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String Math Summer School STRING MATH SUMMER SCHOOL Summer School Program June 2-6, 2014 Pacific Institute for the Mathematical Sciences Rm 2012 Earth Sciences Building (ESB) 2207 Main Mall, Vancouver Getting Started: o Get connected: Select the "ubcvisitor" wireless network on your wireless device. Open up a web browser, and you will be directed to the login page. o Event Evaluation Survey: Please help PIMS to improve the quality of its events and plan for the future by filling out the survey at the end of the conference. It is located at http://goo.gl/JB5gTh Conference Floor Guide: Main Mall ESB 1012 ESB 2012 ESB Main Entrance N ESB Atrium Bathrooms REGISTRATIO ESB 1013 ESB South Entrance o UBC Map link: http://www.maps.ubc.ca/PROD/images/pdf/ubcmap.pdf (See also, back of page) o Public Transit: Feel free to search and plan your public transport rides by visiting http://www.translink.ca/, where directions, ticket costs and bus schedules are indicated. o Parking at UBC: http://www.parking.ubc.ca/visitor.html Week at a Glance: Time Mon June 2 Tue June 3 Wed June 4 Thur June 5 Time Fri June 6 Registration and 8:30am- Check in (ESB 8:55am Atrium) 9:00am - 9:00am- 10:00am Eric Zaslow Eric Zaslow Eric Zaslow Andy Neitzke 10:00am Andy Neitzke Coffee Break (ESB 2012 Lobby) (Coffee Break) 10:30am- 10:15am- 11:30pm Balazs Szendroi Balazs Szendroi Balazs Szendroi Balazs Szendroi 11:00am Eric Zaslow Lunch (Self Catered, See list of campus eateries) (Coffee Break) 1:30pm- 11:30- 2:30pm Tony Pantev Tony Pantev Tony Pantev Kevin Costello 12:30pm Tony Pantev Coffee Break (ESB 2012 Lobby) Conclusion 3:00pm- 4:00pm Kevin Costello Kevin Costello Kevin Costello Andy Neitzke Stretch Break 4:30pm - Discussion session: Discussion session: Discussion session: 5:30pm T. Johnson-Freyd T. Johnson-Freyd Andy Neitzke T. Johnson-Freyd **All Sessions will be hosted in the Earth Sciences Building (and Home of PIMS) In ESB Room 2012. Course Titles and Abstracts: Kevin Costello (Northwestern): Towards the mathematics of type IIB superstring theory and AdS/CFT. Supsersymmetric objects in physics often have twistings which are much easier to analyze mathematically than the full untwisted theory. This course will focus on twisted supersymmetric gauge theories which arise from D-branes in type IIB string theory. We will discuss how to define these twisted theories mathematically, and we will rederive some results in the physics literature. I will also spend a little time explaining twisted type IIB supergravity and a conjectural mathematical formulation of the AdS/CFT correspondence. Andy Neitzke (Texas): Open string mirror symmetry and Hitchin’s equations. Suppose given a complex curve C and a Lie group G. From these data one can construct an interesting system of nonlinear PDEs known as Hitchin’s equations. The moduli space of solutions of these equations has the marvelous property of being hyperkahler: it thus has various avatars corresponding to its different complex structures, including one in which it is a complex integrable system, and another in which it is the moduli space of complex flat connections. One difficulty in 2 understanding the nature of this space is that its hyperkahler structure is difficult to write down explicitly. I will explain some aspects of a strategy for constructing the hyperkahler structure concretely; this strategy appeared in joint work with Davide Gaiotto and Greg Moore, motivated by the problem of BPS state counting in supersymmetric quantum field theory. Depending on one’s point of view, one might view this strategy either as an application of the exact WKB method for differential equations depending on a small parameter, or as an application of mirror symmetry; the “Stokes curves” appearing in the former approach get related to “holomorphic triangles” appearing in the latter. Tony Pantev (University of Pennsylvania): Shifted structures and quantization. I will introduce a version of algebraic symplectic geometry that is suitable for dealing with derived or stacky resolutions of singular spaces. I will explain how this generalization arises naturally in the study of moduli spaces and will outline interesting connections to ordinary symplectic geometry. I will also give non-trivial examples and will describe a several constructions of shifted symplectic structures. In addition I will discuss a number of topics on the structure theory of derived symplectic stacks, including the Darboux theorem, the existence of isotropic and Lagrangian structures, constructions of derived lagrangian foliations, existence of shifted potentials, and various results in the direction of shifted quantization and formality. The lectures are based on various joint works with Calaque, Katzarkkov, Toen, Vaquie, and Vezzosi. Balazs Szendroi (Oxford): Cohomological Donaldson-Thomas theory. I will start with a summary of the aims and objectives of Donaldson-Thomas theory, the theory of attaching invariants to moduli spaces of sheaves on Calabi-Yau threefolds and more generally objects in 3-Calabi-Yau categories. I will discuss what's known about the local and global structure of such moduli spaces. After a technical interlude on constructible sheaves, vanishing cycles and mixed Hodge modules, I will introduce the main construction, cohomological DT invariants. I will then concentrate on a local model, categories of representations of a quiver with potential, introducing the Kontsevich-Soibelman COHA, which is an algebra structure on cohomological DT. If time permits, I will discuss wall crossing, and an application of the theory in the study of quantum cluster transformations. Eric Zaslow (Northwestern): Knots, Sheaves and Physics. I will discuss various relationships between Legendrian knots, constructible sheaves, and the Fukaya category. Lecture 1: Legendrian knots, the Chekanov-Eliashberg dga, and the category of augmentations. Lecture 2: Microlocalization: constructible sheaves and the Fukaya category. Lecture 3: Sheaf-theoretic perspective on Legendrian knots, microlocal monodromy, recovery of topological knot invariants. Lecture 4: Comments on higher dimensions and the relationship to the Hitchin system. Theodore Johnson-Freyd (North Western): Discussion Session Facilitator 3 List of Participants: 1. Hassan Babaei Koc University 2. Thomas Baird Memorial University of Newfoundland 3. Florian Beck University Freiburg 4. Francis Bischoff University of Toronto 5. Dylan Butson University of Toronto 6. Dominic Culver University of Notre Dame 7. Alberto Cazzaniga Oxford University 8. Richard Eager IPMU, Japan 9. Suzanne Findleton Queen's University 10. Ilmar Gahramanov Humboldt-University Berlin 11. Honghao Gao Northwestern University 12. Jonathan Gleason University of California, Berkeley 13. Marco Gualtieri University of Toronto 14. Changho Han University of Toronto 15. Andrew Harder University of Alberta 16. Aron Heleodoro Northwestern University 17. Ting Chen Leo Hsu University of British Columbia 18. Mathias Hudoba de Badyn University of Washington 19. Ivan Ip University of Tokyo 20. Drew Johnson University of Utah 21. Atsushi Kanazawa Harvard University 22. Hoil Kim Kyungbook National University 23. Martijn Kool UBC/ PIMS 24. Joel Lamy-Poirier University of Waterloo 25. Oliver Leigh University of Melbourne/ UBC 26. Jun Li University of Minnesota 27. Kevin Luk University of Toronto 28. Jeremy Mann University of Notre Dame 29. Matthew Mahowald Northwestern University 30. Brendan McLellan Northeastern University 31. Hironori Mori Osaka University 32. Nikita Nikolaev University of Toronto 33. Andrew O'Desky Case Western Reserve 34. Natalie Peternell University of Freiburg 35. Nicolo' Piazzalunga SISSA 4 36. Brent Pym University of Oxford 37. Charles Rabideau UBC 38. Eugene Rabinovich Duke University 39. Ziv Ran UC Riverside 40. Jie Ren Kansas State University 41. Jörgen Rennemo Imperial College London 42. Pooya Ronagh UBC 43. Philippe Sabella-Garnier UBC 44. Ingmar Saberi California Institute of Technology 45. Michail Savvas Stanford University 46. Sam Selmani McGill University 47. Carlos Shahbazi Alonso CEA-Saclay 48. Tom Sutherland University of Sheffield 49. Alan Thompson University of Alberta 50. Alexander Torres Gomez Universidad Austral de Chile 51. Arnav Tripathy Stanford 52. Matthew Wheeler University of Pittsburgh 53. Philsang Yoo Northwestern University 54. Matthew Young University of Hong Kong 55. Ahmed Jihad Zerouali Univ. Quebec, Montreal 56. Marco Zini Universitá di Modena e Reggio Emilia 5 Recreational Activities at the University of British Columbia Aquatic Centre 6121 University Boulevard (604) 822- 4522 www.aquatics.ubc.ca The UBC Aquatic Centre features a 50-metre indoor pool, seasonal 55-yard outdoor pool, whirlpool, fitness/weight room, sauna/steam rooms, seasonal patio area and diving boards from one to ten meters. Summer Hours: Please call for swim times, lessons, etc. Beaty Biodiversity Museum 2212 Main Mall (604) 827- 4955 www.beatymuseum.ubc.ca A new public museum dedicated to enhancing the public’s understanding and appreciation of biodiversity. It is home to over 20,000 fossils from all over the world, including the largest blue whale exhibit in Canada Summer Hours: Wed- Sun: 11:00am-5:00pm Belkin Art Gallery 1825 Main Mall (beside Fredric Wood Theatre) (604) 822- 2759 www.belkin.ubc.ca The Morris and Helen Belkin Art Gallery’s mandate is to research, exhibit, collect, publish, educate and develop programs in the field of contemporary art and in contemporary approaches to the practice of art history and criticism. Summer Hours: Tues-Fri: 10:00am-5:00pm Sat-Sun: 12:00pm-5:00pm Botanical Garden 6804 Marine Drive (604) 822- 9666 www.ubcbotanicalgarden.org Established in 1916, the UBC Botanical Garden has an outstanding collection of temperate plants displayed according to their geographic areas. Exhibits of regional plants include the Native Garden and Alpine Garden. Summer Hours: Daily 9:00am-5:00pm Tennis Courts 2525 West Mall & 6010 Thunderbird Boulevard (604) 822- 2505 All guests staying at the University of British Columbia are welcome to use the tennis courts located at Place Vanier and Totem Park Residences. There are additional courts at the UBC Coast Club located at 6160 Thunderbird Blvd.
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