovered via the noncommutative geometry approach which we previously used for principal torus T-duality is a discrete symmetry in string theory that re- bundles. This work has several interesting byproducts, lates topologically distinct torus fibrations and provides a including a study of the K-theory of crossed products by dictionary for translating geometrical structures between Oe(2) = Isom(R), the universal cover of O(2), and some in- them. The duality is mathematically well-understood in teresting facts about equivariant K-theory for /2. These type II theories and the purpose of this talk is to ex- Z results are then extended to the case of bundles with plain how it can be extended to the heterotic setting. singular fibers, or in other words, non-free O(2)-actions. The setup naturally involves string structures and reduc- This is joint work with Jonathan Rosenberg. tion of Courant algebroids. This is joint work with David Baraglia.

A motivic approach to Potts models Special Session 13 Measurable and Topological Dynamics Matilde Marcolli Height reducing problem California Institute of Technology, USA [email protected] Shigeki Akiyama University of Tsukuba, Japan The use of motivic techniques in Quantum Field Theory [email protected] has been widely explored in the past ten years, in rela- tion to the occurrence of periods in the computation of Feynman integrals. In this lecture, based on joint work We say that an algebraic number α has height reduc- with Aluffi, I will show how some of these techniques can ing property (HRP) if there is a positive integer B that be extended to a motivic analysis of the partition func- Z[α] = B[α], i.e., every number in Z[α] has an equiva- tion of Potts models in statistical mechanics. An esti- mate of the complexity of the locus of zeros of the par- lent representation with coefficients in {−B,...,B}. This tition function, can be obtained in terms of the classes problem is studied for algebraic integers, since it has inti- mate connection to the construction of self-affine tilings. in the Grothendieck ring of the affine algebraic varieties In this talk, we consider HRP for general algebraic num- defined by the vanishing of the multivariate Tutte poly- bers and obtain some ‘almost’ if and only if condition nomial, based on a deletion-contraction formula for the for HRP. The proof relies on a quantitative version of Grothendieck classes. Kronecker’s approximation theorem. This is a joint work with Toufik Zaimi. The Wess-Zumino-Witten model on SL (2; R) Large deviation principle for chaotic dynami- cal systems David Ridout The Australian National University, Australia [email protected] Yong Moo Chung Hiroshima University, Japan [email protected] The prototypical examples of string theories on target spaces with non-trivial topologies are the Wess-Zumino- Witten (WZW) models for which the target is a compact We will discuss a class of chaotic dynamical systems for reductive Lie group. However, the non-compact case is which the full large deviation principle holds. It con- physically more relevant and is mathematically richer as tains intermittent maps and quadratic maps on inter- well. While the pioneering work of Maldacena and Ooguri vals, almost Anosov diffeomorphisms on tori and count- able Markov shifts with return time functions of ’gentle’ proposed string spectra and proved a no-ghost theorem slopes. for the WZW model on SL (2; R), recent work has shown that the underlying conformal field theory is far richer, at least for certain levels, and provides an example of a so- Chaotic dynamics of continuous-time topolog- called logarithmic conformal field theory. This talk will ical semiflow on Polish space review this recent work and what it suggests for other theories with non-compact target spaces. Xiongping Dai Nanjing University, China M-branes and higher bundles [email protected]

Hisham Sati Differently from Li-Yorke and others in literature, we will University of Pittsburgh, USA introduce the concept—chaos—for a continuous semiflow [email protected] f : R+ × X → X on a Polish space X without isolated points, which is useful for the theory of ODE and is in- variant under topological equivalence. Our definition is We describe the M-branes in M-theory via higher geome- weaker than Devaney’s since here f may have neither try, including String structures, String bundles with con- fixed nor periodic elements; but it still implies the sen- nections, higher (stacky) notions of Chern-Simons theory, sitive dependence on initial data similar to Devaney’s and relation to higher WZW models. This is joint work chaos. We will show that f always has a maximal chaotic with Domenico Fiorenza and Urs Schreiber. subsystem. In addition, we will consider the chaotic be- havior on minimal center of attraction of a motion. T-duality for circle bundles via noncommuta- tive geometry Random dynamical systems

Mathai Varghese Anthony Dooley The University of Adelaide, Australia University of Bath, UK [email protected] [email protected] 26 PRIMA 2013 Abstracts

In joint work with Guo-Hua Zhang, we have extended Subword complexity and Sturmian colorings the notion of random dynamical system from Z actions of trees to actions of discrete amenable groups. In this setting, we introduce local fiber topological pres- sure and establish a variational principle related to Seonhee Lim measure-theoretic entropy. Seoul National University, Korea [email protected] One can then define both topological and measure- theoretic entropy tuples, and apply the variational princi- ple to obtain a relationship between them. These results In this talk, we introduce subword complexity of colorings recover and extend many recent results in local entropy of regular trees. We characterize colorings of bounded theory. subword complexity and then introduce Sturmian color- ings, which are colorings of minimal unbounded subword complexity. Local entropy dimension for a measure and a We classify Sturmian colorings using their type sets. We variational principle show that any Sturmian coloring is a lifting of a coloring on a quotient graph of the tree which is a geodesic or a ray, Dou Dou with loops possibly attached, thus a lifting of an "infinte word". We further give a complete characterization of Nanjing University, China the quotient graph for eventually periodic ones. We will [email protected] provide several examples. This is a joint work with Dong Han Kim. The notion of entropy dimension measures the subexpo- nential complexity of entropy zero dynamical systems. Shadowing properties with average tracing of By considering topological entropy via hausdorff dimen- sion and measure-theoretical local entropy, we intro- pseudo-orbits. duce Bowen’s type entropy dimension DB (T,K) and lo- cal (lower) entropy dimension Dloc(T ) in entropy zero Piotr Oprocha µ AGH University of Science and Technology, Poland systems. When restrict to a compact subset K, we [email protected] prove the following variational principle: DB (T,K) = sup{Dloc(T ): µ ∈ M(X), µ(K) = 1}. µ Average shadowing properties generalize standard defini- tions of shadowing (e.g. shadowing property, limit shad- Decomposition problems in symbolic dynam- owing property, etc.) by controlling average error of trac- ing instead of its control in each iteration. Clearly, the ics definition of pseudo-orbit have to be modified accordingly. This modification enables application of average shadow- Uijin Jung ing in dynamical systems where we cannot control error Ajou University, Korea in each step, but we can ensure that average error is suf- [email protected] ficiently small. In particular, there are maps with aver- age shadowing property but without shadowing property (and vice-versa). A code is a homomorphism between shift dynamical sys- In this talk we will survey recent results on average shad- tems. Problems concerning decompositions of one code owing properties. We will present a few sufficient con- into a composition of several codes were considered in ditions that ensure average shadowing and comment on symbolic dynamics for coding purpose. Although a lot is relations between average shadowing and notions from known about the decompositions of factor codes between topological dynamics, like shadowing property, mixing, subshifts with equal entropy, not much is known for the specification, proximality and the like. case of unequal entropies. The first part of the talk will be devoted to the history and known results on the de- composition problems. For the remaining part, our recent developments will be presented. Especially we focus on Higher order Bohr problem and related topics the set of possible entropies of intermediate subshifts aris- ing from decomposing a given code. This is a joint work with Soonjo Hong and In-Je Lee. Song Shao University of Science and Technology of China, China [email protected] Overlap and strong coincidences on substitu- tion tilings In this talk we will discuss higher order Bohr problem and related questions. An old problem about Bohr sets says Jeong-Yup Lee that for any syndetic set S, is the set S − S a Bohr0 set? Kwandong University, Korea We study the higher order version of this problem: for [email protected] any d does the common difference of arithmetic progres- sion with length d + 1 appeared in a syndetic set coincide with a Nild Bohr0 set? We show that one side of this Pisot number is an algebraic integer whose all the other question holds: for any Nild Bohr0-set A, there exists a Galois conjugates are less than 1 in absolute. Substitu- syndetic set S such that A contains the common differ- tion sequences can be constructed replacing a letter by a ence of arithmetic progression with length d + 1 appeared word from a given finite letters. Incidence matrix is de- in S. And we show that other side of the problem can be fined by the numbers of letters coming from each letter. deduced from some result by Bergelson-Host-Kra if mod- If the largest eigenvalue of this matrix is a Pisot num- ulo a set with zero density. This is a joint work with W. ber, we say that the substitution is “Pisot”. We construct Huang and X.D. Ye. a tiling space collecting all the locally indistinguishable tiling from the given Pisot substitution tiling. It has been conjectured that the tiling space of a Pisot Negativity of Lyapunov exponents in generic substitution tiling whose substitution matrix is irre- random dynamical systems of complex poly- ducible has discrete dynamical spectrum. This is called nomials “Pisot substitution conjecture” which has not been solved for many years. Many notions of coincidences in substi- tution tilings have been introduced in the study of the Hiroki Sumi discrete dynamical spectrum of the tiling spaces. Osaka University, Japan Here we consider two well-known coincidences in the area, [email protected] namely overlap coincidence and strong coincidence, whose relations are not completely understood. We establish one direction of the implication from overlap coincidence In this talk, we consider random dynamical systems of to strong coincidence. complex polynomial maps on the Riemann sphere C.ˆ It 27 PRIMA 2013 Abstracts

is well-known that for each rational map f on Cˆ with τ} satisfy an analogue of the Weyl law. These results deg(f) ≥ 2, the Julia set J(f) is a non-empty perfect com- can be regarded as a generalization of a classical result of pact subset of Cˆ (thus J(f) contains uncountably many Selberg on the zeta function named after him. points), f : J(f) → J(f) is chaotic (at least in the sense of Devaney), and Local weak mixing in dynamical systems

ˆ 1 n dimH ({x ∈ C | lim infn→∞ n log kDf (x)k > 0}) > 0, Guo-Hua Zhang Fudan University, China where dimH denotes the Hausdorff dimension with re- [email protected] spect to the spherical distance on Cˆ and k · k denotes the norm of the derivative with respect to the spherical By a topological dynamical system we mean a compact metric on C.ˆ However, we show that for generic i.i.d. metric space equipped with a continuous self-map. Given random dynamical systems of complex polynomials, all a topological dynamical system, people are interested in of the following (1) and (2) holds. the study of complexity of the system (and its subsets). To understand the complexity of a subset, in this talk, I (1) For all points x ∈ Cˆ, the orbit of the Dirac measure shall discuss the local weak mixing behavior in the system based on several joint papers with Piotr Oprocha. δx at x under the dual of the transition operator of the system converges to a periodic cycle of proba- bility measures on C.ˆ

(2) For all but countably many points x ∈ Cˆ, for almost Special Session 14 Multiscale Analysis and Algorithms every sequence γ = (γ1, γ2, γ3, ··· ) of polynomials, the Lyapunov exponent along γ starting with x is negative. More precisely, there exists a constant A hybrid method for solving Laplace equa- c < 0, which depends only on the system, such that tions with Dirichlet data using local boundary for all but countably many points x ∈ Cˆ, for almost integral equations and random walks every sequence γ = (γ1, γ2, γ3, ··· ) of polynomials, Wei Cai χ(γ, x) := lim 1 log kD(γ ◦ · · · ◦ University of North Carolina at Charlotte, USA and n→∞ n n Shanghai Jiao Tong University, China γ1)(x)k exists and χ(γ, x) ≤ c. [email protected]

Note that each of (1) and (2) cannot hold in the usual In this talk, we will present a new approach for solv- iteration dynamics of a single rational map f with ing Laplace equations in general 3-D domains. The ap- deg(f) ≥ 2. Therefore the picture of the random proach is based on a local computation method for the complex dynamics is completely different from DtN mapping of the Laplace equation by combining a that of the usual complex dynamics. We remark deterministic (local) boundary integral equation method that even the chaos of the random system disappears in and the probabilistic Feynman-Kac formula of PDE so- C0 sense, the chaos of the system may remain in C1 sense, lutions. This hybridization produces a parallel algorithm and we have to consider the “gradation between the non- where the bulk of the computation has no need for data chaoticity and the chaoticity”. communications. Given the Dirichlet data of the solu- References tion on a domain boundary, a local boundary integral [1] H. Sumi, Random complex dynamics and semigroups equation (BIE) will be established over the boundary of of holomorphic maps, Proc. London. Math. Soc. (2011), a local region formed by a hemisphere superimposed on 102 (1), 50–112. the domain boundary. By using a homogeneous Dirich- [2] H. Sumi, Cooperation principle, stability and let Greenąŕs function for the whole sphere, the resulting bifurcation in random complex dynamics, preprint, BIE will involve only Dirichlet data (solution value) over http://arxiv.org/abs/1008.3995. the hemisphere surface, but over the patch of the domain boundary intersected by the hemisphere, both Dirichlet and Neumann data will be used. Then, firstly, the so- The semi-classical zeta function for contact lution value on the hemisphere surface is computed by Anosov flow the Feynman-Kac formula, which will be implemented by a Monte Carlo walk on spheres (WOS) algorithm. Sec- Masato Tsujii ondly, a boundary collocation method is applied to solve the integral equation on the aforementioned local patch Kyushu University, Japan of the domain boundary to yield the required Neumann [email protected] data there. As a result, a local method of finding the DtN mapping is obtained, which can be used to find all the Neumann data on the whole domain boundary in a We consider the semi-classical (or Gutzwiller-Voros) zeta ∞ parallel manner. Finally, the potential solution in the function for a C contact Anosov flow. This is defined whole space can be computed by an integral representa- by the formula tion using both the Dirichlet and Neumann data over the domain boundary.  ∞  X X e−s·m·|γ| (joint work with Changhao Yan and Xuan Zeng, micro- Zsc(s) = exp −  electronics, Fudan University) m · | det(Id − Dm)|1/2 γ∈Γ m=0 γ where Γ is the set of prime periodic orbits. (|γ| and Dγ Solving nonlinear eigenvalue problem in reso- denote the prime period and the transversal Jacobian of nant tunneling diodes γ ∈ Γ respectively. ) Investigating the spectrum of transfer operators associ- Weiguo Gao ated to the flow, we prove that the zeros of Zsc(s) are Fudan University, China contained in the region [email protected]

{s ∈ C | |<(s)| < τ or <(s) < −χ0 + τ} In this talk, we propose a deflation strategy for solving the nonlinear eigenvalue problem in resonant tunneling for arbitrarily small τ > 0 up to finitely many exceptions, diodes with multi-mode approximation. Numerical ex- where χ0 is the hyperbolicity exponent of the flow. Fur- periments show the efficiency of our method. This is a ther we show that the zeros in the strip {s ∈ C | |<(s)| < joint work with Shengyao Xu. 28 PRIMA 2013 Abstracts

Quantum, kinetic and hydrodynamic descrip- Multiscale modeling and computation of nano tions on spin transfer torque optical responses

Carlos J. García-Cervera Di Liu University of California, Santa Barbara, USA Michigan State University, USA [email protected] [email protected]

Magnetic storage devices rely on the fact that ferromag- We introduce a new framework for the multiphysical netic materials are typically bistable, and that it is pos- modeling and multiscale computation of nano-optical re- sible to switch between diïňĂerent states by applying a sponses. The semi-classical theory treats the evolution of magnetic ïňĄeld. The discovery of the Giant MagnetoRe- the electromagnetic field and the motion of the charged particles self-consistently by coupling Maxwell equations sistance eïňĂect has enabled the use of layered ferromag- with Quantum Mechanics. To overcome the numerical netic materials in magnetic devices, such as magnetic challenge of solving high dimensional many body Schr memories (MRAMs). Even in the absence of thermal odinger equations involved, we adopt the Time Depen- eïňĂects, there are limitations in the storage capacity of dent Current Density Functional Theory (TD-CDFT). In such devices due to the fact that as the size is decreased, the regime of linear responses, this leads to a linear sys- the magnitude of the switching ïňĄeld increases, due to tem of equations determining the electromagnetic eld as an increase in shape anisotropy. Given that magnetic well as the current and electron densities simultaneously. ïňĄelds have long range interactions, the density of such A self-consistent multiscale method is proposed to deal devices is limited. with the well separated space scales. Numerical exam- A new mechanism for magnetization reversal in multi- ples arepresented to illustrate the resonant condition. layers was proposed by Slonczweski and Berger. In this new mechanism, an electric current ïňĆows perpendicu- lar to the layers. The current is polarized in the ïňĄrst Convergence of force-based atomistic-to- layer, and the polarization travels with the current to the continuum methods second layer, where it interacts with the underlying mag- netization. Since currents are localized in each cell, long Jianfeng Lu range eïňĂects can be reduced. Duke University, USA In this talk we will discuss the connection between sev- [email protected] eral models for the description of the spin transfer torque at different physical scales. Specifically, we connect the quantum and kinetic descriptions with the help of the The numerical analysis of atomistic-to-continuum meth- Wigner transform, and the kinetic and diffusion models ods, in particular, for two or three dimensional systems, by a specific parabolic scaling. Numerical examples will is challenging and important for understanding multi- presented to illustrate the applicability and limit of the scale methods for solids. In this talk, we will discuss different models. some recent progress in stability and convergence analy- This is joint work with Jingrun Chen and Xu Yang at sis of force-based hybrid methods coupling together atom- UCSB. istic models and Cauchy-Born elasticity with smooth and sharp transitions. We will focus on the requirement of stability conditions due to interfaces. (Joint work with From discrete velocity model to moment Pingbing Ming) method Ghost forces for multiscale coupling methods Ruo Li in solids Peking Univerisity, China [email protected] Pingbing Ming Institute of Computational Mathematics, Chinese In the numerical approaches for Boltzmann equation, the discrete velocity model and the moment method are for- Academy of Sciences, China mally very different. The difference is so big that the [email protected] communities working on the two approaches are in certain competitive relation. In this talk, I will try to show the intrinsic connection between these two approaches. Pre- In this talk, I will report some recent progress on the cisely, the Grad type moment method with appropriate ghost force issue for multiscale coupling methods in solids. closure can be regarded as a discrete velocity model with Quantitative estimates for the influence of the ghost force some adaptivities in setup of the velocity points. The will be presented. Examples for high dimensional prob- globally hyperbolic regulazation of the moment method lems, dynamic problem and the crack problem will be plays an essential role in connecting both approaches to- discussed. gether. The growing string method for saddle point Atomic level interpretation of fracture crite- search ria Weiqing Ren Xiantao Li National University of Singapore and Institute Of High Pennsylvania State University, USA Performance Computing, Singapore [email protected] [email protected]

Fracture in brittle materials has been a subject of in- The string method was originally designed for finding tensive studies following the pioneering works of Griffith minimum energy paths between two minima on a poten- and Irwin. The propagation of a crack is often predicted tial (or free) energy landscape. It evolves a continuous based on the energy release rate or the stress intensity curve in the path space by the steepest descent dynam- factors. This talk will present our recent studies of crack propagation in the framework of bifurcation theory. This ics. In this talk, we discuss how the string method can be has been motivated by the fact that structural stability is modified to find saddle points of a potential energy using a well-defined concept in the theory of bifurcation. The a minima as the only input. Compared to the existing bifurcation study is based on molecular dynamics mod- algorithms, the new method has the advantage that the els, which provide a direct microscopic view of the critical computed saddle points are guaranteed to be directly con- events in the process of fracturing. More importantly, we nected to the minima. We will also discuss the accelera- will re-interpret several important concepts in the con- tion of the convergence using an inexact Newton method. ventional fracture mechanics. Applications to the diffusion of a cluster of atoms on a 29 PRIMA 2013 Abstracts

solid substrate and the wetting transition of a droplet on Wuhan University, China a rough surface will be presented. [email protected]

Multiscale methods for wave propagation Continuum mechanics quantities can be computed from problems molecular dynamics (MD) models based on the classi- cal Irving-Kirkwood (IK) formalism. Practical implemen- tations of IK formulas involve a spatial averaging using Olof Runborg a smooth kernel function. The obtained results usually KTH Royal Institute of Technology, Sweden need to be further processed to reduce the fluctuation, [email protected] e.g., by ensemble or time averaging. In this talk the IK formalism is extended to systematically incorporate both spatial and temporal averaging into the expression of con- Multiscale wave propagation problems are computation- tinuum quantities. We will present the results both in ally costly to solve by traditional techniques because the Lagrangian and Eulerian coordinates. smallest scales must be represented over a domain deter- mined by the largest scales of the problem. We consider numerical methods for multiscale wave propagation in the framework of the heterogeneous multiscale method. These methods couple simulations on macro- and mi- Special Session 15 croscales for problems with rapidly oscillating coefficients. Number Theory and Representation Theory The complexity is significantly lower than that of tradi- tional techniques with a computational cost that is es- On a classification of irreducible modulo p rep- sentially independent of the microscale. In this talk we show analysis of how the method works in the long time resentations of p-adic groups case, where the macroscale solution show dispersive be- havior, and how the method, although designed for wave Noriyuki Abe problems, can be beneficial for solving multiscale elliptic Hokkaido University, Japan problems. [email protected]

Modeling and simulation of three-component Barthel-Livné introduced the notion of modulo p super- flows on solid surface singular representations of GL2. It is generalized to split groups by Herzig and to connected reductive groups by Henniart and Vignéras. In this talk, we discuss about a Xiao-Ping Wang classification of irreducible modulo p representations in Hong Kong University of Science and Technology, Hong terms of supersingular representations. Kong, China This is joint work with G. Henniart, F. Herzig and M.-F. [email protected] Vignéras.

We propose a phase field model for the study of three- component immiscible flows with boundary. The model Parity sheaves on the affine Grassmannian is a generalization of the two-component model. We first and the Mirković–Vilonen conjecture study certain consistency conditions for the forms of the bulk free energy and surface energy. We then develop Pramod N. Achar an adaptive mesh refinement(AMR) technique to solve Louisiana State University, USA the system in order to improve the efficiency of the prob- [email protected] lem. Several numerical results are given, including the liquid lens spreads between two phases, the buoyancy- driven droplet through a fluid-fluid interface, spreading The geometric Satake equivalence gives a realization of of a compound droplet on a stationary substrate, and the category of representations of a split reductive alge- shear flows of a compound droplet on a channel. braic group over any field in terms of perverse sheaves on the affine Grassmannian for the dual group. In this set- ting, Mirković and Vilonen conjectured that the perverse A path way based mean field model for E. coli sheaves corresponding to Weyl modules should enjoy a chemotaxis parity-vanishing property, similar to that of `-adic inter- section cohomology complexes. This conjecture has now been proved (with a few exceptions in small characteris- Xu Yang tics) in joint work with Laura Rider. I will discuss the University of California, SantaBarbara, USA ingredients in the proof, along with potential applications [email protected] of our techniques to questions in modular representation theory. In this talk, we give a mathematical derivation of a pathway- based mean-field model for E. coli chemotaxis based on the moment closure in kinetic theory. The path- Rectifiers and the local Langlands correspon- way based model incorporate the most recent intracel- dence lular chemical dynamics. The derived moment system, under some assumptions, gets to the chemotaxis model Moshe Adrian proposed in [G. Si, T. Wu, Q. Quyang and Y. Tu, Phys. University of Utah, USA Rev. Lett., 109 (2012), 048101], especially an important [email protected] physical assumption made in which can be understood explicitly in this new moment system. We obtain the Keller-Segal limit by considering the moment system in Abstract: In this talk, I will recall the notion of a rec- the regime of long time and strong tumbling rate. Nu- tifier as in the work of Bushnell/Henniart in the local merical experiments are presented to show the agreement Langlands correpsondence for GL(n). I will then propose of the moment system with (individual based) signaling a definition for rectifier for general unramified groups G. pathway- based E. coli chemotaxis simulator ([L. Jiang, I will describe rectifiers in this setting, and show that our Q. Ouyang and Y. Tu, PLoS Comput. Biol., 6 (2010), definition agrees with Bushnell/Henniart’s in the depth e1000735]). zero case. This is joint work with David Roe.

Generalized Irving-Kirkwood formula for the Uniform in p estimates for orbital integrals calculation of continuum quantities in molec- ular dynamics models Julia Gordon University of British Columbia, Canada Zhijian Yang [email protected] 30 PRIMA 2013 Abstracts

This talk is about a method, based on model theory, that Kong, China can be used to get some uniform in p estimates for inte- [email protected] grals over p-adic fields in the cases when it is hard to see directly how such integrals behave for different places p. In the 1970’s Thurston conjectured that every hyperbolic One example of such a situation is orbital integrals on manifold admits a finite cover with non-zero first Betti p-adic groups. Let G be a reductive p-adic group. It was number. In the arithmetic case, this property is related proved by Harish-Chandra that the orbital integrals, nor- to the congruence subgroup problem for SO(n, 1). For malized by the discriminant, are bounded (for a fixed test arbitrary dimension n there are two types of arithmetic function). However, it is not easy to see how this bound hyperbolic manifolds, which arise from either quadratic behaves if we let the p-adic field vary (for example, if the forms over totally real number fields, or skew-hermitian group G is defined over a number field F , and we consider forms over certain quaternion algebras. In 1976 Millson proved Thurston’s conjecture for the first type of arith- the family of groups Gv = G(Fv), as v runs over the set of metic hyperbolic manifolds using geometric methods. For finite places of F ), and how it varies for a family of test the second type of manifolds, similar results were estab- functions. Using a method based on model theory and lished in the 1990’s . motivic integration, we prove that the bound on orbital In this talk we will briefly review this history, and discuss integrals can be taken to be a fixed power (depending an improved version of an old construction which leads to on G) of the cardinality of the residue field. This state- some modest related results. We will also discuss some ment has an application to the recent work of S.-W. Shin related open problems. and N. Templier on counting zeroes of L-functions. This project is joint work with R. Cluckers and I. Halupczok. On the elliptic part of the trace formula for Spf (2n) On the center of Lie algebras Wen-Wei Li Masoud Kamgarpour Chinese Academy of Sciences, China University of Queensland, Australia [email protected] [email protected] In this talk, I will introduce the stabilization of Arthur- I will discuss the center of the universal enveloping alge- Selberg trace formula for reductive groups and its appli- bra of four different kinds of Lie algebras: cations, then proceed to its generalization to the meta- (1) Harish-Chandra’s description of the centre of a simple plectic twofold cover Spf(2n) of Sp(2n). Based on the algebra g. recent progress on geometric transfer and the invariant (2) Duflo-Kirillov’s description of the centre of an arbi- trace formula for metaplectic group, I will explain the trary finite dimensional algebra. stabilization of the elliptic terms in the trace formula of (3) Center of the algebra of jets g[[t]] and g((t)). Spf(2n). (4) Feigin-Frenkel description of center of the vertex Lie algebra associated to g, via Langlands dual group. I will then define the notion of quasi-Verma modules for Endoscopic classification of automorphic rep- the abovementioned vertex algebra, and stipulate how the resentations of classical groups Feigin-Frenkel Center should act on these modules. Chung Pang Mok A homological study of Green polynomials McMaster University, Canada [email protected]

Syu Kato Kyoto University, Japan We will give an exposition of the recent works on en- doscopic classification of automorphic representations for [email protected] classical groups. Some recent arithmetic applications of the endoscopic classification will be discussed. We first explain how to categorify the Green/Kostka poly- nomials of reductive groups. Then, we discuss how they Twisted spectral transfer for real groups are related to the relevant orthogonality relation of some modules of affine Hecke algebras and p-adic groups, and their consequences. Paul Mezo Carleton University, Canada [email protected] On the structure of Selmer groups Kottwitz and Shelstad generalized the framework of en- Masato Kurihara doscopy to include twisting by group automorphisms or Keio University, Japan central characters. This generalization contained conjec- [email protected] tural identities between orbital integrals, constituting a transfer from functions on a group to functions on one of its endoscopic groups. This geometric transfer has re- As a refinement of Iwasawa theory, which gives a re- cently been proven by Shelstad. Dual to geometric trans- fined relationship than the usual main conjecture be- fer is spectral transfer, which is a collection identities be- tween Selmer groups and p-adic L-functions, I describe tween characters of L-packets of a group and one of its the structure as an abelian group of the classical Selmer endoscopic groups. We show how some work of Bouaziz, group of an elliptic curve, using modular symbols. I also Duflo and Shelstad may be adapted to the twisted en- talk on Euler systems and Kolyvagin systems of Gauss doscopy of real reductive groups in order to achieve spec- sum type, which give nontrivial elements in Galois coho- tral transfer. mology groups. Zelevinsky involution and `-adic cohomology On the first Betti number of hyperbolic arith- of Rapoport-Zink spaces metic manifolds Yoichi Mieda Jianshu Li Kyoto University, Japan Hong Kong University of Science and Technology, Hong [email protected] 31 PRIMA 2013 Abstracts

Rapoport-Zink spaces are certain moduli spaces of quasi- of its proof. This is a report of a joint work with Chen-Bo isogenies of p-divisible groups with additional structures, Zhu. and can be regarded as local analogues of Shimura va- rieties. It is conjectured that the `-adic cohomology of Rapoport-Zink spaces can be precisely decribed by means L-functions and theta correspondence of the local Langlands correspondence for general reduc- tive groups. In this talk, I will give results on relationship between the `-adic cohomology of Rapoport-Zink spaces Shunsuke Yamana and the Zelevinsky involution. I will also explain some Kyushu University, Japan applications to compute the `-adic cohomology. [email protected]

Geometrizing characters of tori The doubling method of Piatetski-Shapiro and Rallis ap- plies in the local situation to define local factors of rep- resentations of classical groups. On the one hand, the David Roe L-factor is defined as a g.c.d. of the local zeta integrals University of Calgary, Canada for all good sections. On the other hand, it is defined [email protected] from the gamma factor by using the Langlands classifica- tion. In this talk I develop a theory of the zeta integral and prove that the two candidates of the L-factor agree. The passage from functions to sheaves has proven a valu- Applications include a characterization of nonvanishing of able tool in the geometric Langlands program. In this global theta liftings in terms of the analytic properties of talk I’ll describe a “geometric avatar” for the group of the complete L-functions and the occurrence in the local characters of T (K), where T is an algebraic torus over a theta correspondence. local field K. I will then give some potential applications to the classical Langlands correspondence. This is joint work with Clifton Cunningham.

Twisted Bhargava cubes Special Session 16 Operator Algebras and Harmonic Analysis Gordan Savin Uncertainty principles for infinite abelian University of Utah, USA groups [email protected] Liming Ge, Jingsong Wu, Wenming Wu & Wei Yuan Let G be a reductive group and P = MN a maximal University of New Hampshire, USA parabolic subgroup. The group M acts, by conjugation, [email protected] on N/[N,N]. It is well known that, over an algebraically closed field, the group M acts transitively on a Zariski open set. However, over a general field, the structure of In this paper, we shall revisit uncertainty principle on orbits may be quite non-trivial. A description my involve finite abelian groups and determine the functions that unexpected invariants. A notable example is when G is give Tao’s lower bound in above inequality. Our main focus then moves to the additive integer group . Its a split, simply connected group of type D4, and P is the Z maximal parabolic corresponding to the branching point dual is identified with R/Z (= [0, 1)). Since there is no of the Dynkin diagram. The space N/[N,N] is also known countably additive invariant (probability) measure on Z, as the Bhargava cube, and it was the starting point of his we shall use von Neumann’s invariant mean which is a investigations of prehomogeneous spaces. We consider a finitely additive for any disjoint subsets. With respect to a given mean on and Lebesgue measure on / , version of this problem for the triality D4. This is a joint Z R Z we show that there is a subset S of Z with mean 1 so work with Wee Teck Gan. that any square summable functions f supported on S have “full” supported Fourier transform in the sense that Stability and sign changes in p-adic harmonic the closure of supp(f) is equal to [0, 1]. Symmetrical, we analysis show that there is subset G of Z with mean 0 so that, for any x ∈ [0, 1] and any  > 0, all functions supported on ˆ Loren Spice G together with those f with supp(f) ⊂ [x, x + ] span 2 Texas Christian University, USA a dense subset of l (Z), the Hilbert space of all square [email protected] summable functions.

Reeder has described a conjectural candidate for the Operator theoretic analogue for Lehmer’s partition of certain supercuspidal representations con- problem structed by Yu (the so called toral, unramified supercusp- idals) into L-packets, and verified that it satisfies most of Kunyu Guo the necessary properties. However, the problem of stabil- Fudan Unversity, China ity of the appropriate character sums remained outstand- [email protected] ing. In this talk, I will discuss joint work with DeBacker that shows the necessary stability. A key ingredient is the study of a sign associated to combinatorial data in- In this talk, we will establish a fascinating connection volving Galois orbits on a root system, which we compute between Lehmer’s problem and operator theory. This is unconditionally in the unramified case. a joint work with Jiayang Yu.

Conservation relations for local theta corre- Convolution algebras associated with locally spondence compact quantum groups Binyong Sun Zhiguo Hu Academy of Mathematics and Systems Science, CAS, China University of Windsor, Canada [email protected] [email protected]

I will introduce Kudla-Rallis conjecture on first occur- We consider the convolution algebras L1(G) and rences of local theta correspondence, and explain the idea T (L2(G)) associated with a locally compact quantum 32 PRIMA 2013 Abstracts

group G, where T (L2(G)) is the space of trace class op- there is an automorphism α with the Rokhlin property erators on L2(G) with the convolution induced by the which has that given K-theoretical data. right fundamental unitary of G. We obtain a natural iso- morphism between the completely bounded right multi- plier algebras of L1(G) and T (L2(G)), and characterize Spectral gap actions and invariant states the regularity of the quantum group G in terms of the convolution on T (L2(G)). We show that T (L2(G)) is Chi-Keung Ng strongly Arens irregular in the sense of Dales and Lau Nankai University, China if and only if G is finite. Some commutation relations [email protected] of completely bounded multipliers of L1(G) will also be discussed. This is joint work with Matthias Neufang and Zhong-Jin Ruan. We define spectral gap actions of discrete groups on von Neumann algebras and study their relations with invari- ant states. We will show that a finitely generated ICC Complex geometry and similarity of Cowen- group Γ is inner amenable if and only if there exist more Douglas operators than one inner invariant states on the group von Neu- mann algebra L(Γ). Moreover, a countable discrete group Γ has property (T ) if and only if for any action α of Γ on Chunlan Jiang a von Neumann algebra N, every α-invariant state on N Hebei Normal University, China is a weak-∗-limit of a net of normal α-invariant states. [email protected] Quantum correlations and Tsirelson’s prob- In this talk, we discuss the similarity invariant of the ge- lem ometry operator induced by the holomorphic bundle. We give a complete similarity invariant of this kind of geom- etry operator by using K-group and curvature. Narutaka Ozawa Kyoto University, Japan [email protected] Minimum phase operators and the Polya- Schur problem The EPR paradox tells us quantum theory is incompat- ible with classic realistic theory. Indeed, Bell has shown Michael P. Lamoureux that quantum correlations of independent bipartite sys- University of Calgary, Canada tems have more possibility than the classical correlations. [email protected] To study what the possibilities are, Tsirelson has intro- duced the set of quantum correlation matrices, but de- pending on the interpretation of independence, there are We set a mathematical framework for understanding min- two plausible definitions of it. Tsirelson’s problem asks imum phase preserving physical processes and obtain the whether these definitions are equivalent. It turned out following. The natural analytic setting for these time- that this problem in quantum information theory is in limited signals is Hilbert-Hardy space. The minimum fact equivalent to Connes’s embedding conjecture, one of phase (or impulsive) signals correspond to the outer func- the most important open problems in theory of operator tions in Hardy space. The minimum phase preserving algebras. I will talk some recent progress on Tsirelson’s processes correspond to linear operators which preserve problem. the set of shifted outer functions. Our main result shows these linear operators on Hardy space are completely characterized as a combination of Ergodic theory over locally compact quantum a multiplication and a composition operator involving groups holomorphic functions of a specific form. The proof of this result makes essential use of Hadamard’s Theorem Volker Runde and the Weierstrass product representation. Remarkably, University of Alberta, Canada this result also extends to provide constructive solutions [email protected] to the Polya-Schur problem of finding linear operators that preserve the zero-sets of families of complex poly- nomials. Returning to the physical problem, these pro- We develop the elements of an ergodic theory over lo- cesses thus consist of a stationary filtering combined with a frequency-dependent Q-attenuation. cally compact quantum (semi)groups and extend results by Zsidó et al.. This is joint work with Ami Viselter. Joint with Peter. C. Gibson and Gary F. Margrave

∗ Extending derivations to dual Banach alge- Kishimoto’s conjugacy theorems in simple C - bras algebras of tracial rank one Ebrahim Samei Huaxin Lin University of Saskatchewan, Canada University of Oregon, USA [email protected] [email protected] If D : A → X is a derivation from a Banach algebra to Let A be a unital separable simple amenable C*-algebra a contractive, Banach A-bimodule, then one can equip with finite tracial rank which satisfies the UCT. Suppose X∗∗ with an A∗∗-bimodule structure, such that the sec- ond transpose D∗∗ : A∗∗ → X∗∗ is again a derivation. α and β are two automorphisms with the Rokhlin prop- ∗∗ erty. We show that α and β are strongly co-cycle con- I present an analogous extension result, where A is re- jugate and uniformly approximately conjugate, i.e., there placed by the enveloping dual Banach algebra F(A) (as in- ∗∗ exists a sequence of unitaries {un} ⊂ A and a sequence of troduced by V. Runde), and X by an appropriate kind strong asymptotically inner automorphisms σn such that of universal, enveloping, normal dual bimodule of X. Our approach is motivated by earlier results of F. Gourdeau. −1 I apply these constructions to obtain some new character- α = Ad un ◦ σn ◦ β ◦ β and lim kun − 1k = 0, n n→∞ izations of Connes-amenability of F(A). In particular, we show that F(A) is Connes-amenablity if and only if A ad- provided that they induce the same K-theoretical data. mits a so-called WAP-virtual diagonal. Also, in the case We also show that converse also holds. We also give a where A = L1(G), we show by modifying arguments of K-description as exactly when α and β are co-cycle con- Runde that existence of a WAP-virtual diagonal is equiv- jugate. We also show that given a K-theoretical data, alent to the existence of a virtual diagonal in the usual 33 PRIMA 2013 Abstracts

sense. Our approach does not involve invariant means for University of Manitoba, Canada G. [email protected] p-variations of Fourier algebras Let G be a locally compact group and ω a continu- ous weight on G. It is well-known that the weighted 1 Nico Spronk group algebra L (G, ω) is amenable as a Banach algebra University of Waterloo, Canada if and only if G is an amenable group and the function [email protected] Ω(t) = ω(t)ω(t−1) is bounded on G. We show that, for an abelian locally compact group G, L1(G, ω) is weakly amenable if and only if there is no nontrivial continuous Let G be a compact group and A(G) its Fourier algebra. group homomorphism φ: G → ( , +) such that About a half decade ago, an invesitgation of B. Forrest, C E. Samei and the speaker brought up a curious Banach |φ(t)| algebra A∆(G) which plays a role relative to operator sup < ∞. amenability problems for A(G), in the same manner as a t∈G Ω(t) certain algebra Aγ (G) of B. Johnson plays to amenabil- ity problems. The algebra Aγ (G) may be understood In other words, Ω(t) shall grow slower then any φ in order as a type of “Beurling-Fourier algebra" on G, in a man- L1(G, ω) to be weakly amenable. ner which has been recently invesigated by H.H. Lee, E. Samei, J. Ludwig, L. Turowska and the speaker, in vari- We will also consider the weak amenability of L1(G, ω) ous articles. and its center ZL1(G, ω) for non-commutative locally I will present a context in which we may understand compact groups G, discussing some special cases. In gen- A∆(G) as the case p = 2 in a class of Banach algebras eral, how to characterize the weak amenability of a non- Ap(G) (1 ≤ p ≤ ∞). Here A1(G) = A(G), but the rest of commutative L1(G, ω) and how to characterize the weak the algebras may be understood via interpolation. These amenability of its center algebra are still open problems. algebras do not exhibit the same functorial properties as Fourier algebras, and hence allow us to exhibit some un- usual Banach algebras on tori. This talk represents joint work with H.H. Lee and E. Special Session 17 Samei. Optimization Zero products and norm preserving orthog- Regularized interior proximal alternating di- onally additive homogeneous polynomials on rections method C*-algebras Felipe Alvarez Ngai-Ching Wong Universidad de Chile, Chile National Sun Yat-sen University, Taiwan [email protected] [email protected] We consider convex constrained optimization problems Let P : A → B be a bounded orthogonally additive with a special separable structure. We propose a class of and zero product preserving n-homogeneous polynomial alternating directions methods (ADM) where their sub- between C*-algebras. We show that, in the commuta- problems are regularized with a general interior proximal tive case that A = C0(X) and B = C0(Y ), there exist metric which covers the double regularization proposed by a bounded continuous function h in C(Y ) and a map Silva and Eckstein. Under standard assumptions, global n convergence of the primal-dual sequences produced by the ϕ : Y → X such that P f = h · (f ◦ ϕ) . In the general algorithm is established. case, we show that there is a central invertible multiplier h of B and a surjective Jordan homomorphism J : A → B such that P a = hJ(a)n, provided that P (A) ⊇ B+. Sim- Linear conic programming and interior-point ilar Banach-Stone type theorems also hold for orthogo- algorithms nally additive n-homogeneous polynomials which are n- isometries. Using these results, we provide the full struc- ture of orthogonally additive and orthogonally multiplica- Yanqin Bai tive holomorphic functions on commutative C*-algebras. Shanghai University, China This is a joint work with Qingying Bu (Univ. of Missis- [email protected] sippi) and Ming-Hsiu Hsu (Nat’l Sun Yat-sen Univ.) Linear conic programming extends the popularly used lin- Recent development of analysis on noncom- ear programming models from linearity to non-linearity mutative tori as well as from convexity to non-convexity in polynomial- time computations. Linear conic programming problems are linear programming models with the additional con- Quanhua Xu straint of products of nonlinear cones which include two Wuhan University, China and University of Franche- classes of important cones. One class is symmetric cone Comté, France which leads to symmetric cone optimization problems such as linear, semideąěnite and second-order cone pro- gramming problems in which the cone constraints are self- Noncommutative tori are fundamental examples in oper- dual and homogeneous. These symmetric conic program- ator algebras and noncommutative geometry. This talk ming can be solved eąÀciently using polynomial-time will present a survey on the recent development of anal- interior-point methods. Another class is nonsymmetric ysis on noncommutative tori. The results presented will cone optimization problems such as copositive cone pro- include those on harmonic analysis and Sobolev embed- gramming problems and the cone programming of non- ding inequalities on quantum tori. This talk is based on negative quadratic function over a set. For these conic joint works with Zeqian Chen, Xiao Xiong and Zhi Yin. programming the cone constraints are not self-dual and in particular requires special purpose algorithm. The pro- pose of this talk is to introduce a very rich formulation of Amenability properties of weighted group al- linear conic programming and present the general model, gebras the conjugate duality theory, path-following interior point approaches and illustrative applications of linear conic Yong Zhang programming. 34 PRIMA 2013 Abstracts

Design of robust truss structures for mini- (a.s.) smoothing sample average approximation (SSAA) mum weight using the sequential convex ap- method to minimize the expected residual function. We proximation method show that the residual minimization problem and its SSAA problems have minimizers in a compact set and any cluster point of minimizers and stationary points of Alfredo Canelas the SSAA problems is a minimizer and a stationary point Universidad de la República, Uruguay of the expected residual minimization problem (a.s.). Our acanelas@fing.edu.uy examples come from applications involving traffic flow Miguel Carrasco problems. We show that the conditions we impose are Universidad de los Andes, Chile satisfied and that the solutions, efficiently generated by [email protected] the SSAA procedure, have desirable properties. Julio Lopez Joint work with Roger Wets and Yangfan Zhang. Universidad Diego Portales, Chile [email protected] Stability of two-stage stochastic programs with quadratic continuous recourse Trusses are mechanical structures in Rd, where d is 2 for planar trusses or 3 for three-dimensional ones. They con- Zhiping Chen sist of an ensemble of N nodes joint by m ≥ 2 bars which Xi’an Jiaotong University are made of a linear elastic, isotropic and homogeneous [email protected] material. Long bars overlapping small ones are not al- Youpan Han lowed, and therefore m ≤ N(N − 1)/2 for a mesh full Xi’an Polytechnic University of bars. Trusses are designed to support some external nodal loads taking into account the properties of the bar material. We assume that there exists a set of primary We consider the stability of the two-stage quadratic external loads, applied only in the nodes of the truss, and stochastic programming problem with quadratic contin- that there exists a set of secondary nodal ones that are uous recourse when the underlying probability distribu- uncertain in size and direction, which can be viewed as tion is perturbed. For the case that all the coefficients a perturbation of the main loads. Our main objective is in the objective function and the right-hand side vector to minimize the total amount of material or weight, with in second-stage constraints are random, we firstly show the purpose of finding the most economic structure, that the locally Lipschtiz continuity of the optimal value func- is robust under load perturbations. tion of the recourse problem; then under suitable prob- ability metric, we derive the Lipschitz continuity of the We formulate a model in order to include the mechanical equilibrium constraint and stress constraints, as well as expected optimal value function with respect to the first- bounds on displacements, considering also stability con- stage variable and the probability distribution; and fur- straints under perturbation of the main load. More pre- thermore, we establish the qualitative and quantitative cisely, we will study the properties of the following non– stability results of the optimal value function and the convex semi-infinite mathematical programming problem optimal solution set with respect to the Fortet-Mourier probability metric. For the more complex situation that m the recourse costs, the recourse matrix, the technology X matrix and the right-hand side vector in the second-stage (Pw) min xi x≥0 problem are all random, and that the second-stage ob- i=1 jective function might be non-convex, we obtain the uni- |uj (ξ, x)| ≤ u¯j j ∈ J ⊆ {1, . . . , n}, formly boundedness and locally Lipschtiz continuity of the second-stage feasible solution set when it is regu- |σi(ξ, x)| ≤ σ¯i i ∈ I ⊆ {1, . . . , m}, lar and bounded; we also establish the locally Lipschtiz ξ ∈ E, continuity of the corresponding optimal value function; then we show the Lipschitz continuity of the expected where x represents the volume of each bar, u is the vector value function of the second-stage problem with respect i to both the first-stage variables and the probability met- of displacements, and σi the stress of the i-th bar. The set E ⊆ Rn corresponds to the set of secondary loads, ric involved in the second-stage problem; utilizing these and we implicitly assume the mechanical equilibrium con- results, we finally derive the qualitative and quantita- straint K(x)u(ξ, x) = f + ξ. To address the infinite num- tive stability results of the optimal value function and the optimal solution set of two-stage quadratic stochastic ber of constraints we reformulate (Pw) as a non–convex programs with respect to the Fortet-Mourier probability bilevel mathematical program. The main idea is to solve metric. this problem assuming that the set E of secondary loads takes the form of a particular ellipsoid, similar to the ap- proached by Ben-Tal and Nemirovski . Based on the work Existence of minimizers on drops of Beck et al., we have obtained encouraging preliminary numerical results for this alternative, which approach con- Rafael Correa sists on approximating some non–convex constraints and Universidad de Chile, Chile solving a sequence of parametric conic problems. [email protected]

Expected residual minimization for stochastic For a boundedly generated drop [a, E] (property which variational inequalities holds, for instance, whenever E is bounded), where a belongs to a real Banach space X and E ⊂ X is a Xiaojun Chen nonempty convex set, we show that for every lower semi- The Hong Kong Polytechnic University, Hong Kong, continuous function h : X −→ R ∪ {+∞} that satisfies China inf h(x) supδ > 0x ∈ E + δBx > h(a)(BX being the uni- [email protected] tary open ball in X), there exists x ∈ [a, E] such that h(a) ≥ h(x) and x is a strict minimizer of h on the drop This talk discusses a variety of computational approaches [x, E]. for stochastic variational inequalities and presents a new expected residual minimization formulation for a class of stochastic variational inequalities by using the gap The robust stability of every equilibrium in function. The objective function of the expected resid- economic models of exchange ual minimization problem is nonnegative and Lipschitz continuous. Moreover, it is convex for some stochas- tic linear variational inequalities, which helps us guar- Alejandro Jofre antee the existence of a solution and convergence of ap- University de Chile, Chile proximation methods. We propose a globally convergent [email protected] 35 PRIMA 2013 Abstracts

In an economic model of exchange of goods, the structure We introduce a new class of forward-backward algorithms can be specified by utility functions. Under utility condi- for structured convex minimization problems in Hilbert tions identified here even more broadly than usual, except spaces. Our approach relies on the time discretization of for concavity in place of quasi-concavity, every equilib- a second-order differential system with two potentials and rium will simultaneously be stable with respect to shifts Hessian-driven damping. This system can be equivalently in the associated holdings of the agents and with respect written as a first order-system in time and space, each of to the dynamic Walrasian tatonnement process of price the two constitutive equations involving only one of the adjustment. This fact, seemingly contrary to widespread two potentials. Its time dicretization naturally leads to belief, is revealed by paying close attention not only to the introduction of forward-backward splitting algorithms prices but also to the proximal status of initial holdings. with inertial features. Using a Liapunov analysis, we The conditions on the concave utility functions are stan- show the convergence of the algorithm under conditions dard for stability investigations, in that they invoke prop- improving the classical step size limitation. Then, we erties coming from second derivatives, but significantly specialize our results to gradient-projection algorithms, relaxed in not forcing all goods to be held only in pos- and give some illustration to sparse signal recovery and itive amounts. Recent advances in variational analysis feasibility problems. provide the support needed for working in that context. The stability results also point the way toward further developments in which an equilibrium might evolve in Second-order analysis in conic programming: response to exogenous inputs to the agents’ holdings, or Applications to stability extractions. Héctor Ramírez C. Solving mathematical programs with equilib- Universidad de Chile rium constraints as constrained equations [email protected]

Gui-Hua Lin In this talk we review some recent results obtained for Shanghai University, China conic programs from the application of a second-order [email protected] generalized differential approach. It is used to calculate Lei Guo appropriate derivatives and coderivatives of the corre- sponding solution maps. These developments allow us Dalian University of Technology, China to obtain verifiable conditions for the strong regularity, [email protected] the Aubin property and isolated calmness of the consid- Jane J. Ye ered solution maps. The main results obtained in the University of Victoria, Canada general conic programming setting are specified for and [email protected] illustrated by the second-order cone programming

This paper aims at developing effective numerical meth- [1] J. F. Bonnans and H. Ramírez C., Perturbation anal- ods for solving mathematical programs with equilibrium ysis of second-order cone programming problems. Math. constraints. Due to the complementarity constraints, the Program., 104 (2005), pp. 205-227. usual constraint qualifications such as the Mangasarian- [2] J. V. Outrata and H. Ramírez C., On the Aubin prop- Fromovitz constraint qualification do not hold at any fea- erty of critical points to perturbed second-order cone pro- sible point and there are various stationarity concepts grams, SIAM J. Optim., 21 (2011), pp. 798-823. such as Clarke/Mordukhovich/strong stationarity sug- [3] B. Mordukhovich, J. V. Outrata and H. Ramírez C., gested in the literature. In this paper, we reformulate Second-order variational analysis in conic programming these stationarity conditions as smooth equations with with application to optimality and stability. Submitted box constraints. We then present a modified Levenberg- (2013). Marquardt method for solving these constrained equa- tions. We show that, under some weak local error bound conditions, the method is locally and superlinearly con- Facially exposed cones are not always nice vergent. Furthermore, we give some sufficient conditions for local error bounds to hold and show that these condi- tions are not very stringent by a number of examples. Vera Roshchina University of Ballarat, Australia [email protected] A feasible direction algorithm for nonlinear second-order cone optimization problems We show that Gabor Pataki’s conjecture that facially ex- posed cones are nice is true in three-dimensional case, but does not hold for higher dimensions by presenting a Julio López four-dimensional counterexample. We also discuss impli- Universidad Diego Portales, Chile cations of this result and state some open problems. [email protected] Asymptotic convergence analysis for distri- In this work, we propose a feasible direction algorithm butional robust optimization and equilibrium for solving nonlinear convex second-order cone programs. This kind of problems consists of minimizing a con- problems vex function over the Cartesian product of second-order cones. Our approach computes feasible descend directions by using the same formulation as in FDIPA proposed by Hailin Sun Herskovitz [J. Optim. Theory Appl., vol. 99 (1998), pp. Harbin Institute of Technology, China 53–58]. Under suitable assumptions, some results prelim- [email protected] inaries of convergence are obtained. Finally, to show how Huifu Xu our algorithm works in practice, computational results City University of London, UK applied to support vector machines under uncertainty is [email protected] presented. In this paper, we study distributional robust optimization A dynamical approach to an inertial forward- approaches for a one stage stochastic minimization prob- backward algorithm for convex minimization lem, where the true distribution of the underlying ran- dom variables is unknown but it is possible to construct a set of probability distributions which contains the true Juan Peypouquet distribution and optimal decision is taken on the basis of Universidad Técnica Federico Santa María, Chile worst possible distribution from that set. We consider the [email protected] case when the distributional set is constructed through 36 PRIMA 2013 Abstracts

samples and investigate asymptotic convergence of opti- Kyoto University, Japan mal values and optimal solutions as sample size increases. [email protected] The analysis provides a unified framework for asymptotic convergence of some data-driven problems and extends the classical asymptotic convergence analysis in stochas- Consider the d-dimensional Brownian motion in a random tic programming. The discussion is extended to a stochas- potential defined by attaching a non-negative and poly- tic Nash equilibrium problem where each player takes a nomially decaying potential around Poisson points. We robust action on the basis of their subjective expected introduce a repulsive interaction between the Brownian objective value. path and the Poisson points by weighting the measure by the Feynman-Kac functional. Under the (annealed) weighted measure, it is shown that the Brownian motion tends to localize around the origin and the properly scaled Special Session 18 process converges in law to a Ornstein-Uhlenbeck process. Probability Martingale problem under non-linear expec- The motion of a tagged particle in the simple tations exclusion process Xin Guo Dayue Chen & Peng Chen University of California, Berkeley, USA Peking University, China [email protected] [email protected]

The simple exclusion process is an interacting particle We consider the martingale problem under the framework system. There is no birth or death of particles. Each of nonlinear expectations, analogous to that in a proba- particle perform an independent random walk. The walk bility space in the seminal paper of Stroock and Varadhan is suspended when a particle jumps to the site of another (1969). particle. Therefore a tagged particle behaviors very much We first establish an appropriate comparison theorem and like a random walk with a fixed rate of slow down. In the existence result for the associated state-dependent this talk we shall review some limit theorems of a tagged fully non-linear parabolic PDEs. We then construct the particle in the simple exclusion and report our progress conditional expectation from the viscosity solution of the in this direction. PDEs, and solve the existence of martingale problems. Under this non-linear expectation space, we further de- velop the stochastic integral and the Itô’s type formula, Multivariate normal approximation by Stein’s which are consistent with Peng’s G-framework. As an application, we introduce the notion of weak solution of method: the concentration inequality ap- SDE under the non-linear expectation. proach Scaling limits of interacting particle systems Louis H. Y. Chen in high dimensions. National University of Singapore, Singapore [email protected] Mark Holmes University of Auckland, New Zealand In this talk we will describe Stein’s method for normal [email protected] approximation and explain the role of concentration in- equalities in proving Kolmogorov bounds in one dimen- sion. We will then discuss multivariate extensions of both A number of (interacting) particle systems at criticality, the normal approximation and the concentration inequal- ities. The multivariate concentration inequalities are then such as the voter model, the contact process, oriented applied to multivariate normal approximation for inde- percolation, and lattice trees, have been conjectured or pendent summands as well as for locally dependent sum- proved to behave like the critial branching random walk, mands. This talk is based on joint work with Xiao Fang. when the dimension is high enough so that the interaction is weak. One version of this statement is that appropri- ately rescaled versions of these models converge to super- Brownian motion. We will discuss what is known and not Stable processes with drift known about these models in the context of convergence to super-Brownian motion. Zhen-Qing Chen University of Washington, USA [email protected] Parabolic Littlewood-Paley inequality for φ(−∆)-type operators and applications to Suppose that d ≥ 1 and α ∈ (1, 2). Let Y be a rota- stochastic integro-differential equations tionally symmetric α-stable process on Rd and b an Rd- d valued measurable function on R belonging to a certain Panki Kim Kato class of Y . We show that dXt = dYt + b(Xt)dt with Seoul National University, Korea d X0 = x has a unique weak solution for every x ∈ R . Let [email protected] Lb = −(−∆)α/2 + b · ∇, which is the infinitesimal genera- b ∞ d tor of X . Denote by Cc (R ) the space of smooth func- In this talk we introduce a parabolic version of the tions on Rd with compact support. We further show that Littlewood-Paley inequality for the operators of the type b ∞ d the martingale problem for (L ,Cc (R )) has a unique φ(−∆), where φ is a Bernstein function. As an applica- solution for each initial value x ∈ Rd. Moreover, sharp tion, we construct an Lp-theory for the stochastic integro- two-sided estimates for the transition density function of differential equations of the type du = (−φ(−∆)u+f) dt+ X can be obtained as well as that of its subprocess killed g dWt. This is a joint work with Ildoo Kim and Kyeong- upon leaving a C2-smooth open set. This talk is based Hun Kim. on a joint work with Longmin Wang. Quenched invariance principles for random Brownian motion in a heavy tailed Poissonian walks and random divergence forms in ran- potential dom media with a boundary

Ryoki Fukushima Takashi Kumagai 37 PRIMA 2013 Abstracts

Kyoto University, Japan [11] J.J. McDonald, R. Nabben, M. Neu- [email protected] mann,H. Schneider, M.J. Tsatsomeros Inverse tridiagonal Z-matrices. Linear and Multilinear Algebra 45 (1998), 75–97. We will consider the following two models and establish quenched invariance principles; [12] R. Nabben, On Green’s matrices of trees. SIAM 1. Simple random walks on the infinite clusters for super- Journal Matrix Analysis and its Applications, 22, no. 4, critical percolations on half and quarter planes in d- (2001), 1014–1026. dimensional Euclidean spaces. 2. Uniform elliptic divergence forms with random sta- From Stein’s method to self-normalized mod- tionary coefficients on cones in Euclidean spaces. erate deviations Note that because of the lack of translation invariance we cannot apply the method of the ’corrector’. ÂăIn- stead we make full use of the heat kernel estimates and Qi-Man Shao Dirichlet form techniques to resolve the problem. This is The Chinese University of Hong Kong, Hong Kong, China a joint work with Z.Q. Chen (Seattle) and D.A. Croydon [email protected] (Warwick). In this talk we shall review recent developments on Ultrametric potentials Stein’s method and self-normalized limit theory. The fo- cus will be on randomized concentration inequalities and their applications to self-normalized Cramer type moder- Jaime San Martin ate theorems. Universidad de Chile, Chile [email protected] Backward stochastic differential equations driven by G-Brownian motion In matrix theory an important question is the so called inverse M-matrix problem. Recall that an M-matrix is a nonsingular matrix whose off diagonal elements are non- Yongsheng Song positive and whose inverse is non-negative. So, the ques- Chinese Academy of Sciences, China tion is which nonnegative matrices are inverses of M- [email protected] matrices?. The inverse of an M-matrix is naturally linked to the In this paper, we study the backward stochastic dif- potential of a transient Markov chain and then one can ferential equations driven by G-Brownian motion in use a Theorem of Choquet-Deny to characterize these ma- R T trices. The main drawback of this result is that the char- the following form: Yt = ξ + t f(s, Ys,Zs)ds + acterization is difficult to check for a given matrix. R T R T t g(s, Ys,Zs)dhBis − t ZsdBs − KT + Kt. Under a We connect this problem with the notion of ultramet- Lipschitz condition of f and g in Y and Z, the existence ric matrices and filtered matrices. Using these concepts we provide a large class of inverse M-matrices that are de- and uniqueness of the solution (Y,Z,K) is proved, where scribed in combinatorial terms. Special attention is given K is a decreasing G-martingale. to one dimensional random walks and random walks on trees. We also discuss extensions to diffusions. Some of the useful bibliography is given below. Symmetric rearrangements around infinity with applications to Lévy processes [1] C. Dellacherie, S. Martínez and J. San Martín, Ul- trametric matrices and induced Markov chains. Advances Rongfeng Sun in Applied Mathematics, 17 (1996), 169–183. National University of Singapore, Singapore [2] C. Dellacherie, S. Martínez and J. San Martín, De- [email protected] scription of the Sub-Markov kernel associated to gener- alized ultrametric matrices. An algorithmic approach. Linear Algebra and its Applications, 318 (2000), 1-21. We prove a new rearrangement inequality for multiple integrals, which partly generalizes a result of Friedberg [3] C. Dellacherie, S. Martínez, J. San Martín, and Luttinger (1976) and can be interpreted as involv- Hadamard functions of inverse M-Matrices. SIAM Jour- ing symmetric rearrangements of domains around infin- nal on Matrix Analysis and Applications (2009) 31, 2, ity. As applications, we prove two comparison results for 289–315. general Lévy processes and their symmetric rearrange- [4] C. Dellacherie, S. Martínez S., J. San Martín, Ultra- ments. The first application concerns the survival proba- metric and tree potential. Journal of Theoretical Proba- bility of a point particle in a Poisson field of moving traps bility (2009) 22, 2, 311–347. following independent Lévy motions. We show that the survival probability can only increase if the point particle [5] F.R. Gantmacher and M.G. Krein, Oszillationsma- does not move, and the traps and the Lévy motions are trizen, Oszillationskerne und kleine Schwingungen mech- symmetrically rearranged. This essentially generalizes an anischer Systeme, (1960) Akademie-Verlag, Berlin. isoperimetric inequality of Peres and Sousi (2011) for the Wiener sausage. In the second application, we show that [6] T.L. Markham, Nonnegative matrices whose in- the q-capacity of a Borel measurable set for a Lévy pro- verses are M-matrices. Proceedings of the American cess can only increase if the set and the Lévy process Mathematical Society, 36 (1972), 326–330. are symmetrically rearranged. This result generalizes an [7] S. Martínez, G. Michon and J. San Martín, Inverses inequality obtained by Watanabe (1983) for symmetric of ultrametric matrices are of Stieltjes types, SIAM Jour- Lévy processes. Based on joint work with Alex Drewitz nal Matrix Analysis and its Applications, 15 (1994), 98– and Perla Sousi. 106. [8] S. Martínez, J. San Martín, X. Zhang. A new class Bismut formula and gradient estimates for of inverse M-matrices of tree-like type. SIAM Journal SDEs driven by multiplicative Lévy noise on Matrix Analysis and Applications, 24-4 (2003), 1136– 1148. [9] S. Martínez, J. San Martín, X. Zhang. A class of Feng-Yu Wang, Lihu Xu & Xicheng Zhang M-matrices whose graphs are trees. Linear and Multilin- Beijing Normal University, China ear Algebra 52-5 (2004), 303–319. [email protected] [10] J.J. McDonald, M. Neumann, H. Schneider, M.J. Tsatsomeros, Inverse M-matrix inequalities and gen- Bismut formula and Gradient estimates are derived for eralized ultrametric matrices. Linear Algebra and its Ap- the semigroup associated to a class of stochastic differen- plications, 220 (1995), 321–341. tial equations driven by multiplicative Lévy noise, where 38 PRIMA 2013 Abstracts

the noise is realized as a subordination of the Brown- Vanishing properties of Jack polynomials ian motion. In particular, the estimates are sharp for α-stable type noises. To derive these estimates, a new derivative formula is established for the semigroup by us- Stephen Griffeth ing the Malliavin calculus and a finite-jump approxima- Universidad de Talca, Chile tion argument. sgriff[email protected]

Viscosity solutions of path dependent PDEs (Joint work with Christine Berkesch and Steven Sam) We describe some interactions between representations of rational Cherednik algebra, especially unitary repre- Jianfeng Zhang sentations, and questions arising in combinatorial com- University of Southern California, USA mutative algebra and mathematical physics. These ques- [email protected] tions all have to do with highly symmetric linear sub- space arrangements and the ideals of polynomials vanish- ing on them. Among other things, we will indicate how to use representation theory to prove a number of con- Path Dependent PDEs (PPDEs, for short) is a conve- jectures of Bernevig and Haldane on the order of vanish- nient tool to characterize the value functions of various ing of certain Jack polynomials along these arrangements, types of stochastic control problems in non- Markovian and present our own conjecture describing a Bernstein- framework. Its typical examples include Backward SDEs Gelfand-Gelfand type resolutions of unitary representa- (semi- linear PPDEs), second order BSDEs (path de- tions of the Cherednik algebra. Any such resolution is pendent HJB equations), path dependent Bellman-Isaacs automatically a minimal free resolution for the ideal of equations, and Backward Stochastic PDEs. PPDEs can the corresponding linear arrangement, so we predict a combiantorial formula for the graded equivariant Betti rarely have classical solutions. In this talk we shall pro- numbers of these ideals. pose a notion of viscosity solutions for PPDEs and estab- lish its wellposedness. Our definition relies heavily on the Functional Ito formula initiated by Dupire. Unlike the The modular generalized Springer correspon- viscosity theory of standard PDEs, the main difficulty dence in path dependent case is that the state space is not lo- cally compact. To overcome such difficulty, we replace the pointwise maximization in standard theory with an Anthony Henderson optimal stopping problem under Peng’s nonlinear expec- University of Sydney, Australia tation. The talk will be based on joint works with Nizar [email protected] Touzi, and Ibrahim Ekren, Christian Keller, Triet Pham. Given a connected reductive algebraic group G with Weyl group W , the Springer correspondence realizes the cate- gory of representations of W as a quotient of the cate- Special Session 19 gory of G-equivariant perverse sheaves on the nilpotent Representation Theory and Categorification cone. In the original definition, the representations and sheaves were over a field of characteristic zero, but we have recently shown that the same formalism works with Geometric reciprocity for algebraic tori over modular coefficients, where the categories are no longer non-Archimedean local fields semisimple. In the characteristic-zero case, Lusztig de- fined a generalized Springer correspondence to interpret the whole category of G-equivariant perverse sheaves on Clifton Cunningham the nilpotent cone in terms of representations of relative University of Calgary, Canada Weyl groups. We define and determine a modular gen- [email protected] eralized Springer correspondence in the case G = GL(n). This gives a geometric explanation for the fact that, in the modular case, the category of modules over the Schur Recent work with David Roe has shown that the ge- algebra can be obtained by successive recollements of cat- ometrization of admissible characters of T (K), where T egories of representations of suitable products of symmet- is an algebraic torus over a non-Archimedean field K, is ric groups. achieved by introducing the tensor category of character sheaves on the Greenberg transform of the Neron model of T . On the other hand, earlier worth with Achar, Kam- Knot invariants and their categorifications via garpour and Salmasian, closely related to ideas of Vogan, shows that the geometrization of Langlands parameters Howe duality for T is achieved by passing to the category of equivari- ant perverse sheaves on an ind-variety formed from LT . Aaron Lauda In this talk I will use the class field theory of Serre and University of Southern California, USA Hazewinkel to relate these two categories. [email protected]

Schubert calculus and cohomology of Lie It is a well understood story that one can extract link groups invariants associated to simple Lie algebras. These in- variants are called Reshetikhin-Turaev invariants and the famous Jones polynomial is the simplest example. Kauff- Haibao Duan man showed that the Jones polynomial could be described Institute of Mathematics, Chinese Academy of Sciences, very simply by replacing crossings in a knot diagram by China various smoothings. In this talk we will explain Cautis- [email protected] Kamnitzer-Licata’s simple new approach to understand- ing these invariants using basic representation theory and the quantum Weyl group action. Their approach is based The problem of determining the cohomology of Lie groups on a version of Howe duality for exterior algebras called was raised by E. Cartan in 1929, and has been a focus of skew-Howe duality. Even the graphical (or skein theory) algebraic topology for the fundamental roles of Lie groups description of these invariants can be recovered in an el- playing in geometry and topology. On the other hand ementary way from this data. The advantage of this ap- Schubert calculus begun with the intersection theory of proach is that it suggests a ‘categorification’ where knot the 19 century, and clarifying this calculus had been a homology theories arise in an elementary way from higher major theme of the 20 century algebraic geometry. representation theory and the structure of categorified We bring a connection between these two topics both quantum groups. with distinguished historical backgrounds, and demon- strate how Schubert calculus is extended as to give an explicit and unified construction of the integral cohomol- Center at the critical level and commutative ogy rings of all compact and 1-connected Lie groups. subalgebras 39 PRIMA 2013 Abstracts

Alexander Molev Paul Sobaje University of Sydney, Australia University of Melbourne, Australia [email protected] [email protected]

For each simple Lie algebra g the vacuum module over Let G be a reductive algebraic group over an algebraically the corresponding affine Kac-Moody algebra has a ver- closed field of characteristic p, and denote by G its tex algebra structure. For each Lie algebra g of classical (r) type, we use explicit generators of the center of this ver- r-th Frobenius kernel. Each G(r)-module M has asso- tex algebra to produce explicit constructions of maximal ciated to it a cohomological support variety, which can commutative subalgebras of the universal enveloping al- be shown in most cases to be homeomorphic to a closed gebras U(g). subset of the variety of commuting r-tuples of p-nilpotent elements in the Lie algebra of G. We will give some of the details about this homeomorphism, and also discuss explicit computations in the case that M is the restriction Cluster algebras and singular supports of per- of either a simple G-module or a Weyl module. verse sheaves

Hiraku Nakajima Decomposition numbers for the symmetric Kyoto University, Japan groups and Schur algebras [email protected] Kai Meng Tan We propose an approach to Geiss-Leclerc-Schroer’s con- National University of Singapore, Singapore jecture on the cluster algebra structure on the coordinate [email protected] ring of a unipotent subgroup and the dual canonical base. It is based on singular supports of perverse sheaves on the space of representations of a quiver, which give the The complete determination of the decomposition num- canonical base. bers for the symmetric groups and Schur algebras in pos- itive characteristic p is a famous open problem; a com- plete solution of which does not seem to be forthcoming On orbits in double flag varieties for symmet- in the near future. In this talk, we present our recent ric pairs results which provide closed formulas for the decomposi- tion number dλµ when the partition λ is obtained from µ by moving some nodes whose p-residues are pairwise Hiroyuki Ochiai non-adjacent. Kyushu University, Japan [email protected] Hodge theory and representation theory Let G be a connected, simply connected semisimple alge- braic group over the complex number field, and let K be Kari Vilonen the fixed point subgroup of an involutive automorphism of Northwestern University, USA G so that (G, K) is a symmetric pair. We take parabolic [email protected] subgroups P of G and Q of K respectively and consider the product of partial flag varieties G/P and K/Q with diagonal K-action, which we call a double flag variety for I will explain how Hodge theory can be used in the repre- a symmetric pair. It is said to be of finite type if there sentation theory of real groups to attack the problem of are only finitely many K-orbits on it. In this paper, we the unitary dual. give a parameterization of K-orbits on G/P × K/Q in terms of quotient spaces of unipotent groups without as- suming the finiteness of orbits. As a result, we get sev- Globalizing crystal basis for quantum super- eral useful criteria for the finiteness of orbits. If one of algebras P ⊂ G or Q ⊂ K is a Borel subgroup, the finiteness of or- bits is closely related to spherical actions. In such cases, the criteria enable us to obtain a complete classification Weiqiang Wang of double flag varieties of finite type. As a consequence, University of Virginia, USA we obtain classifications of K-spherical flag varieties G/P [email protected] and G-spherical homogeneous spaces G/Q. Canonical basis (or global crystal basis) for quantum Elementary subalgebras of modular Lie alge- groups and their integrable modules was introduced and bras developed by Lusztig and subsequently by Kashiwara. We will present a construction for the first time, moti- vated by categorification, of canonical basis for a class Julia Pevtsova of quantum superalgebras and their integrable modules. University of Washington, USA This is joint work with Sean Clark and David Hill. [email protected]

Let g be a p-Lie algebra. We call a subalgebra E of g elementary of rank r if it is an abelian Lie algebra with Special Session 20 trivial p-restriction of dimension r. For a fixed r we con- Singularities in Geometry and Topology sider a projective variety (r, g) that parameterizes all E The topology of real suspension singularities elementary subalgebras of g of rank r. This variety is a n natural generalization of the rank variety introduced by of type fg¯ + z Carlson for elementary abelian p-groups and the support variety for Lie algebras of Friedlander and Parshall. Haydée Aguilar Cabrera We’ll identify this projective variety in various classical National Autonomous University of Mexico, Mexico cases. We’ll also show how representations of g with spe- [email protected] cial properties lead to constructions of families of vector bundles on E(r, g), thereby extending the study of “mod- ules of constant Jordan type" and their geometric appli- In this talk we present some results on the topology of cations to this more general context. 3 the family of real analytic germs F :(C , 0) → (C, 0) with isolated critical point at 0, given by F (x, y, z) = r Support varieties for reductive groups f(x, y)g(x, y)+z , where f and g are holomorphic,r ∈ Z+ 40 PRIMA 2013 Abstracts

and r ≥ 2. We describe the link LF as a graph mani- The obtained formula is then applied to weighted lattice fold using its natural open book decomposition, related to point counting in lattice polytopes. Secondly, in the case the Milnor fibration of the map-germ fg¯ and the descrip- of simplicial toric varieties, we make use of the Lefschetz- tion of its monodromy as a quasi-periodic diffeomorphism Riemann-Roch theorem in the context of the geometric through its Nielsen invariants. Furthermore, such a germ quotient description of such varieties. In this setting, we F 5 1 define mock Hirzebruch classes of simplicial toric varieties F gives rise to a Milnor fibration |F | : S \LF → S . and investigate the difference between the (actual) homol- We present a join theorem, which allows us to describe ogy Hirzebruch class and the mock Hirzebruch class. We the homotopy type of the Milnor fibration of F and we show that this difference is localized on the singular locus, show some cases where the open book decomposition of and we obtain a formula for it in which the contribution 5 of each singular cone is identified explicitly. This is joint S given by the Milnor fibration of F cannot come from 3 work with Jörg Schürmann. the Milnor fibration of a complex singularity in C .

On Griffiths numbers for higher dimensional On the topology of real analytic maps isolated singularities José Luis Cisneros Molina National Autonomous University of Mexico, Mexico Rong Du [email protected] East China Normal University, China [email protected] Joint work with Nivaldo G. Grulha Jr. and José Seade. We will discuss some numerical invariants for isolated sin- In this talk we present some recent results on the topol- ogy of real analytic maps. Every real analytic map germ gularities and their relations. In particular, we will show n p f : R → R , p ≥ 1, with arbitrary critical set, has a that S. Yau’s conjecture on inequalities for (n−1)-th Grif- Milnor-Lê type fibration. Now assume also that f has fiths number and (n − 1)-th Hironaka number holds for the Thom af -property, and its zero-locus has positive di- irregular singularities and it is not true in general. mension. Also consider another real analytic map germ n k g : R → R with an isolated critical point at the ori- gin. We have Milnor-Lê type fibrations for f and for Equisingularity and integral closure of ideals n p+k and modules: two partners in a dance (f, g): R → R , and we prove for these the analogous of the classical Lê-Greuel formula, expressing the differ- ence of the Euler characteristics of the fibers Ff and Ff,g Terence Gaffney in terms of an invariant associated to these maps. Northeastern University, USA t.gaff[email protected] Intersection theory on mixed curves

A family of sets or mappings is equisingular if the singu- Mutsuo Oka larities of the family are similar, in a well defined sense depending on the equisingularity condition. The theory of Tokyo University of Science, Japan integral closure is an important tool for studying equisin- [email protected] gularity conditions. It provides invariants which describe the condition, and provide means of proving the condi- 0 2 tions hold for a family. In this talk we will quickly reprise We consider two mixed curve C,C ⊂ C which are de- results for Whitney equisingularity, then discuss how to fined by mixed functions of two variables Z = (z1, z2). We apply the same ideas to construct an infinitesimal theory have shown in our previu paper that they have canoni- cal orientations. If C and C0 are smooth and intersect of bi-Lipschitz equivalence. 0 transversely at P , the intersection number Itop(C,C ; P ) is topologically defined. We will generalize this defini- Improved bounds on the ranks of the Milnor tion to the case when the intersection is not necessarily fiber cohomology transversal or either C or C0 may be singular at P using the defining mixed polynomials. David B. Massey Northeastern University, USA Newton-Puiseux analysis [email protected] Laurentiu Paunescu As we showed 25 years ago, the Lê numbers provide up- The University of Sydney, Australia per bounds on the ranks of the cohomology of the Milnor [email protected] fiber of a function with a critical locus of arbitrary dimen- sion. Our new results deal with when the maps in the Lê Complex analysis is extended to the Newton-Puiseux complex can be zero, and so give us improved bounds on field. We give analogues of several clasic results and, as the Milnor fiber cohomology. Our results in the classi- a corollary, a short proof of the Kuo-Lu theorem. cal case follow from more general results on the vanishing cycles of perverse sheaves. Singularities of several geometric objects re- Characteristic classes of singular toric vari- lated to null curves in Minkowski 3-space eties Donghe Pei Laurentiu Maxim Northeast Normal University, China University of Wisconsin-Madison, USA [email protected] [email protected] In this article, we investigate the singularities of null We discuss the computation of the homology Hirzebruch Darboux developables, Gaussian surfaces and pseudo- characteristic classes of (possibly singular) toric varieties. spherical Darboux Images associated with a null Cartan We present two different perspectives for the computation curve in Minkowski 3−space. This is a joint work with of these characteristic classes. First, we take advantage of Zhi-Gang Wang. the torus-orbit decomposition and the motivic properties of the homology Hirzebruch classes to express the latter in terms of the (dual) Todd classes of closures of orbits. Broken Lefschetz fibrations and their moves 41 PRIMA 2013 Abstracts

n −1 Osamu Saeki locally trivial fibration C \ f (Bf ) −→ C \ Bf to Kyushu University, Japan CR we obtain a geometric monodromy automorphism [email protected] ∞ −1 −1 Φf : f (R) ' f (R) and the linear maps

A broken Lefschetz fibration (BLF, for short) is a smooth ∞ j −1 j −1 Φj : H (f (R); C) ' H (f (R); C)(j = 0, 1,...) map of a closed oriented 4-manifold onto a closed sur- (8) face whose singularities consist of Lefschetz critical points ∞ (w.r.t. local complex coordinates compatible with the associated to it. We call Φj ’s the (cohomological) mon- orientations) together with indefinite folds. Such a odromies at infinity of f. Recently in [10], by using the class of maps was first introduced by Auroux-Donaldson- Newton polyhedron at infinity Γ∞(f) of f we defined a Katzarkov in relation to near-symplectic structures, and finite subset Af ⊂ C of “bad" eigenvalues which we call now it is known that every closed oriented 4-manifold ad- atypical engenvalues of f. Then we have the following re- mits a BLF over the 2-sphere. In this talk, we give a finement of the main result of Broughton [1]. For λ ∈ C set of explicit moves for BLFs which can connect any two j −1 j −1 homotopic BLFs, and give an elementary and construc- and j ∈ Z let H (f (R); C)λ ⊂ H (f (R); C) be the tive proof to the fact that any map into the 2-sphere is generalized eigenspace for the eigenvalue λ of the mon- ∞ homotopic to a BLF whose indefinite fold has embedded odromy at infinity Φj . image. This is a joint work with R. İnanç Baykur (Max Theorem: (T-Tibăr [10]) Let f ∈ C[x1, . . . , xn] be a Planck Institute for Mathematics). non-convenient polynomial such that dim Γ∞(f) = n. Assume that f is non-degenerate at infinity. Then for Geometry of non-tame polynomial maps any non-atypical eigenvalue λ∈ / Af of f we have the concentration Kiyoshi Takeuchi Hj (f −1(R); C) ' 0 (j 6= n − 1) (9) University of Tsukuba, Japan λ [email protected] for the generic fiber f −1(R) ⊂ Cn (R  0) of f. With this theorem at hand, we can extend the results in For a polynomial map f = (f , . . . , f ): Cn −→ Ck (1 ≤ 1 k [4], [6] and [7] etc. to non-convenient polynomials. In k ≤ n), it is well-known that there exists a proper subset k particular, as in [7] and [3] by using the motivic Milnor B ⊂ C such that the restriction fiber at infinity of f we completely determine the Jordan ∞ normal forms of Φn−1 for non-atypical eigenvalues λ∈ / Cn \ f −1(B) −→ Ck \ B (5) Af of f. See [10] for the details. of f is a locally trivial fibration. We denote by Bf the smallest subset B ⊂ Ck satisfying this condition. The [1] Broughton, S. A. “Milnor numbers and the topology elements of Bf are called bifurcation points of f. When of polynomial hypersurfaces", Invent. Math., 92 (1988): k = 1 many mathematicians obtained various subsets of 217-241. k C = C containing Bf . In particular, Némethi and Za- [2] Chen, Y., Dias, R., Takeuchi, K. and Tibăr, haria [8] showed that for a non-convenient polynomial M. “Invertible polynomial mappings via Newton non- degeneracy", arXiv:1303.6879. f = (f1) such a subset is obtained by the bad faces of its Newton polyhedron at infinity Γ∞(f). In this talk, we [3] Esterov, A. and Takeuchi, K. “Motivic Milnor fibers first introduce the following analogue of their result for over complete intersection varieties and their virtual Betti general k ≥ 1 (see also Nguyen [9] for a related result). numbers", Int. Math. Res. Not., Vol. 2012, No. 15 (2012): 3567-3613. Theorem: (Chen-Dias-T-Tibăr [2]) Assume that f = n k [4] Libgober, A. and Sperber, S. “On the zeta function (f1, . . . , fk): C −→ C is non-degenerate at infinity. k k of monodromy of a polynomial map", Compositio Math., Let Nf ,Kf ⊂ C be the subsets of C defined by the 95 (1995): 287-307. Newton polyhedra at infinity of f1, . . . , fk in [2]. Then we have [5] Matsui, Y. and Takeuchi, K. “Milnor fibers over singular toric varieties and nearby cycle sheaves", Tohoku Bf ⊂ f(singf) ∪ Nf ∪ Kf . (6) Math. J., 63 (2011): 113-136. Note that if k = 1 this result coincides with that of [8]. [6] Matsui, Y. and Takeuchi, K. “Monodromy zeta When k = 1 and n = 2, Némethi and Zaharia [8] proved functions at infinity, Newton polyhedra and constructible the equality Bf = f(singf)∪Nf ∪Kf and conjectured its sheaves", Mathematische Zeitschrift, 268 (2011): 409- validity also in the higher-dimensional case n ≥ 3. In this 439. talk, we next introduce our approach to this conjecture. [7] Matsui, Y. and Takeuchi, K. “Monodromy at in- By using the results in [5] we will show that it can be finity of polynomial maps and Newton polyhedra, with verified in many cases. Finally, we restrict ourselves to the Appendix by C. Sabbah", Int. Math. Res. Not., Vol. case k = 1. If f = (f1) is convenient and non-degenerate 2013, No. 8 (2013): 1691-1746. at infinity, then by a result of Broughton [1] we have the [8] Némethi, A. and Zaharia, A. “On the bifurcation set cohomological concentration of a polynomial function and Newton boundary", Publ. Res. Inst. Math. Sci., 26 (1990): 681-689. Hj (f −1(R); C) = 0 (j 6= 0, n − 1) (7) [9] Nguyen, T. T., “Bifircation set, M-tameness, asymptotic critical values and Newton polyhedrons", for the generic fiber f −1(R) (R  0) of f. However, arXiv:1205.0939v5, to appear in Kodai Math. J. many polynomials that we usually encounter are not con- [10] Takeuchi, K. and Tibăr, M. “Monodromies at in- venient. They are not tame at infinity. The study of finity of non-tame polynomials", arXiv:1208.4584. non-tame polynomials is important also for the Jacobian conjecture since they are the only interesting objects for it (see [2] etc.). The main reason why non-tame polynomials Characteristic points, fundamental cubic could not be studied successfully before is that one cannot form and Euler characteristic of projective expect to have the cohomological concentration for them. Here we partially overcome this difficulty on non-tame surfaces polynomials by improving the above-mentioned result of Broughton [1] as follows. Let CR = {x ∈ C | |x| = R} Ricardo Uribe-Vargas (R  0) be a sufficiently large circle in C such that Université de Bourgogne, France Bf ⊂ {x ∈ C | |x| < R}. Then by restricting the [email protected] 42 PRIMA 2013 Abstracts

Joint work with M. Kazarian. Generic surfaces in projec- Seoul National University, Korea tive 3-space have isolated characteristic points (invariant [email protected] under projective trasformations and stable under small perturbations of the surface) called elliptic nodes, hyper- The restricted three body problem has an intriguing dy- bolic nodes and godrons (also known as cusps of Gauss). namics. In joint work with Peter Albers, Gabriel Pa- These characteristic points have interesting properties ternain and Otto van Koert we showed that below and and deserve special attention. We give a geometric defini- slightly the first critical level energy hypersurfaces of tion of the characteristic points (there are several equiva- the restricted three body problem are of contact type. lent definitions) and we define natural local invariants for This result allows us to apply global methods coming from Gromov-Witten theory, Floer theory, and Symplec- them (a sign ±). tic Field theory to this old problem. I will explain how Our formulas for global counting of these invariants on we can use these global methods to detect global surfaces the surface (or on domains in it) involve the Euler char- of section were the perturbative methods used so far fail. acteristic of the surface (or of the respective domains) providing restrictions on the coexistence of characteristic points. Mean Euler characteristic: the degenerate case One way to prove our counting formulas (we know three ways) is considering the fundamental cubic form: in the same way as the second fundamental quadratic form mea- Viktor L. Ginzburg sures the quadratic deviation of a surface from its tangent University of California, Santa Cruz, USA plane, the cubic fundamental form measures the cubic de- [email protected] viation of the surface from its quadratic part. The fun- damental cubic form is a local intrinsic invariant defined for every point of the surface, which vanish at the char- The mean Euler characteristic (MEC) is an invariant of acteristic points. a contact manifold, which is on the one hand sensitive Our exposition will be rather geometrical and for a wide enough to distinguish interesting contact structures and, audience. on the other, relatively easily computable in terms of the dynamics of the Reeb flow. This invariant was introduced by van Koert. As has been shown by Kerman and the Topological classification of multiaxial U(n)- speaker, the MEC can be expressed in terms of local, purely topological, invariants of closed Reeb orbits when- actions ever the Reeb flow is non-degenerate and has finitely of such orbits. This expression generalizes the resonance Min Yan (joint with S. Cappell and S. Weinberger) relation for the mean indices of closed characteristics es- tablished by Viterbo for convex hypersurfaces, and it has Hong Kong University of Science and Technology, Hong been further refined and generalized by Espina. Kong, China [email protected] In this talk, based on a joint work with Yusuf Goren, we will discuss a version of such a local formula for the MEC when the closed orbits are degenerate. This work builds on the previous results of Long et al. and Hryniewicz and A manifold under the action of the unitary group U(n) Macarini, and its main new feature is that, as in the non- is multiaxial if all the isotropy groups are unitary sub- degenerate case, the contributions of individual orbits are n groups. Such manifolds are often modeled on kC ⊕ jR, purely topological. We will also touch upon applications n where C has the canonical U(n)-action and R has triv- of this resonance relation to dynamics. ial U(n)-action. One of the major achievements about multiaxial manifolds was M. Davis and W.C. Hsiang’s concordance classification in late 1970s for the smooth The Hill-type formula and Krein-type trace category and under the assumption k ≤ n. formula

We study the structure set SU(n)(M) of a multiaxial U(n)-manifold M, which is the homeomorphism classes Xijun Hu of the topological U(n)-manifolds equivariantly homotopy Shandong University, China [email protected] equivalent to M. We show that SU(n)(M) can be decom- posed into simpler structure sets. We discuss the implica- tion of the decomposition and compute explicitly for the In the study of the motion of lunar perigee, Hill got a for- case M is the canonical representation sphere. All the mula which relates the characteristic polynomial of the results do not assume k ≤ n. monodromy matrix for a periodic orbit and a kind of infi- nite determinant. Hill’s formula is useful in understand- ing the property of the monodromy matrix. Motivated Milnor fibers of real line arrangements by the previous works, we build up the Hill-type formula for S-periodic solutions for first-order ordinary differential equations and Lagrangian systems. The S-periodic solu- Masahiko Yoshinaga tion is a solution such that x(t) = Sx(t + T ) for some or- Hokkaido University, Japan thogonal matrix S, which comes naturally from the study [email protected] of symmetry periodic orbits in n-body problem. Based on it, we get the Trace formula for linear ODE, include The Milnor fiber of a line arrangement is a certain cyclic the case of standard Sturm-Liouville systems, which can covering space of the complexified complement equipped be consider as a generalization of Krein’s work in 1950’s. with monodromy action. We will discuss the monodromy Especially, for the eigenvalue problem Lu + λR(x)u = 0, P k action on the first homology group. We will present a where L is the Sturm-Liouville operator, 1/λj can be new algorithm computing multiplicities of monodromy computed by the trace formula. Some applications for eigenvalues, which uses real and combinatorial structures the stability problem is given. (chambers). I will also give an upper bounds and several conjectures. The extremal Kahler metrics on toric mani- folds Special Session 21 Symplectic Geometry and Hamiltonian Dy- An-Min Li Sichuan University, China namics [email protected] Contacting the moon We study the prescribed scaler curvature problem on toric Urs Frauenfelder manifolds, following Donaldson’s program. Let ∆ be an 43 PRIMA 2013 Abstracts

n open Delzant polytope in R with ∆¯ compact. The pre- (Q, λ, J) where λ is a contact form and J : ξ → ξ is an scribed scalar curvature problem reduces then to finding endomorphism with J2 = −id compatible to dλ. We call a smooth convex solution in ∆ for the 4-th order PDE it the contact triad connection of (Q, λ, J) which exists uniquely. This is partially a joint work with Rui Wang. X ∂2uij = −A. (10) ∂ξi∂ξj i,j Anti-symplectic involution and Floer theory subjecting to the Guillemin’s boundary conditions. This is the Abreu’s equation. It is well known that the solution Kaoru Ono u gives an extremal metric if and only if A is a linear Kyoto University, Japan function in ∆. [email protected] Denote by S the set of continuous convex functions u on ∆¯ such that u satisfies the Guillemin’s boundary conditions. For a fixed point p ∈ ∆, we set I will present the work on anti-symplectic involution and o its effect on Floer theory for Lagrangian submanifolds based on a joint work with K. Fukaya, Y.-G. Oh and Spo = {u ∈ S : u ≥ u(po) = 0}. H. Ohta. There are interesting example of Lagrangian submanifolds, which appear as the fixed point set of an anti-symplectic involution. Then we study when they Donaldson introduced a stronger version of stability, are unobstructed in Floer theoretical sense and its con- which we call the uniform stability. We show that the sequences. We can identify the quantum cohomology of uniform stability is a necessary condition for existing a smooth solution. (X, ω) and Lagrangian Floer thoery on the diagonal in (X × X, −ω ⊕ ω) and define higher operations on quan- Theorem 1(Bohui Chen, An-Min Li and Li Sheng) If tum cohomology. the Abreu equation (1) has a smooth solution in S, then (∆,A) is uniform stable. Witten equation and the geometry of LG- model We would suggest a modification on the original con- jecture posed by Donaldson: Conjecture 2 (M, ω) has a metric within the class [ω] Yongbin Ruan that solves the Abreu equation (1) if and only if (∆,A) University of Michigan, Ann Arbor, USA [email protected] is uniformly K-polystable.

We derived interior estimates for any dimension: The study of moduli space of solutions of nonlin- Theorem 3(Bohui Chen, Qing Han, An-Min Li and Li ear PDE has revolutionized the geometry and topol- Sheng) Let ∆ be a bounded open polytope in n and A be ogy for last twenty years. The famous examples are R Donaldson/Seiberg-Witten theory and Gromov-Witten a smooth function on ∆¯ . Suppose (∆,A) is uniformly K- theory. In the talk, I will discuss another family of PDE stable and u is a solution in Spo of the Abreu’s equation introduced by Witten in the context of so called Landau- (1). Then, for any Ω ⊂⊂ ∆, any nonnegative integer k Ginzburg model. As expected, it is revolutionizing the and any constant α ∈ (0, 1), subject of Landau-Ginzburg model right now.

kuk ≤ CkAk , Ck+3,α(Ω) Ck(∆)¯ Isotopy of Lagrangian tori revisited where C is a positive constant depending only on n, k, α, Ω, and λ in the uniform K-stability. For n=2, Donaldson Mei-Lin Yau solved the conjecture 2 for A = constant, we are able to National Central University, Taiwan prove the conjecture 2 for almost any A. [email protected]

Definition Let A be a smooth function on ∆¯ . It is called edge-nonvanishing if it does not vanish on any edge of ∆. Over the last twenty years, isotopy problems of La- grangian tori (and more generally, Lagrangian submani- folds) have been under investigations from many different Theorem 4(Bohui Chen, An-Min Li and Li Sheng) Let approaches. Yet it seems that more can be explored, even M be a compact toric surface and ∆ be its Delzant poly- for Lagrangian tori in R4. ∞ ¯ tope. Let A ∈ C (∆) be an edge-nonvanishing function. In this talk I will review the construction of mon- If (M,A) is uniformly stable, then there is a smooth T 2- odromy groups for Lagrangian submanifolds and report invariant metric on M that solves the Abreu equation. on some recent results concerning the three types (Hamil- tonian/Lagrangian/smooth) of monodromy groups Clif- 4 Canonical connection and analysis of contact ford tori and Chekanov tori in R . Cauchy-Riemann equation If time permits, i will also talk about some very recent work in progress on the construction of Lagrangian sur- faces via surgery, as well as a potentially new symplectic Yong-Geun Oh invariant of Lagrangian surfaces to detect the surgery ef- University of Wisconsin-Madison, USA & IBS-Center for fect on the Hamiltonian isotopy class of Lagrangian sur- Geometry and Physics, Korea faces. [email protected]

In this talk, we explain the analysis of the following sys- π ∗ Special Session 22 tem of (degenerate) elliptic equation ∂ w = 0, d(w λ ◦ Symplectic Geometry and Mathematical j) = 0 associated for each given contact triad (Q, λ, J) on Physics a contact manifold (Q, ξ), which was first introduced by Hofer. We directly work with this equation on the contact A classifying space for commutativity manifolds without involving the symplectization process. We explain the basic analytical ingredients towards the construction of moduli space of solutions, which we call contact instantons. For the needed tensorial calculations, Alejandro Adem we introduce a canonical affine connection on the contact University of British Columbia, Canada manifold (Q, ξ), which is associated to each contact triad [email protected] 44 PRIMA 2013 Abstracts

Let G denote a Lie group. In this talk we will discuss explanation of mirror maps. This is joint work with I. a classifying space constructed from the commuting ele- Ciocan-Fontanine. ments in G. We compute its cohomology and describe its geometry and homotopy type. The Eynard-Orantin recursion in singularity theory Virtual neighborhood techniques in Gromov- Witten theory Todor Milanov Kavli Institute for the Physics and Mathematics of the Universe, Japan Bohui Chen [email protected] Sichuan University, China [email protected]> It was proved recently that the correlation functions of a semi-simple cohomological field theory satisfy the so Abstract: In this talk, I will explain the construction of called local Eynard–Orantin topological recursion. In my virtual orbifolds for the moduli spaces of stable curves. talk, I would like to explain this result in the settings of In particular, I will explain how to deal with the non- singularity theory. In my earlier work with B. Bakalov, smoothness issues arised from the infinite dimensional we have constructed a certain twisted representation of set-ups. the Heisenberg vertex operator algebra associated with the vanishing cohomology of the singularity. The kernel of the Eynard-Orantin recursion is essentially obtained from the so called operator product expansion of the fields that Algebra of Legendrian surgery define the representation. Finally, I would like to report my progress on finding the global recursion, which seems Yakov Eliashberg to be related to the theory of W -algebras. Stanford University, USA eliash math.stanford.edu Orbifold Hurwitz numbers and Eynard- Orantin invariants I will discuss algebraic structures arising in connection with Legendrian surgery, which enter the computation of holomorphic curve invariants of Weinstein domains and Paul Norbury their boundaries. This is a joint work with F. Bourgeois University of Melbourne, Australia and T. Ekholm. [email protected]

Fock sheaf of Givental quantization I will describe a generalisation of simple Hurwitz num- bers due to Johnson, Pandharipande and Tseng and prove that they satisfy the topological recursion of Eynard and Hiroshi Iritani Orantin. This generalises the Bouchard-Marino conjec- Kyoto University, Japan ture and places Hurwitz-Hodge integrals, which arise in [email protected] the Gromov-Witten theory of target curves with orbifold structure, in the context of the Eynard-Orantin topolog- ical recursion. I will talk about joint work with Tom Coates (Imperial College London) on a global version of Givental quantiza- tion. Based on a generalized variation of Hodge structure Translated points and contact rigidity (the so-called semi-infinite variation of Hodge structure), we construct a sheaf of Fock spaces which can be identi- Sheila Sandon fied with Givental’s Fock space infinitesimally. An oppo- Université de Nantes, France site subspace which yields a Frobenius structure on the [email protected] base plays a role of polarization in the context of geomet- ric quantization. As applications, we discuss modularity of Gromov-Witten potential of local projective plane, and I will discuss the role played by translated points of also holomorphic anomaly equation. contactomorphisms in contact rigidity phenomena such as non-squeezing, orderability and the existence of bi- invariant metrics on the contactomorphism group. I will then either concentrate on presenting the construction of Categories and dynamical systems the discriminant metric on the contactomorphism group (which is joint work with Vincent Colin) or discuss an Ludmil Katzarkov analogue for translated points of the Arnold conjecture University of Miami, USA and University of Vienna, Aus- on fixed points of Hamiltonian symplectomorphisms, and tria a joint work in progress with Yasha Savelyev and Egor [email protected] Shelukhin to prove this conjecture by constructing a Floer homology theory for translated points. In this talk we will discuss recent developments in the theory of stability conditions of categories. We will out- On a certain generalization of Virasoro con- line some parallels with classical results from dynamical systems. straints for Frobenius manifolds

Youjin Zhang Quasimap invariants and mirror maps Tsinghua University, China [email protected] Bumsig Kim Korea Institute for Advanced Study, Korea We show that the Virasoro operators associated to an [email protected] arbitray Frobenius manifold admit certain deformations which give additional constraints for the genus zero free The moduli spaces of stable quasimaps unify various mod- energy of the Frobenius manifold. We discuss applica- uli appearing in the study of Gromov-Witten Theory. tions of such additional constraints and their analogues We introduce big I-functions as the quasimap version of for higher genus free energies. J-functions, generalizing Givental’s small I-functions of smooth toric complete intersections. The J-functions are the GW counterparts of periods of mirror families. We Gopakumar-Vafa invariants of local Calabi- discuss some advantages of I-functions, in particular an Yau 3-Folds 45 PRIMA 2013 Abstracts

Jian Zhou side can now be understood on the other side. Part of Tsinghua University, China this is joint work in progress with Lutz Hille. [email protected] Singular equivalences with examples We will present a formula for Gopakumar-Vafa BPS invariants of local Calabi-Yau geometries given by the canonical line bundles of toric surfaces under some tech- Xiao-Wu Chen nical conditions. This verifies and extends a conjecture University of Science and Technology of China, China made by Katz-Klemm-Vafa based on M-theory. [email protected]

Two finite dimensional algebras are said to be singularly equivalent if there is a triangle equivalence between their Special Session 23 singularity categories in the sense of Buchweitz and Orlov; Triangulated Categories in Representation this triangle equivalence is called a singular equivalence. Theory of Algebras We will report recent progress on singular equivalences with examples. Derived simple algebras The representation type of non-degenerate Lidia Angeleri Hügel QPs University of Verona, Italy [email protected] Christof Geiss National Autonomous University of Mexico, Mexico An algebra is said to be derived simple if its derived cate- [email protected] gory cannot be deconstructed into ‘smaller’ derived cate- gories, more precisely, it is not the middle term of a non- trivial recollement where the two outer terms are again Let Q be a 2-acyclic quiver, and W a non-degenerate derived categories of algebras. potential for Q. We show, that up to a few exceptions We will see that being derived simple strongly depends the Jacaobian algebra P(Q, W ) is tame if and only if the on the choice of derived categories: whether at bounded quiver is mutation finite. or unbounded level, whether considering finitely gener- The exceptions are the following: The mutation finite ated or arbitrary modules. We will clarify the connection quivers X6,X7 (found by Derksen and Owen) and the m- between the different choices by discussing when recolle- Kronecker quiver for m ≥ 3 yield wild Jacobian algebras. ments can be lifted or restricted between different levels The mutation finite quivers T1 and T2 corresponding to of derived categories. We will then characterize derived triangulations of a torus with one puncture resp. with simpleness on each level in terms of the height of lad- one marked point admit non-degenerate potentials which ders, that is, the number of adjacent recollements at un- can be either tame or wild. bounded level. This is joint work with Steffen Koenig, Qunhua Liu, Dong Yang. The tame cases include virtually all known "derived- tame phenomena": (extended) Dynkin, tubular, skewed- clannish and deformations. Thus we obtain many exam- The decorated mapping class group of a ples of "tame" triangulalated 2-CY categories. marked surface If time permits we discuss the uniqueness of non- degenerate potentials for most mutation finite quivers. Thomas Brüstle Bishops’s University and Université de Sherbrooke, Canada Geigle-Lenzing spaces and canonical algebras [email protected] of dimension d (I)

The main character of this talk is the decorated mapping Martin Herschend class group MCGp(S, M) of a marked surface (S, M). We Norwegian University, Norway show that (in most cases) it is isomorphic to a group [email protected] formed by automorphisms of the cluster algebra associ- ated to (S, M), which can also be interpreted as a group of auto-equivalences of the corresponding cluster category This is the first half of a report on ongoing joint work with Osamu Iyama, Hiroyuki Minamoto, and Steffen Op- C(S, M). Moreover we describe the suspension functor of permann. The second half will be given by Osamu Iyama. C(S, M) geometrically, as an element in the decorated Weighted projective lines were introduced by Geigle and mapping class group of (S, M). Lenzing. One key property of these is that they give rise to hereditary categories with tilting objects, whose endo- morphism rings are canonical algebras. Both weighted Autoequivalences under derived equivalences projective lines and canonical algebras have proven to be interesting objects in representation theory, and been studied intensively. In our talks we will introduce the no- tion of d-dimensional Geigle-Lenzing spaces, generalizing Ragnar-Olaf Buchweitz the concept of weighted projective lines. Also in this case University of Toronto Scarborough we obtain a nice tilting bundle, whose endomorphism ring [email protected] we call a d-canonical algebra. We will then focus on some properties of weighted projective lines which generalize nicely to the d-dimensional setup. There are many examples where derived categories of coherent sheaves on some smooth projective variety are equivalent to the derived category of finite length mod- Geigle-Lenzing spaces and canonical algebras ules over an artinian algebra, or to the singularity cate- gory of graded modules over a graded Gorenstein algebra, in dimension d (II) or both. In these case, often one of the partners in the derived Osamu Iyama equivalences carries obvious autoequivalences, such as Nagoya University, Japan twists by line bundles on the geometric side or degree [email protected] shifts in the graded case, that are quite mysterious on the equivalent incarnations. We will review this situation and explain some classical This is the second half of a report on ongoing joint work examples where the "obvious" autoequivalences on one with Martin Herschend, Hiroyuki Minamoto and Steffen 46 PRIMA 2013 Abstracts

Oppermann. The first half will be given by Steffen Op- these results to a conjecture of Fomin-Zelevinsky stating permann. that the exchange graph of a cluster algebra does not de- Weighted projective lines were introduced by Geigle and pend on the choice of the ring of coefficients over which Lenzing. One key property of these is that they give rise the algebra is defined. (This is joint work with G.Cerulli to hereditary categories with tilting objects, whose endo- Irelli, B.Keller and D.Labardini-Fragoso.) morphism rings are canonical algebras. Both weighted projective lines and canonical algebras have proven to be interesting objects in representation theory, and been Triangulated categories and tau-tilting theory studied intensively. In our talks we will introduce the no- tion of d-dimensional Geigle-Lenzing spaces, generalizing the concept of weighted projective lines. Also in this case we obtain a nice tilting bundle, whose endomorphism ring Idun Reiten we call a d-canonical algebra. We will then focus on some Norwegian University of Science and Technology, Nor- properties of weighted projective lines which generalize way) nicely to the d-dimensional setup. [email protected]

Cohomological length functions This talk is based upon work with Adachi and Iyama. We explain how work on triangulated categories (cluster Henning Krause categories and more generally, 2-Calabi-Yau categories) Universität Bielefeld, Germany inspired an extension of some aspects of classical tilting [email protected] theory, which we have called tau-tilting theory.

A cohomological functor from a triangulated category From submodule categories to preprojec- into the category of finite length modules over some ring tivealgebras gives rise to an integer valued function on the set of all ob- jects. One might ask: What are the characteristic prop- erties of such a function, and can one recover the functor Claus Michael Ringel from the corresponding function? Somewhat surprisingly, Bielefeld University, Germany and Shanghai Jiao Tong we can offer fairly complete answers to both questions. University, China Examples from representation theory will illustrate these [email protected] answers, and we discuss some cases when all cohomolog- ical length functions can be classified. Let S(n) be the category of invariant subspaces of nilpo- tent operators with nilpotency index at most n. Such Invariant flags for nilpotent operators, and submodule categories have been studied already in 1936 weighted projective lines by Birkhoff, they have attracted a lot of attention in re- cent years, for example in connection with some weighted Helmut Lenzing projective lines (Kussin, Lenzing, Meltzer). On the other Paderborn University, Germany hand, we consider the preprojective algebra of type An; [email protected] the preprojective algebras were introduced by Gelfand and Ponomarev, they are now of great interest, for exam- ple they form an important tool to study quantum groups This is joint work with Dirk Kussin and Hagen Meltzer (Lusztig) or cluster algebras (Geiss, Leclerc, Schroeer). extending a previous analysis of the invariant subspace Direct connections between the submodule category S(n) problem for nilpotent operators (of finite dimensional vec- and the module category of the preprojective algebra of tor spaces over an algebraically closed field k). The prob- type An−1 have been established quite a long time ago by lem itself goes back to G. Birkhoff (1934) and was treated Auslander and Reiten, and recently also by Li and Zhang, in detail by C.M. Ringel and M. Schmidmeier (2006- but apparently this remained unnoticed. The lecture is based on joint investigations with Zhang Pu and will pro- 2008); it is further related to research by D. Simson (2007) vide details on this relationship. As a byproduct we see and Pu Zhang (2011). In previous work with Kussin and that here we deal with ideals I in triangulated categories Meltzer we did establish a relationship of the invariant T such that I is generated by an idempotent and T/I is subspace problem to singularity theory, more specifically abelian. we showed a link to the theory of weighted projective lines X of special weight type (2, 3, c). In this talk, we show that for arbitrary triple weight type (a, b, c), a suit- Exact categories over Cohen–Macaulay rings able factor category S of the category of vector bundles on X, is equivalent to the category of graded representa- Ryo Takahashi tions of nilpotency degree bounded by c, equipped with Nagoya University, Japan two invariant flags of graded sub-representations , where [email protected] the flag lengths are determined by the integers a and b. The category S carries a natural exact structure which is almost-Frobenius, but in general not Frobenius. It’s as- It is known that the following full subcategories of finitely sociated stable category S is triangulated and shown to generated modules are Frobenius categories: be equivalent to the singularity category of the (suitably graded) triangle singularity xa + yb + zc. • the category of maximal Cohen–Macaulay modules over a ,

Cluster categories and independence results • the category of totally reflexive ( = finitely gener- for exchange graphs ated Gorenstein projective) modules over a noethe- rian ring, Pierre-Guy Plamondon • the category of special Cohen–Macaulay modules University of Paris-Sud, France over a rational surface singularity. [email protected] In this talk, we give a systematic generalization of this Cluster categories are triangulated categories that have fact over a Cohen–Macaulay ring. More precisely, we been used to study S.Fomin and A.Zelevinsky’s cluster al- study certain full subcategories of finitely generated mod- gebras. They come equipped with special objects, called ules, and investigate when they are exact categories with cluster-tilting objects, that are obtained from one another enough projectives and enough injectives. This talk is by a process called mutation; this gives rise to an ex- based on joint work with Osamu Iyama. change graph. In this talk, we will study properties of this exchange graph, and see how it is related to the ex- change graph of a cluster algebra. We will then apply Toward repetitive equivalences 47 PRIMA 2013 Abstracts

Jiaqun Wei 4 Contributed Talks Nanjing Normal University, China [email protected] Contributed Talks Group 1 Geometry and Analysis

We say two artin algebras R and S are repetitive equiv- ∗ alent provided that their repetitive algebras are stably Bounded operators on Hilbert C -modules equivalent. By Happel’s result, repetitive equivalences between artin algebras of finite globe dimension imply derived equivalences. On the other hand, by results of Massoud Amini Rickard, Chen etc., if two artin algebras are derived equiv- Institute for Research in Fundamental Sciences, Iran alent, then their repeptitive algebras are derived equiva- [email protected] lent, and hence stably equivalent. Thus, repetitive equiv- alences are more general than derived equivalences. The ∗ paper will suggest a way teward the Morita theory of We study the problem of amenability for the C -algebra repetitive equivalences. B(E) of bounded operators in a Hilbert C∗-module E on a C∗-algebra A. When A is a von Neumann algebra and E is full and self dual, we show that B(E) is amenable Some results related to Poisson (co)homology (nuclear) if and only if A is injective and E is finitely generated. We find similar results for the case where A is a C∗-algebra and E is weakly self dual. We briefly study Quanshui Wu the predual and type theory of B(E) when it is a von Fudan University, China Neumann algebra. This is a joint work with M. Bagher [email protected] Asadi.

Poisson (co)homologies of some Poisson polynomial alge- Gromov-Hausdorff hyperspaces of Rn bras are used to calculate the Hochschild (co)homologies of some Artin-Schelter regular algebras recently. In this talk, I will concentrate on some recent work on Poisson Sergey Antonyan (co)homologies. National University of Mexico, Mexico [email protected] Rigid morphisms, exact pairs and applications The Gromov-Hausdorff distance dGH was introduced in 1981 by M. Gromov. It turns the set GH of all isome- try classes of compact metric spaces into a metric space. Changchang Xi For two compact metric spaces X and Y the number Capital Normal University, China dGH (X,Y ) is defined to be the infimum of all Haus- [email protected] dorff distances dH (i(X), j(Y )) for all metric spaces M and all isometric embeddings i : X → M and j : Y → M. In this talk, we shall introduce relatively exact pairs Clearly, the Gromov-Hausdorff distance between isomet- of ring homomorphisms, define non-commutative tensor ric spaces is zero; it is a metric on the set GH of isom- products over such pairs, which generalize the usual no- etry classes of compact metric spaces. The metric space tion of tensor products over commutative rings, and con- (GH, dGH) is called the Gromov-Hausdorff hyperspace. It struct recollements of derived module categories of rings is a challenging open problem to understand the topolog- involving those non-commutative tensor products. This ical structure of this metric space. The talk contributes consideration is then used to understand the relationship n of finitistic dimensions and algebraic K-theory of rings in towards this problem. We denote by GH(R ) the sub- a recollement. space of GH consisting of the classes [E] whose repre- sentative E is a metric subspace of Rn. We are inter- The content of this talk is taken from a joint work with n Hongxing Chen at CNU. ested in the Gromov-Hausdorff hyperspaces GH(R ) and GH(Rn, d) = {X ∈ GH(Rn) | diam X ≤ d}, d > 0. In particular, we will prove that GH(Rn) is homeomorphic T -structures and torsion pairs in a 2−Calabi- to the Hilbert cube with a removed point. Yau triangulated category

Bin Zhu Developments of harmonic maps into bihar- Tsinghua University, China monic maps [email protected] Yuan-Jen Chiang For an indecomposable 2−Calabi-Yau triangulated cat- University of Mary Washington, Virginia, USA egory C with a cluster tilting object, we prove that [email protected] there are no non-trivial t-structures or non-trivial co-t- structures in C. This allows us to give a classification of Harmonic maps between Riemannian manifolds was first torsion pairs in this triangulated category C. Furthermore we determine the hearts of torsion pairs in the sense of established by Eells and Sampson [11] (Chiang’s PhD Nakaoka: They are equivalent to the module categories advisor) in 1964. Biharmonic maps (generalizing har- over the endomorphism algebras of the cores of the tor- monic maps) were first studied by Jiang [12]–[14] in 1986. sion pairs. We present an overview of the developments of harmonic This is a joint work with Yu Zhou. maps into biharmonic maps based on [1]–[10]. We first discuss the developments of harmonic maps on crucial topics including regularity, maps of surfaces, maps into K¨ahler manifolds, maps into groups and Grassmanni- ans, loop groups and integrable systems, harmonic mor- phisms, maps of singular spaces, and transversally har- monic maps. We then present the developments of bihar- monic maps on topics including Riemannian immersions and submersions, conformally biharmonic maps, bihar- monic morphisms, biharmonic homogeneous real hyper- surfaces, regularity, transversally biharmonic maps, con- servation law, and biharmonic maps into Lie groups and integrable systems. 48 PRIMA 2013 Abstracts

[1] Y.-J. Chiang, Developments of harmonic maps, Xiaobin Li wave maps and Yang-Mills fields into biharmonic Southwest Jiaotong University, China maps, biwave maps and bi-Yang-Mills fields, Birkh¨auser, [email protected] Springer, Basel, in the series of “Frontiers in Mathemat- ics," XXII+399, 2013, in press. [2] Y. J. Chiang, Harmonic maps of V-manifolds, Ann. The study of the moduli space plays an important role in enumerative geometry, symplectic geometry and math- Global Anal. and Geom., Vol. 8 (1990), no. 3, 315–344. 1 0 [3] Y.-J. Chiang, Spectral geometry of V-manifolds and ematical physics. Given X = [P /Zr] and let x = its applications to harmonic maps, Proc. Symp. Pure ([0]a, [∞]b) be the 2-tuple of twisted sectors on X. In Math., Amer. Math. Soc., Vol. 54 (1993), Part 1, 93-99. this talk, we construct two different compactifications of 1 0 [4] Y.-J. Chiang, f-biharmonic maps between Riemannian the moduli space M0,2(X, d[P /Zr], x ): Nonlinear Sigma manifolds, J. of Geom. and Symmetry in Physics, Vol. x0 x0 Model Md and Linear Sigma Model Nd . Relations be- 0 0 27 (2012), 45–58. tween M x and N x are studied and a new gluing recur- [5] Y. J. Chiang, Harmonic and biharmonic maps of Rie- d d x0 mann surfaces, Global J. of Pure and Applied Math., Vol. sive relation on Nd is discussed. 9 (2013), no. 2, 109-124. [6] Y.-J. Chiang and A. Ratto, Harmonic maps on spaces with conical singularities, Bull. Soc. Math. France, Vol. Cb-frames and the completely bounded ap- 120 (1992), no. 3, 251–262. proximation property for operator spaces [7] Y.-J. Chiang and H. Sun, 2-harmonic totally real submanifolds in a complex projective space, Bull. Inst. Rui Liu Math. Acad. Sinica, Vol. 27 (1999), no. 2, 99–107. Nankai University, China [8] Y.-J. Chiang and H. Sun, Biharmonic maps on V- [email protected] manifolds, Inter. J. Math. Math. Sci., Vol. 27 (2001), no. 8, 477–484. [9] Y.-J. Chiang and R. Wolak, Transversally biharmonic We introduce the concept of cb-frames for operator maps between foliated Riemannian manifolds, Internat. spaces, and give characterizations of completely comple- J. of Math., Vol. 19 (2008), no. 8, 981–996. mented subspaces of operator spaces with cb-bases. We apply the results to discrete group C∗-algebras. In par- [10] Y.-J. Chiang and R. Wolak, Transversally f-harmonic ticular, we show that there is a natural cb-frame for the and transversally f-biharmonic maps between foliated reduced free group C∗-algebra C∗(F ) of n-generators Riemannian manifolds, JP J. of Geom. and Top., Vol. r n which is derived from the infinite convex decomposition 13 (2013), no. 1, 93–117. of the biorthogonal system (λ , δ ) . We show that [11] J. Eells and J. H. Sampson, Harmonic mappings s s s∈Fn there is a separable Hilbert operator space which can not of Riemannian manifolds, Amer. J. of Math., Vol. 86 be a subspace of an operator space with a cb-basis, then (1964), 109–160. we introduce a natural question to ask for an essential [12] G. Y. Jiang, 2-harmonic maps and their first and characterization of subspaces of operator spaces with cb- second variational formulas Annals of Math., China, Ser. bases. A7 (1986), no. 4, 389-402. This is joint work with Zhong-Jin Ruan. [13] G. Y. Jiang, 2-harmonic isometric immersions be- tween Riemannian manifolds, Annals of Math., China, Ser. A7 (1986), no. 2, 130-144. Some inequalities for unitarily invariant [14] G. Y. Jiang, The conservation law of biharmonic norms maps between Riemannian manifolds, Acta Math. Sinica, Vol. 30 (1987), no. 2, 220–225. Jagjit Singh Matharu Guru Nanak Dev University, India Hamiltonian group of self product [email protected]

Shengda Hu We shall prove the inequalities Wilfrid Laurier University, Canada ∗ ∗ ∗ ∗ [email protected] |||(A+B)(A+B) |||≤|||AA +BB +2AB ||| ≤|||(A−B)(A−B)∗+4AB∗||| Let (X, ω) be a symplectic manifold and consider the self product (M, Ω) = (X × X, ω ⊕ −ω). We consider for all n × n complex matrices A, B and all unitarily in- the Hamiltonian groups Ham(X, ω) × Ham(X, −ω) and variant norms |||·|||. If furhter A, B are Hermitian positive Ham(M, Ω). There is a natural inclusion from the first definite it is proved that group into the second. We give an example where the inclusion map induces a proper inclusion of the funda- k k Y Y 1−α α 1 ≤ k ≤ n, mental groups. This is joint work with F. Lalonde. λj (A]αB) ≤ λj (A B ), 0 ≤ α ≤ 1, j=1 j=1 A McShane-type identity for closed surfaces where ]α denotes the operator means considered by Kubo and Ando and λj (X), 1 ≤ j ≤ n, denote the eigenvalues Yi Huang of X arranged in the decreasing order whenever these The University of Melbourne, Australia all are real. A number of inequalities are obtained as [email protected] applications.

We prove a McShane-type identity— a series, expressed in terms of geodesic lengths, that sums to 2π for any On automorphism groups of Hua domains closed hyperbolic surface with one distinguished point. To do so, we prove a generalized Birman-Series theorem Feng Rong showing that the set of complete geodesics on a hyperbolic Shanghai Jiao Tong University, China surface with large cone-angles is sparse. [email protected]

A new gluing recursive relation for Linear Hua domains are the generalization of Cartan-Hartogs Sigma Model of P 1-orbifold domains, which were introduced by Weiping Yin around 49 PRIMA 2013 Abstracts

the end of 20th century (named after Chinese mathemati- New heat kernel estimates on manifolds with cian Luogeng Hua). We will first give a brief introduction negative Ricci curvature lower bound to Hua domains, and then give a complete description of their automorphism groups. Xiangjin Xu Binghamton University, USA [email protected] Weighted harmonic spaces

Apply the new Li-Yau type Harnack estimates for the ∗ Luis Manuel Tovar Sánchez , Lino Feliciano Reséndis heat equations on manifolds with Ric(M) ≥ −K, K ≥ 0, ∗ National Polytechnic Institute, Mexico which established by Junfang Li and the author [Advance [email protected] in Mathematics 226(5) (2011), 4456-4491], I prove a new upper bound estimate for the heat kernel H(x, y, t) of In 1994, R. Aulaskari and Peter Lappan introduced the manifolds with Ric(M) ≥ −K, Qp spaces p > 0, of analytic functions defined in the unit disk of the complex plane. Considering that ana- −1/2 −1/2 H(x, y, t) ≤ AK (t)Vx (δ(t))Vy (δ(t)) lytic functions f(z) = u(x, y) + iv(x, y) consist of a pair  2  of harmonic conjugate functions, in this paper we con- d (x, y) 2 · exp − + [1 + d (x, y)]BK (t) , sider weighted harmonic spaces, consisting of real har- 4t monic functions defined in the unit disk of the plane. We study their basic properties and relationships with some where A (t),B (t) : [0, ∞) → [0, ∞) are bounded func- other weighted function spaces. K K tions, and δ(t) ∼ t as t → 0 and δ(t) ∼ 1 as t → ∞. While in the seminal work of Li-Yau [Acta Math. 156 Variable equation of state for a dark energy (1986) 153-201.], the heat kernel upper bound estimates model with linearly varying deceleration pa- had δ-loss: rameter −1/2 √ −1/2 √ H(x, y, t) ≤C(δ, n)Vx ( t)Vy ( t) Ming Shen  d2(x, y)  · exp − + C1δKt , Fuzhou University, China (4 + δ)t [email protected]   where constant C(δ, n) ∼ exp c1 as δ → 0, due that We present a dark energy model in an inhomogeneous δ plane symmetric space-time by considering a linearly there was non-sharp Harnack estimates on manifolds with varying deceleration parameter. In the model, the equa- Ric(M) ≥ −K. tion of state (EoS) parameter ω is found to be time depen- dent. For different cosmic times, we obtain quintessence, vacuum energy and phantom fluid dominated universe. The universe we described has finite lifetime and ends Contributed Talks Group 2 with a big-rip which is a result consistent with recent Algebra and Number Theory cosmological observations. Universal objects for free G-spaces Diversities and the geometry of hypergraphs Natella Antonyan Monterrey Institute of Technology, Mexico Paul Tupper, David Bryant [email protected] Simon Fraser University, Canada [email protected] Throughout G is assumed to be a compact Lie group. A G-space U is called universal for a given class of G- There are well-known connections between certain combi- spaces G-P, if U ∈ G-P and U contains as a G-subspace natorial optimization problems and the geometry of met- a G-homeomorphic copy of any G-space X from the class ric embeddings of graphs. Instead of metrics, we con- G-P. sider diversities, which are a generalization of the con- In this talk we shall present universal G-spaces in the class cept of metrics to functions of finite sets of points, rather of all paracompact (respectively, metrizable, and separa- than just pairs of points. We show that analogous to the relation between flow problems and combinatorial opti- ble metrizable) free G-spaces. Recall that for a G-space mization in graphs, there are intimate relations between X and a point x ∈ X the stabilizer (or stationary sub- diversities and a different set of flow problems, including group) of x is defined by Gx = {g ∈ G | gx = x}. If fractional Steiner tree packing and optimal flows in hyper- Gx = {e} for all x ∈ X then we say that the action of graphs. We discuss polynomial approximation algorithms G is free and X is a free G-space. Denote by Cone G that would result from a effective theory of embedding di- the cone over G endowed with the natural action of G in- versities into `1. duced by left translations. Let J∞(G) be the infinite join G ∗ G ∗ ... ; it is just the subset of the countable product ∞ (Cone G) consisting of all those points (t1g1, t2g2,... ) P∞ On the potential function of gradient steady for which only a finite number of ti 6= 0 and i=1 ti = 1. Ricci solitons We let G act coordinate-wise on J∞(G). Denote by I the unit interval [0, 1] and by Iτ the Tychonoff cube of a Peng Wu given infinite weight τ endowed with the trivial action of G. Cornell University, USA We prove that for every infinite cardinal number τ, the [email protected] τ product J∞(G) × I is universal in the class of all para- compact free G-spaces of weight ≤ τ. A similar result for We prove that the infimum of the potential function of metrizable free G-spaces of weight ≤ τ is also obtained. a gradient steady Ricci soliton decays linearly. As conse- quences, a gradient steady Ricci soliton with bounded po- tential function must be Ricci-flat, and no gradient steady Categorification in topology, geometry and Ricci soliton admits uniformly positive scalar curvature. combinatorics 50 PRIMA 2013 Abstracts

Igor Baković L-functions are equal through the local Langlands cor- University of Warsaw, Poland respondence. If it is, we can use the properties of local [email protected] L-functions from arithmetic side to study local L-packet, the object in the analytic side, which is the set of irre- ducible admissible representations of quasi split group G Categorification become an essential tool in many areas of over p-adic field. The equality of local L-functions has modern mathematics. By generalizing algebraic concepts an interesting application in proving the generic Arthur from the classical set theory to the context of higher cat- L-packet conjecture. The generic Arthur L-packet con- egory theory, a program of higher dimensional algebra is jecture states that if the L-packet attached to Arthur pa- initiated as an attempt to unify quantum field theory with rameter has a generic member, then it is tempered. This traditional algebraic topology. The purpose of the talk is conjecture can be considered as local version of general- to reflect on one of the central themes of Grothendieck’s ized Ramanujan conjecture. In this talk, I will explain work about the deep relation between topos theory and those in the case of split GSpin groups. Furthermore, I homotopy theory, where he emphasized the importance will explain the classification of strongly positive discrete of the sheaf theoretical objects corresponding to higher series representations of GSpin groups over p-adic field categorical structures. Such sheaf-theoretical and coho- which is one of the main tools in the proof of the equality mological structures associated to higher categories are of L-functions. If time permits, I will explain the gener- ubiquitous in many areas of mathematics like (algebraic) alized Ramanujan conjecture for GSpin groups. topology, geometry and combinatorics. We will shed more light on author’s work on fibrations of bicategories, stem- ing from mostly unpublished work by Bénabou, in his Derived equivalences and Gorenstein dimen- investigations of logical aspects of fibred categories, and sion his attempt to give foundations of naive category theory by using fibred categories. We will briefly describe the- ory of 2-fibrations, Grothendieck construction for bicat- Hirotaka Koga egories, fibered bicategorical Yoneda lemma and homo- University of Tsukuba, Japan topy theoretic view of 2-fibrations, connecting the whole [email protected] theory to Lurie’s cartesian fibrations. Finally, we relate the 2-dimensional fibrations with Joyal theory of species of structures in combinatorics. The basis for this con- A ring A is said to be left (resp., right) coherent if every nection is Zawadowski’s interpretation of amalgamated finitely generated left (resp., right) ideal of it is finitely signatures by means of lax monidal fibrations of cate- presented (see [3]). Let A, B be derived equivalent left gories. By categorifying the latter notion, we describe lax monoidal fibrations of bicategories as a natural orga- and right coherent rings (see [5]). In [4] Kato showed nizational tool for categorified signatures which appear in that a standard derived equivalence induces an equiva- a work of Cheng and Hermida, Makkai and Power, and lence between the triangulated categories consisting of which consequently give a basis for generalized species of complexes of finite Gorenstein dimension and that a de- structures. rived equivalence induces an equivalence between the pro- jectively stable categories of modules of Gorenstein di- mension zero (see [1] and [2]) if either inj dim A < ∞ Realising Galois groups via Galois represen- or inj dim Aop < ∞. In this talk, we provide alterna- tations tive proofs of these results from another point of view. Also, we do not assume the existence of standard derived equivalence or finiteness of selfinjective dimension. Shuvra Gupta University of Iowa, USA [email protected] [1] M. Auslander and M. Bridger, Stable module theory, Mem. Amer. Math. Soc., 94, Amer. Math. Soc., Providence, R.I., 1969. Gabor Wiese first realised families of finite simple groups [2] R.-O. Buchweitz, Maximal Cohen-Macaulay mod- as Galois groups over the field of rational numbers, Q, ules and Tate-cohomology over Gorenstein rings by controlling the images of certain Galois representa- (1987), 155, unpublished manuscript, available at tions. Since then, Galois representations have been used https://tspace.library.utoronto.ca/handle/1807/16682. to realise various other families of finite simple groups as [3] S. U. Chase, Direct products of modules, Trans. Galois groups over Q. We will discuss results which en- Amer. Math. Soc. 97 (1960), 457–473. able us to realise some new families of finite simple groups [4] Y. Kato, On derived equivalent coherent rings, and new techniques which enable us to realise non-simple Comm. Algebra 30 (2002), no. 9, 4437–4454. finite groups as Galois groups over Q. Some of this work is joint work and still in progress. [5] J. Rickard, Morita theory for derived categories, J. London Math. Soc. (2) 39 (1989), no. 3, 436–456.

L-functions from Langlands-Shahidi method for GSpin groups and the generic Arthur L- A generalized Koszul theory packet conjecture Liping Li Yeansu Kim University of California, Riverside, USA [email protected] Purdue University, USA [email protected] Let A be a positively graded, locally finite k-algebra where A0 is a finite-dimensional algebra whose finitistic L-functions are very interesting tools that number theo- dimension is 0. In this talk we introduce a generalized rists have been using since 18th century. Those also ap- Koszul theory preserving many classical results, and de- pear in the local Langlands conjecture. Briefly, the local scribe an explicit correspondence between this generalized Langlands conjecture asserts that there exists a ‘natural’ theory and the classical theory. Applications in repre- bijection between two different sets of objects: Arith- sentations of certain categories and extension algebras of metic (Galois or Weil-Deligne) side and analytic (rep- standard modules of standardly stratified algebras will be resentation theoretic) side. In each side, we can define described if time allows. the L-functions of those objects. The L-functions from analytic side are defined by Shahidi (Langlands-Shahidi method) and the L-functions from arithmetic side are On symmetric association schemes with k1 = 3 Artin L-functions. The natural question is whether two and mi = 3 51 PRIMA 2013 Abstracts

Jongyook Park edges receive distinct colours. The minimum number of University of Science and Technology of China, China colours used by an edge colouring of G is a well known [email protected] and studied graph parameter called chromatic index and denoted by χ0(G). It was proved by Holyer in 1981 that computing χ0(G) is in general NP-hard. We consider a In 2006, Bannai and Bannai classified primitive symmet- variation of the edge colouring problem, which may be ric association schemes with m1 = 3. In their paper, the of interest for applications. Specifically, we consider edge hardest case was k1 = 3. Even though, (primitive) sym- colourings of G such that no colour is assigned to more metric association schemes with k1 = 3 were classified by than B edges, where B is a positive integer fixed in ad- Yamazaki in 1998, they avoided the use of the difficult vance (clearly such edge colourings always exist). We call and deep result of Yamazaki. In this talk, we generalize any such colouring a B-bounded edge colouring of G. The the result of Bannai and Bannai. minimum number of colours in a B-bounded edge colour- 0 ing of G is a graph parameter which we denote by χB (G) Triangulated categories from categories of and call B-bounded chromatic index.A B-bounded edge 0 specail exact squences colouring which uses exactly χB (G) colours is called an optimal B-bounded edge colouring of G. It is not difficult to see that, for every graph G, Keyan Song, Yuehui Zhang Shanghai Jiao Tong University, China |E(G)| [email protected] χ0 (G) = max{χ0(G), d e. B B

Let A be an artinian algebra over an algebraically closed 0 field k. Let F be the category consisting of all four-term This prompts the question of whether the parameter χB exact sequences in modA. Let C be the full subcategory of and an optimal B-bounded edge colouring can be com- F consisting of all exact sequences with two middle terms puted in polynomial time for a fixed value of B. Our projective modules in modA. It is proved that C is con- goal in this talk will be to answer this question in the travariantly finite. As applications, it is proved that C is a affirmative. This is joint work with Romeo Rizzi [1]. Frobenius category and has Auslander-Reiten sequences provided A is an selfinjective algebra. Furthermore, it is proved that the stable category C equals to C/H as factor [1] R. Rizzi and D. Cariolaro, Polynomial time complexity categories, where H is the set of all homotopic relations, of Edge Colouring Graphs with Bounded Colour Classes, and they are both equivalent to the stable category modA. Algorithmica (2013), in press, doi: 10.1007/s00453-013- An interesting result is that these three categories C, C/H 9746-7. and modA are equivalent as triangulated categories. Realizing joint degree matrices Contributed Talks Group 3 Discrete Mathematics Aaron Dutle University of South Carolina, USA Numerical verification method for well condi- [email protected] tioned spherical t-designs The Joint Degree Matrix of a graph is a matrix whose Congpei An (i, j) entry is the number of edges connecting vertices of Jinan University, China degree i to vertices of degree j. A given matrix is called [email protected] realizable if it is the joint degree matrix of a simple graph. As in the case of degree sequences, there is a simple set of conditions for when a matrix is realizable, as well as an A set XN of N points on the unit sphere is a spherical t-design if the average value of any polynomial of degree operation that can be used to transform any realization into any other realization. We discuss these problems, at most t over XN is equal to the average value of the polynomial over the sphere. In this talk, we focus on the as well as the extremal question of when a joint degree computational construction of spherical t-designs on the matrix is uniquely realizable. 2 3 2 unit sphere S ⊂ R when N ≥ (t + 1) , the dimension of the space Pt of spherical polynomials of degree at most t. We show how to construct well conditioned spherical Generalization of Legendre polynomials the- designs with N ≥ (t+1)2 points by maximizing the deter- ory minant of a matrix while satisfying a system of nonlinear constraints for 1 ≤ t ≤ 100. Interval methods are then used to prove the existence of a true spherical t-design Lemin Gu very close to the calculated points and to provide a guar- Tongji University, China anteed interval containing the determinant. The resulting [email protected] spherical designs have good geometrical properties (sepa- ration and mesh norm). We discuss some open problems In all of n-order polynomials that highest coefficient on the distribution of point set over the sphere. is 1čňLegendre polynomials are in the interval [−1, 1] This is a joint work with X.Chen, I. H. Sloan and R. S. with the least square error of zero polynomials, that for Womersley. P n(x) = xn + a(n − 1)xn−1 + ... + a1x + a0, making R [P n(x)]2dx = min. Promotes the Legendre multinomi- Edge colouring graphs with bounded colour albasic principle: In all of n-order polynomials that high- classes est coefficient is not 1, namely an 6= 1,there must be a new polynomials Gn(x) = xn + a(n − 1)xn−1 + ... + a1x + a0, making R [Gn(x)]2dx = min. Through discussion of the David Cariolaro square error minimization, leads to the new polynomi- Xi’an Jiaotong-Liverpool University, China als establishment necessity. For convenient on elabora- [email protected] tion in this abstract,called it "Gn(x) polynomial" (Gen- eralization of Legendre polynomial). First the existence An edge colouring of a graph G is a function which assigns of Gn(x) polynomials issues are studied: By establishing a colour to each edge of G in such a way that adjacent Gn(x) equation the ordinary solution expressions in the 52 PRIMA 2013 Abstracts

interval |x| < 1 are given, have proven that when n is pos- on the existence of µ-way k-homogeneous Latin trades, itive integer and the interval is in |x| ≤ 1, two linear inde- including three new constructions that complete the 3- pendence special solutions of them are Gn(x) polynomi- way k-homogeneous Latin trade spectrum for all but a als, and provide the general term expression; Second, the handful of values. We will also provide the directions for geometric meaning of Gn(x) polynomials are discussed, further research motivated by this work. have proven that Gn(x)polynomials are the polynomials that in [−1, 1] with the error squares value are the least; On the fractional metric dimension of tree Third, the main properties of Gn(x) polynomials are in- graphs troducedčňwhich including Gn(x)polynomials recurrence formula, the orthogonality, the odevity, the squares value area, the former n=9 polynomials, the corresponding ge- Suhadi Wido Saputro ometry, and so on. Last, some special applications of Institut Teknologi Bandung, Indonesia Gn(x) polynomials under different boundary conditions [email protected] are given: Combined with the best Chebyshev approxi- mation theory they can constitute maximum error min- imizing least square approximation; Combined with the Let G be a finite, simple, and connected graph. The dis- Least Absolute Deviation approximation theory can con- tance between any two vertices u, v ∈ V (G), denoted by stitute zero error type least square approximation; Under d (u, v), is the length of a shortest (u − v) path in G. the conditions of an=1 form the Legendre polynomial,and G so on. A vertex x ∈ V (G) is called resolve a pair {u, v} of ver- tices of G if dG(u, x) 6= dG(v, x). For u, v ∈ V (G), the set of all vertices which resolve the pair {u, v} is denoted The subsets counting problems and their ap- by RG{u, v}. A real value function g : V (G) → [0, 1] plications is called a resolving function of G if g(RG{u, v}) ≥ 1 for any two distinct vertices u, v ∈ V (G). The frac- Jiyou Li tional metric dimension, denoted by dimf (G), is given Shanghai Jiao Tong University, China by dimf (G) = min{|g| : g is a resolving function of G}, [email protected] where |g| = g(V (G)). In this paper, we determine the fractional metric dimension for tree graph Tn of order n ≥ 3. Let G be an abelian group and D be a finite subset of G. Denote N(b) to be the number of subsets S in D such that P x∈S x = b and Nk(b) to be the number of k-subsets S Unimodality of genus distribution of ladders P in D such that x∈S x = b. When G is the set of inte- gers, the decision version of the subset sum problem, i.e., determining if N(b) > 0, is a well-known NP-complete Liangxia Wan problem. And its counting version, the explicit enumer- Beijing Jiaotong University, China [email protected] ation of N(b) or Nk(b), is a #P-complete problem. In this talk, we will investigate these problems from a math- ematical point of view, and introduce their relations to additive combinatorics, coding theory and computer sci- Given a graph,its genus distribution is unimodal? As ences. though many results about genus distribution of graphs have obtained, there are only several those about uni- modality of genus distribution of graphs. In this talk, Paths and cycles of interval graphs unimodality of genus distri- bution of some graphs are verified. Peng Li Shanghai Jiao Tong University, China The lit-only σ-game [email protected]

Ziqing Xiang We recently find a linear time algorithm for solving the 1- Fixed-Endpoint Path Cover Problem on interval graphs. Shanghai Jiao Tong University, China The design and the analysis of this algorithm motivate [email protected] us to develop many properties on the paths and cycles of interval graphs and graphs. In this short presentation, we Let G be a finite graph with vertex set V which may not report a series of equivalent characterizations of Hamil- V tonian connectedness and other path/cycle properties of necessarily be loopless. For each v ∈ V , let αv ∈ F2 be interval graphs. the map which takes value 1 on w ∈ V if and only if there is an edge between v and w in G; let Tv be the linear map This is joint work with Yaokun Wu. V V on F2 that sends x ∈ F2 to itself if x(v) = 0 and sends V x ∈ F2 to x + αv if x(v) = 1. Note that Tv is a transvec- The spectrum of 3-way k-homogeneous Latin tion when v is not a loop in G while Tv is an idempotent trades when v is a loop in G. We consider the digraph Γ with V V vertex set F2 and arc set {(x, Tv(x): x ∈ F2 , v ∈ V }, which is the phase space of the lit-only σ-game on G. Trent G. Marbach We determine the reachability relation for the digraph Γ. The University of Queensland, Australia V [email protected] A surprising corollary of this work is that, for α, β ∈ F2 , basically, α can reach β in Γ if and only if α − β lies in the binary linear subspace spanned by {αv : v ∈ V }. The theory of Latin trades has a deep and interesting An important step of our work is to define the line graph structure, with connections to permutation groups, geom- of a multigraph and to provide a forbidden subgraph char- etry and topology. The study of µ-way k-homogeneous acterization. If the graph G is loopless, as an application Latin trades has received attention recently. The efforts of our knowledge of the corresponding digraph Γ, we are of five publications completed the spectrum of the or- able to determine the multiplicative group generated by ders of 2-way k-homogeneous Latin trades. This was fol- {Tv : v ∈ V }. We also indicate possible approaches on lowed by a recent paper (Bagheri Gh., et al. 2012), which extending the work here to the general case of G being a focused particularly on the 3-way k-homogeneous Latin digraph. trades with k ≤ 15. In this talk, I will give a brief report This is joint work with Yaokun Wu. 53 PRIMA 2013 Abstracts

Pancyclicity of 4-connected {K1,3,Z8}-free with first order absorbing boundary condition in two and graphs three dimensions. We prove that the proposed HDG methods are stable (hence well-posed) without any mesh constraint. The stability constant is independent of the Hong-Jian Lai, Mingquan Zhan, Taoye Zhang, and Ju polynomial degree. By using a projection-based error Zhou analysis, we also derive the error estimates in L2 norm for Kutztown University of Pennsylvania, USA piecewise polynomial spaces with arbitrary degree. This [email protected] is joint work with Wujun Zhang from University of Mary- land. A graph G is said to be pancyclic if G contains cycles of lengths from 3 to |V (G)|. In this paper, we show that An Uzawa method for solving steady Navier- every 4-connected claw-free Z8-free graph is either pan- Stokes equations discretized by mixed ele- cyclic or is the line graph of the Petersen graph. This ment methods implies that every 4-connected claw-free Z6-free graph is pancyclic, and every 5-connected claw-free Z8-free graph is pancyclic. Jianguo Huang Shanghai Jiao Tong University, China [email protected] The number of subtrees of a tree Numerical solutions of Navier-Stokes equations play fun- Xiao-Dong Zhang damental roles in scientific computing and fluid dynam- Shanghai Jiao Tong University, P.R. China ics. The need to do this frequently occurs in many ap- [email protected] plied sciences. Mixed element methods are widely used for discretizing steady Navier-Stokes equations in applica- In this talk, we consider how to determine the maximum tions. However, it is challenging to devise fast solvers for and minimum number of subtrees a tree with a given the resulting nonlinear system. A typical solver involves degree tree sequence. It is proven that the greedy tree numerical solution of the discretized Oseen equations at among all trees with the same degree sequence has the each iteration step; or equivalently, a non-symmetric sad- maximum number subtrees, while it is tough to determine dle point system must be solved at each iteration step. which tree has minimum number of subtrees. This work is However, it is by no means trivial to solve such a sub- joined with Daniel Gray, Hua Wang, and Xiu-Mei Zhang. problem efficiently. In this talk, we are going to design an Uzawa-type itera- tive method for the previous nonlinear system, for which we require to solve no saddle point system at each itera- Contributed Talks Group 4 tion step. Under some reasonable conditions, we prove its Computational Mathematics & Optimization convergence rate is independent of the finite element mesh size h, even for the shape regular triangulation. Finally, A semidefinite approximation for symmetric we provide a series of numerical experiments to show the travelling salesman polytopes accuracy and performance of the method proposed. This is a joint work with Puyin Chen and Huashan Sheng.

Julián Ariel Romero Barbosa University of los Andes, Colombia Semi-classical limit for the Schrödinger equa- [email protected] tion with lattice potential, and band-crossing

In this talk we will present a positive semidefinite approx- Qin Li imation of compact convex sets introduced by A. Barvi- University of Wisconsin-Madison, USA nok and E. Veomett [1]. In particular we will discuss [email protected] the behaviour of this relaxation when the convex sets to be approximated are the Traveling Salesman Polytopes Tn and Tn,n associated to the complete graphs Kn and In this talk, I am going to present the derivation of the Kn,n respectively. E. Veomett has shown that the scal- semi-classical limit of the Schrödinger equation with lat- ing of the k−th approximation by n/k + O(1/n) contains tice potential, where the lattice constant and the Planck the polytope Tn for k ≤ bn/2e . Here, we will show constant are at the same order. Bloch theory is used to that these metric bounds can be improved by a factor of decompose the solution into eigenfunctions. Here we en- 1 q k−1 2 counter two problems: 1. eigenvalues degenerate, when n + for the case when n is even. Finally, we this happens one cannot distinguish the associated eigen- 3 2 −1 3 will show new metric bounds for the approximation of functions, and the so called transition rate between en- the polytope Tn,n. ergy bands should be introduced; 2. the evolution of the projection coefficients follow a coupled integro-differential This results are joint work with M. Velasco and are part equation, which can be hard to compute. By carrying of my master’s dissertation at the University of los Andes. out the Wigner transformation of all the Bloch bands, we find a complete basis on the phase space. The coef- [1] Veomett, Ellen. A positive semidefinite approximation ficients for them are controlled by a simple hyperbolic of the symmetric traveling salesman polytope. Discrete equation, and the transition rates at the point of the degeneracy are characterized explicitly. A domain de- Comput. Geom. 38 (2007), no. 1, 15-28. composition method based on the distances between en- ergy bands is designed associated to this newly developed model. This is a joint work with Lihui Chai and Shi Jin. An analysis of HDG methods for the Helmholtz equation Legendre pseudospectral method for solving Jintao Cui three-dimensional non-linear hyperbolic par- University of Arkansas at Little Rock, USA tial differential equations [email protected] Abdur Rashid In this talk we discuss the hybridizable discontinuous Gomal University, Pakistan Galerkin (HDG) methods for the Helmholtz equation [email protected] 54 PRIMA 2013 Abstracts

In this talk, numerical solutions of three-space non-linear deal with the incompressible fluid-compressible structure hyperbolic partial differential equations will be presented interaction problem with fictitious domain approach. by using Legendre pseudospectral method. The dis- In the second approach-phase field formulation, the de- cretization of the spatial derivatives of the problem have rived full Eulerian FSI model effectively demonstrates the been solved by using Legendre pseudospectral method. A interaction between fluid flow and solid structure in terms system of non-linear ordinary differential equations is gen- of an uniform system of governing equations defined in a erated. The values of unknown function u can be found single domain, thus the computational grid is fixed, and by using kronecker product. The representation of this the re-meshing and interpolation techniques which are al- kind of product can easily be extended to higher dimen- ways required by other FSI modeling approaches are no sions. The numerical results are obtained and compare longer needed here. A stabilized solution skill is devel- with exact solutions to validate the high precision of the oped to effectively solve the Euler equation which is es- Legendre pseudospectral method [1-6]. sentially the Eulerian description of solid motion for the incompressible hyperelastic material. Numerical experi- ment is carried out for a cross spinning around its central Efficient duality method to a class of global axis due to the passing flow field, and the numerical re- optimizations problems with nonconvex ob- sults dramatically show the spinning motion of the cross jective function due to the interaction with the fluid, showing that our model and numerical methods are effective to simulate the dynamic fluid-structure interaction phenomena. Ning Ruan University of Ballarat, Australia [email protected] Linear numerical schemes for epitaxial thin film growth model In this talk, the speaker presents a comprehensive re- view and some important developments on the canonical duality theory for solving a broad classes of minimiza- Cheng Wang tion problem with nonconvex objective function. These University of Massachusetts Dartmouth, USA problems arise in many real-world applications. By using [email protected] the canonical dual transformation, the nonconvex primal problem can be converted into a canonical dual problem A few linear schemes for nonlinear PDE model of thin (i.e., either a concave maximization or a convex minimiza- film growth model without slope selection are presented tion problem) with zero duality gap. The idea and the in the talk. In the first order linear scheme, the idea of method presented in this talk can be generalized to solve convex-concave decomposition of the energy functional is many other difficult problems in nonconvex mechanics, applied, and the particular decomposition places the non- network communication, and scientific computations. linear term in the concave part of the energy, in contrast to a standard convexity splitting scheme. As a result, the numerical scheme is fully linear at each time step Math and gaming and unconditionally solvable, and an unconditional en- ergy stability is guaranteed by the convexity splitting na- ture of the numerical scheme. To improve the numerical Xingzhong Shi accuracy, a second order temporal approximation for the Wenzhou-Kean University, China nonlinear term is recently reported, which preserves an [email protected] energy stability. To solve this highly non-trivial nonlin- ear system, a linear iteration algorithm is proposed, with an introduction of a second order artificial diffusion term. Math is indispensable and fundamental in computer video Moreover, a contraction mapping property is proved for games. Relationship between Math and game develop- such a linear iteration. As a result, the highly nonlinear ment is briefed. Computer video game classification, system can be decomposed as an iteration of purely lin- computer programming languages for creating computer ear solvers. Some numerical simulation results are also video games and some game API’s (Application Program- presented in the talk. ming Interfaces) and engines or libraries are introduced. Gaming elements related to Math are identified. The Cartesian coordinates in Math and the Screen Coordi- Application of MILP to solve complex nate System in gaming are compared. The "Dark GDK" Library is used to demonstrate how to draw basic shapes scheduling problems and create interactive video games. Sample C++ pro- grams and their results are shown for developing video Wei Weng games using "DarkGDK", from basic 2-D shapes to in- teractive video games. Waseda University, Japan [email protected]

Full Eulerian finite element methods for fluid- structure interaction problem in fictitious do- This talk describes the role of mixed integer linear pro- main and phase field approaches gramming (MILP) in solving scheduling problems in com- plex production processes such as reentrant flexible job shops (RFJS). We modeled such scheduling problems by Pengtao Sun using several different MILP models. The first model was University of Nevada Las Vegas, USA based on the traditional way of MILP modeling, which de- [email protected] notes the machines, workstations, jobs, operations, and the time slots that arrange the operations on each ma- chine. The second model improved the efficiency of the In this talk we will present a full Eulerian model for a dy- traditional design by reducing the variable for machines namic fluid-structure interaction (FSI) problem by means through the relationship between machines and opera- of Lagrange multiplier/fictitious domain approach and tions. The third model further and significantly reduced phase field formulation, and design its full Eulerian finite the computational complexity of the second model by element discretization and effective iterative method. In utilizing the relationship between jobs on the same ma- the fictitious domain approach, the fluid domain and com- chine to replace the role of time slots, which were com- putational mesh are fixed by extending the fluid to the monly used in previous studies. Accordingly, the im- structural domain, and the FSI interfacial conditions are proved model can obtain the solution for RFJS problems reinforced by Lagrange multiplier. Thus an interpolation with dozens of jobs whereas the traditional model, in most technique is needed to interpolate the fluid variables into cases, is unable to obtain even a feasible solution for the the structural domain. We also demonstrate a method to same problems. 55 PRIMA 2013 Abstracts

Efficient numerical method for boundary con- the problem of calculating areas and volumes when the ditions of kinetic equations axis is rotated, and use basic tools from geometry and linear algebra to formulate the corresponding definite in- tegrals. We present some insights as well as difficulties Chang Yang encountered in setting-up the integrals, and in evaluating Université Claude Bernard Lyon 1, France them analytically or numerically using graphing calcula- [email protected] tors or online math tools.

In this talk we present a new algorithm based on Carte- Inversion of geothermal heat flux in a thermo- sian mesh for the numerical approximation of the kinetic mechanically coupled Stokes ice sheet model models on complex geometry boundary. Due to the high dimensional property, numerical algorithms based on un- structured meshes for a complex geometry are not ap- Hongyu Zhu, Noemi Petra, Georg Stadler, Toby Isaac, propriate. Here we propose to adapt the inverse Lax- Omar Ghattas, Thomas J.R. Hughes Wendroff procedure, which was recently introduced for University of Texas at Austin, USA conservation laws [1], to the kinetic equations. We first [email protected] apply this algorithm for Boltzmann type operators (BGK, ES-BGK models) in 1D × 3D and 2D × 3D [2]. Then we extend a similar method to bacterial chemotaxis mod- Modeling the dynamics of polar ice sheets is critical for els [3], which is a coupling problem of kinetic equation projection of future sea level rise. Yet, there remain and parabolic equation. Numerical results illustrate the large uncertainties in the basal boundary conditions (e.g., accuracy properties of these algorithms. geothermal heat flux) of the ice sheet. Here we target the inversion of the basal geothermal heat flux using sur- face velocity measurements. The flow of ice sheets and [1] S. Tan and C.-W. Shu, Inverse Lax-Wendroff pro- glaciers is modeled as a sheer thinning, viscous incom- cedure for numerical boundary conditions of conserva- pressible fluid with temperature-dependent viscosity via tion laws, Journal of Computational Physics, 229 (2010), a thermomechanically coupled Stokes model. The inverse 8144-8166. problem is formulated as a nonlinear least-squares opti- [2] F. Filbet and C. Yang, Inverse Lax-Wendroff method mization problem with a cost functional that contains the for boundary conditions of Boltzmann equations, Journal misfit between surface velocity observations and model of Computational Physics, accepted. predictions and a Tikhonov regularization term to ren- [3] F. Filbet and C. Yang, Numerical Simulations of Ki- der the problem well-posed. We use an adjoint-based netic Models for chemotaxis, submitted. inexact Newton method for the solution of this least squares optimization problem. Results for 2-D and 3-D model problems demonstrate the ability of inverting for a MD simulations for motions of evaporative smoothly varying geothermal heat flux in cold ice regions. droplets driven by thermal gradients This capability will be incorporated into a state-of-the-art continental-scale ice sheet dynamics model.

Congmin Wu Xiamen University, China Modelling of temperature and pricing [email protected] weather derivatives: a comparison for mainland China The driving mechanism of fluid transport at nanoscale is one of the key problems on the design of micro- and Manuela Ender, Lu Zong nanofluidic devices. We performed molecular dynamics Xi’an Jiaotong-Liverpool University, China simulations to study the motions of evaporative droplets [email protected] driven by thermal gradients along nanochannels. The ef- fect of droplet size and the effect of the co-existent fluid temperature on the motions of droplets are investigated. Temperature-based weather derivatives are a promising Our simulation results are in semi-quantitative agreement financial instrument to hedge weather risk. In most ma- with the prediction of the continuum model (Xu and Qian ture financial markets of the world, weather derivatives 2012 Phys. Rev. E 85 061603). It is found that the are traded for several years now. However in Mainland droplet mobility is inversely proportional to a dimension- China, such a market does not exist yet. To make the less coefficient associated with the total rate of dissipation launch of such instruments possible, multi-regional re- due to droplet movement. Our results show that this co- search is needed to find the most suitable temperature efficient is of order unity and increases with the droplet model for Mainland China. The contribution of this pa- size for the small droplets (∼ 10nm). Through a theo- per is to compare the performance of several up-to-date retical analysis on the size of the thermal singularity, it temperature models to data from twelve cities from all can be shown that the droplet mobility decreases with de- climatic zones in China. The models are compared in creasing coexistence temperature. This is also observed terms of fitting the daily average temperature, normal- in our MD simulations. ity of residuals, simulation errors and model risk when This is a joint work with Xinpeng Xu and Tiezheng Qian used for pricing futures and options. The comparison in- from HKUST. cludes a model with monthly contant volatility (Alaton et al, 2002), with daily volatility (Benth et al, 2007), a model with stochastic volatility like proposed by Benth Calculating areas and volumes with rotated and Benth (2011) and a model using a Spline approach axis for surface modelling similar to Schiller et al (2012). This is the first paper on multi-regional temperature modelling and weather derivatives pricing using such a large number Pablo Zafra, Christopher Flores of cities in a comparison of different models in Mainland Kean University, USA China. [email protected] fl[email protected]

Finding areas under a curve and volumes of solid of rev- Contributed Talks Group 5 olutions are standard applications of definite integrals in Differential Equations a Calculus class. Conventional examples in calculus text- books use the regular Cartesian coordinate system with Nonlinear impulsive differential equations vertical and horizontal axes. We explore in this research arising from chemotherapeutic treatment 56 PRIMA 2013 Abstracts

Baili Chen In this talk I will discuss the refraction of shocks on the Gustavus Adolphus College, USA interface for 2-d steady compressible flow. Particularly, [email protected] the class of E-H type regular refraction is defined and its global stability of the wave structure is verified. The 2-d steady potential flow equations is employed to describe We prove the existence of periodic solutions of systems the motion of the fluid. The stability problem of the E-H of nonlinear impulsive differential equations arising from type regular refraction can be reduced to a free bound- chemotherapeutic treatment for cancer. Our analysis is ary problem of nonlinear mixed type equations in an un- based on Mawhin’s continuation theorem of coincidence bounded domain. The corresponding linearized problem degree theorem. has similarities to a generalized Tricomi problem of the linear Lavrentiev-Bitsadze mixed type equation, and it can be reduced to a nonlocal boundary value problem Analysis of some nonlinear PDEs from multi- of an elliptic system. The latter is finally solved by es- scale geophysical applications tablishing the bijection of the corresponding nonlocal op- erator in a weighted Hölder space via careful harmonic analysis. Bin Cheng This is a joint work with CHEN Shuxing and HU Dian. University of Surrey, UK [email protected] Multiplicity of positive solutions for a p-q- Laplacian equation with critical nonlinearities This talk is regarding PDE systems from geophysical ap- plications with multiple time scales, in which linear skew- self-adjoint operators of size 1/epsilon gives rise to highly Tsing-San Hsu oscillatory solutions. Analysis is performed in justifying Chang Gung University, Taiwan R.O.C. the limiting dynamics as epsilon goes to zero; further- [email protected] more, the analysis yields estimates on the difference be- tween the multiscale solution and the limiting solution. In this talk, we study the effect of the coefficient f(x) We will introduce a simple yet effective time-averaging of the critical nonlinearity on the number of positive so- technique which is especially useful in general domains lutions for a p-q-Laplacian equation. Under suitable as- where Fourier analysis is not applicable. sumptions for f(x) and g(x), we should prove that for sufficiently small λ > 0, there exist at least k positive solutions of the following p-q-Laplacian equation Some piston problems in fluid dynamics p∗−2 r−2 −∆pu−∆qu=f(x)|u| u+λg(x)|u| u in Ω, Min Ding Shanghai Jiao Tong University, China u = 0 on ∂Ω, [email protected] where Ω ⊂ RN is a bounded smooth domain, N > p, 1 < q < N(p−1) < p ≤ max{p, p∗ − q } < r < p∗, The piston problem is analyzed from the mathematical N−1 p−1 ∗ Np point of view. Some features and phenomena caused by p = N−p is the critical Sobolev exponent and ∆su = the motion of the piston are revealed. We discuss some div(|∇u|s−2∇u) is the s-Laplacian of u. piston problems for both classical Euler equations and relativistic Euler equations of compressible fluids. In par- ticular, we focus on strong shock front solutions. The linear hyperbolic initial boundary value problems in a domain with corners Over-compressive shock profile associated with a simplified system from MHD Aimin Huang Indiana University, USA [email protected] Linglong Du National University of Singapore, Singapore [email protected] In this article, we consider linear hyperbolic Initial Boundary Value Problems (IBVP) in a rectangle in both the constant and variable coefficients cases. We use semi- In this talk, we present the wave propagation around an group method instead of Fourier analysis to achieve the over-compressive shock profile with large amplitude for a well-posedness of the linear hyperbolic system, and we simplified system from MHD, which is a rotationally in- find by diagonalization that there are only two simple variant system of viscous conservation laws. We show modes in the system which we call hyperbolic and elliptic that the solution converges pointwise to another over- modes. The hyperbolic system in consideration is either compressive profile exponentially, when the perturbations symmetric or Friedrichs-symmetrizable. of the initial data to a given profile are sufficiently small. We also give the explicit structure of the solution for the linearized system. The approach begins with an ex- On quasilinear elliptic equations with variable traction of non-decaying component stacked at the shock exponents front, followed by an iterated approximation process for the remainder. This sharp estimate is strong enough to Yun-Ho Kim study the nonlinear problem and conclude the stability of profile. Sangmyung University, Korea [email protected] This is a joint work with Professor Shih-Hsien Yu. We study the following elliptic equations with variable Global stability of E-H type regular refraction exponents of shocks on the interface between two media −div(φ(x, |∇u|)∇u) = λf(x, u) in Ω

Beixiang Fang which is subject to Dirichlet boundary condition. Un- Shanghai Jiao Tong University, China der suitable conditions on φ and f, employing the vari- [email protected] ational methods, in particular, mountain pass theorem 57 PRIMA 2013 Abstracts

and fountain theorem, we establish the existence of non- Fang Wang trival solutions for a class of quasilinear elliptic problems Princeton University, USA with variable exponents. Also we show the existence of [email protected] positivity of the infimum of all eigenvalues for the above problem. Definitions for the radiation field by Lax-Phillips and Friedlander are introduced for standard wave equation Overdetermined boundary value problems on Minkowski space-time, which can be generalized to with strongly nonlinear elliptic PDE curved space-time (such as Schiwarzschild space-time) and nonlinear wave equations (such as Einstein vacuum equations). Regularities of the radiation field are stud- Fengquan Li (with Boqiang Lv, Weilin Zou) ied. Mapping property for Moller wave operator, which Dalian University of Techology, China maps initial data to the radiation field, are investigated. [email protected] In the case that the Molloer wave operator is an (or a local) isomorphism, the characteristic initial problem is We consider the strongly nonlinear elliptic Dirichlet prob- considered. lem in a connected bounded domain, overdetermined with the constant Neumann condition F (∇u) = c on the boundary. Here F is convex and positively homogeneous Relationship between ω-limit Sets and Mini- of degree 1, and its polar F ∗ represents the anisotropic mal Sets norm on Rn. We prove that, if this overdetermined boundary value problem admits a solution in a suitable Larry Wang weak sense, then Ω must be of Wulff shape. Southern Polytechnic State University, USA [email protected] Stability of boundary layers for the non- isentropic compressible circularly symmetric In this paper, we study the relation between ω-limit sets 2D flow and minimal sets. It is known that every minimal set is a ω-limit set. However, not every ω-limit set is a minimal set, although it contains a minimal set. We would like to Cheng-Jie Liu know under what condition an ω-limit set turns out to Shanghai Jiao Tong University, China be a minimal set. We establish a necessary and sufficient [email protected] condition under which every ω-limit set is minimal.

In this paper, we study the asymptotic behavior of the cir- cularly symmetric solution to the initial boundary value The regularity of semi-hyperbolic patches at problem of the compressible non-isentropic Navier-Stokes sonic lines for the pressure gradient equation equations in a two-dimensional exterior domain with im- in gas dynamics permeable boundary condition when the viscosities and the heat conduction coefficient tend to zero. By multi- scale analysis, we obtain that away from the boundary Qin Wang the compressible non-isentropic viscous flow can be ap- Shanghai Jiao Tong University, China proximated by the corresponding inviscid flow, and near [email protected] the boundary there are boundary layers for the angu- lar velocity, density and temperature in the leading or- We study the uniform regularity of semi-hyperbolic der expansions of solutions, while the radial velocity and patches of self-similar solutions near sonic lines to a gen- pressure do not have boundary layers in the leading or- eral Riemann problem for the pressure gradient equation. der. The boundary layers of velocity and temperature are This type of solutions, in which one family of charac- described by a nonlinear parabolic coupled system. We teristics starts on a sonic line and ends on a transonic prove the stability of boundary layers and rigorously jus- ∞ shock wave, is common for the Riemann problems for the tify the asymptotic behavior of solutions in the L −norm Euler system in two space dimensions. The global ex- for the small viscosities and heat-conduction limit in the istence of smooth solutions was established in Song and Lagrangian coordinates, as long as the strength of the boundary layers is suitably small. Finally, we show that Zheng(2009), but the smoothness near the sonic lines is not clear. We establish that the smooth solutions are uni- the similar asymptotic behavior of the small viscosities formly smooth up to their sonic boundaries and the sonic and heat conduction limit holds in the Eulerian coordi- 1 nates for the compressible non-isentropic viscous flow. lines are C continuous.

Dynamics in immune reactions during wound Constructing global Lyapunov function for healing processes complex systems

XinAn Wang Jianzhong Sua), Larrissa Owensa) and Akif Ibraguimovb) a) Shanghai Jiao Tong University, China University of Texas at Arlington, USA [email protected] b)Texas Tech University [email protected] Lyapunov function, as one of the most significant con- cepts in dynamical systems, has been widely applied in We propose a partial differential equation model adapted many disciplines. However, the classical Lyapunov func- from the principles of wound healing studies and ana- tion in the theory of ordinary differential equations are lyze it to gain insights regarding the dynamics of immune usually restricted to the analysis of the stability near the cells/proteins following the insertion of a foreign body. equilibriums of the system, and no general constructive Specifically we look at the multiple roles of macrophages method has been found. Thus, it cannot be applied to and the conditions for stabilizing/destabilizing the equi- more complex dynamical behaviors, such as multi-stable librium state. Furthermore, we investigate the impact of states, periodic attractor like limit cycle, and chaos. Re- diffusion and chemotaxis on the stability and the tran- cently, a series of works based on the construction of po- sient behavior of the system. tential function in physics for stochastic dynamical pro- cess demonstrate potential function plays a critical role in the quantitative analysis of dynamical systems. In de- On the radiation field for wave equations terministic cases, the potential function is the Lyapunov 58 PRIMA 2013 Abstracts

function globally constructed for the systems. In this talk, obtain a necessary and sufficient condition for the lin- we first present a novel numerical constructive method ear stability of supersonic planar contact discontinuities on the Lyapunov function for a wide series of dynamical and a priori estimates of solutions to the linearized prob- systems. Then, we apply this method in some famous lem. The weak stability of this contact discontinuity examples, such as the Van Der Pol oscillator and Lorenz also results in a loss of regularity with respect to the system. On the other hand, we analytically construct the source terms in the interior domain and on the bound- Lyapunov function in a chaotic system and the compet- ary in the a priori estimates of solutions to the linearized itive Lotka-Volterra systems. The structure of the at- problem. Contact discontinuities with tangential veloc- tractors, such as fractal, are demonstrated clearly by the ity fields on two sides of the discontinuous front parallel Lyapunov function. or non-parallel are both considered. Moreover, using the calculus of paradifferential operators and taking advan- tage of the control of non-characteristic components of The half line versus finite domain problems of unknowns by the equations and the problems satisfied by vorticities of velocity fields, we get estimates of high order the Modified Buckley-Leverett equation derivatives of solutions to the linearized problem of a non- planar contact discontinuity. As there is a loss of regular- Ying Wang ity in the estimates of solutions to the linearized problem, we adapt the Nash-Moser-Hörmander iteration scheme to University of Minnesota, USA obtain the nonlinear stability of supersonic contact dis- [email protected] continuities in three dimensional compressible isentropic steady Euler equations. This is a joint work with Ya- Guang Wang. Buckley-Leverett (MBL) equation describes two-phase flow in porous media. The MBL equation differs from the classical Buckley-Leverett (BL) equation by including a balanced diffusive-dispersive combination. The disper- Global structure of admissible BV solutions sive term is a third order mixed derivatives term, which to strictly hyperbolic conservation laws in one models the dynamic effects in the pressure difference be- space dimension tween the two phases. The classical BL equation gives a monotone water saturation profile for any Riemann prob- lem; on the contrast, when the dispersive parameter is Lei Yu large enough, the MBL equation delivers non-monotone Scuola Internazionale Superiore di Studi Avanzati, Italy water saturation profile for certain Riemann problems [email protected] as suggested by the experimental observations. In this talk, we show that the solution of the finite interval [0,L] boundary value problem converges to that of the half-line In [1], we describe the qualitative structure of an admis- [0, +∞) boundary value problem expoentially fast for the sible BV solution to a strictly hyperbolic system of con- servation laws whose characteristic families are piecewise MBL equation as L → +∞. (This is a joint work with genuinely nonlinear. More precisely, we prove that there Chiu-Yen Kao.) are a countable set of points Θ and a countable family of Lipschitz curves T such that outside T ∪Θ the solution is continuous, and for all points in T\Θ the solution has Blowup of classical solutions to the compress- left and right limit. This extends the corresponding struc- ible Navier-Stokes equations tural result in [2] for genuinely nonlinear systems. The proof is based on the introduction of subdiscontinuities of a shock, whose behavior is qualitatively analogous to the Wei Yan discontinuities of the solution to genuinely nonlinear sys- Institute of Applied Physics and Computational Mathe- tems. An application of this result is the stability of the matics, China 1 wave structure of solution w.r.t. Lloc-convergence. Also [email protected] a remark on the generalization of the results of general strictly hyperbolic conservation laws will be given. In this talk, we present our recent results on the finite [1] S. Bianchini and L. Yu, Global structure of ad- time blow up of smooth solutions to the Compressible missible BV solutions to piece- wise genuinely nonlinear, Navier-Stokes system. We prove that any classical solu- strictly hyperbolic conservation laws in on space di- men- tions of viscous compressible fluids without heat conduc- sion. To appear on Comm. Partial Differential Equa- tion will blow up in finite time, as long as the initial data tions (arXiv:1211.3526), 2012. has an isolated mass group (see definition in the paper). [2] A. Bressan and P. G. LeFloch, Structural stability The results hold regardless of either the size of the initial and regularity of entropy solutions to hyperbolic systems data or the far fields being vacuum or not. This improves of conservation laws, Indiana Univ. Math. J., 48 (1999), the blowup results of Xin (1998, CPAM) by removing the pp. 43–84. crucial assumptions that the initial density has compact support and the smooth solution has finite total energy. Furthermore, the analysis here also yields that any clas- sical solutions of viscous compressible fluids without heat conduction in bounded domains or periodic domains will Contributed Talks Group 6 blow up in finite time, if the initial data have an isolated Probability and Statistics mass group satisfying some suitable conditions. Estimates of Itô integral and applications to random dynamical systems Stability of supersonic contact discontinuities for three dimensional compressible steady Eu- ler flows Xiaoming Fan Southwest Jiaotong University and Beijing Normal Uni- versity, China Fang Yu [email protected] Shanghai Jiao Tong University, China [email protected] This paper obtains two estimates of Itô integral and their stochastic Gronwall’s inequalities, which present an ulti- In this talk, we discuss the nonlinear structural stabil- mate way to deal with almost sure estimates for stochas- ity of supersonic contact discontinuities in three dimen- tic (partial) differential equations with white noises of sional compressible isentropic steady Euler equations. We any type. As examples, they are applied to present a 59 PRIMA 2013 Abstracts

formula estimating the Hausdorff dimensions of the tem- pered compact random invariant sets and investigate the existence and the Hausdorff dimensions of random attrac- tors for a stochastic wave equation with noisy damping.

Data fusion based on evidence theory

Yanyan He Florida State University, USA [email protected]

Data fusion techniques integrate data from multiple sources (such as sensors, institutions, and etc.), and the combined information can help to reach more accurate and more specific inference. In this presentation, evidence theory based combination approaches are introduced to combine distinct sources of uncertain information. The uncertainty in each source of information is represented by a belief function individually, which are then combined to produce a single belief function representing informa- tion from all the sources. The approaches are illustrated with examples.

The generalized Itô-Wentzell formula for Itô’s process and the stochastic first integral

Elena Karachanskaya Paciŕc National University, Russia [email protected]

We present the Generalized Itô-Wentzell formula, which is the generalization of Itô-Wentzell formula for a multide- mentional Itô’s process with the Wiener and the Poisson perturbations. This result allowed to set equations for the stochastic first integrals of a stochastic differential equations system.

An explicit cross entropy scheme for mixtures

Xiang Zhou City University of Hong Kong, Hong Kong, China [email protected]

The key issue in importance sampling is the choice of the alternative sampling distribution, which is often chosen from the exponential tilt family of the underlying distri- bution. However, when the problem exhibits certain kind of nonconvexity, it is very likely that a single exponential change of measure will never attain asymptotic optimal- ity and may lead to erroneous estimates. In this paper we introduce an explicit iterative scheme which combines the traditional cross-entropy method and the EM algorithm to find an efficient alternative sampling distribution in the form of mixtures. We also study the applications of this scheme to option price estimation.

Asymptotic analysis for tipping points prob- lems

Jielin Zhu University of British Columbia, Canada [email protected]

A tipping point, observed as a rapid change in climate or ecology, can be induced by a slowly varying control parameter of a saddle-node bifurcation. The position of the tipping point can be significantly changed by small noise or periodic terms. A local multiple scaling method is used to describe the behaviour of the system based on the relation of the drifting rate, noise and frequency of the periodic terms. A one-dimensional canonical slowly vary- ing system with a saddle-node bifurcation is analysed, to find out the effect of the noise or the frequency of the pe- riodic terms separately. We also show results for a global energy balance model in climate dynamics.

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