DOCSLIB.ORG

2007 Integral

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text

Load more

Autumn 2007 Volume 2 Massachusetts Institute of Technology 1ntegral news from the mathematics department at mit Inside • New faculty • Leighton and Akamai • Awards and achievements • Campaign for Math update • The UMO • Faculty chairs 7 • Project Laboratory • News bits • Putnam Competition • Simons Lectures Dear Friends, Welcome to the second edition of Integral, Speaking of undergraduate education, a careers. That conference is planned for our department’s annual newsletter. major MIT task force has just completed April 12-13, 2008, and will follow a A year has flown by since we published a comprehensive review of the General meeting of the department’s Visiting our inaugural edition in September 2006. Institute Requirements (GIRs) that shape Committee. Much has happened and much more is the undergraduate experience of all MIT planned. students and it has made recommendations Thanks to the overwhelming support for various changes in these requirements. of our alumni and other friends, our First of all, we’ve had an ambitious recruit- MIT faculty and administrators are cur- $15 million fundraising “Campaign for ment effort and are delighted to be rently reviewing these proposed changes, Mathematics” has been going exceedingly welcoming six new faculty to the depart- some of which will undoubtedly be imple- well. At the present time, we are 90 percent ment this year: Professors Paul Seidel mented. Our department is considering the of the way to our goal, so that means you and James McKernan; tenured Associate impact of these changes on our programs still have time to participate and we hope Professors Ju-Lee Kim and Jacob Lurie; and whether we ought to review our own you do! Please look inside for additional and Assistant Professors Jon Kelner and offerings and requirements. Feel free to details. Abhinav Kumar. You can learn more send ideas about restructuring our math- about them and about their mathematics ematics major programs directly to me at As we move forward and look toward an on page 2. [email protected]. unusually high number of faculty eligible for retirement over the next few years, The job market for mathematicians is This year, the huge turnouts for our we are planning to continue our active quite strong these days, a big change from Simons lectures given by Terry Tao and recruitment efforts. To that end, we are what I remember back in the 1970s, when David Donoho necessitated finding larger also thinking about the directions within jobs were few and far between. Now we lecture halls. MIT helped with publicity mathematics that we want to develop within face very tough competition from other by spotlighting the series on the main the department. The MIT administration great mathematics departments for Institute home page. The Simons lecturers has been tremendously supportive of our top people, yet we’ve been remarkably next spring will be John Conway and efforts and we have a close relationship successful. We are excited about the Peter Teichner. In the fall term, Assaf with the new dean of science, Marc Kastner. diversity of experience they will bring Naor of New York University’s Courant Our future looks very bright indeed. to our community, and we are proud to Institute of Mathematical Sciences will welcome them to MIT. give the Wiener Lectures. Our fantastic students are another source We’re in the early stages of planning a of great pride. With the stunning achieve- conference for women mathematics ments of our undergraduate students on PhDs who are graduate and undergraduate Michael Sipser the Putnam and MCM competitions, and alumnae of the MIT Department of Department Head the spectacular successes of our graduate Mathematics. Participants will speak about students at getting offers of the very best their research, and will lead panel discus- faculty positions, we know we’re doing sions of their individual experiences of something right. what helped or hindered them in their Mathematics welcomes six new faculty James McKernan, Professor of Mathematics, is a major figure in higher dimensional algebraic geometry. Paul Seidel, Professor of Mathematics, is well known for his A recipient of a 2007 Clay Research outstanding work in symplectic topology, a field originating in the Award for his groundbreaking work with study of Hamiltonian mechanics and now connected to string Christopher Hacon on the Minimal theory. A recipient of the European Mathematical Society Prize Model Program, he earned a BA from in 2000, he received his Diploma from Heidelberg University Trinity College in 1985 and a PhD from in 1994 and the PhD from Oxford University in 1998. Harvard University in 1991. Jacob Lurie, Associate Professor of Mathematics with tenure, is a rising star in algebraic topology. A winner of several awards, including 1st place in the 1996 Westinghouse Science Talent Ju-Lee Kim, Associate Professor of Mathematics with tenure, Search, the 2000 Morgan Prize, and an AIM five-year fellowship has made important contributions to p-adic representation theory in 2004, he holds a BA from Harvard University in 2000 and a and harmonic analysis, with connections to the local Langlands PhD from MIT in 2004. program. Her undergraduate studies in the Korea Advanced Institute of Science and Technology were completed in 1991 and she received her PhD from Yale University in 1997. Abhinav Kumar, Assistant Professor of Jonathan Kelner, Assistant Professor of Mathematics, is a Mathematics, works in number theory. theoretical computer scientist. Recipient of the 2002 David A 1998 IMO Gold Medalist and Putnam Mumford Award and the 2004 STOC best student paper award, Fellow in 1999 and 2000, he received he earned a BA from Harvard University in 2002 and a PhD his SB from MIT in 2002 and his PhD from MIT in 2006. from Harvard in 2006. Awards and achievements Tom Mrowka received the AMS Oswald Veblen Prize in Geometry with Peter Kronheimer from Harvard, “for their joint contributions to both three and four- dimensional topology through the devel- opment of deep analytical techniques and applications.” Gil Strang received the MAA Deborah and Franklin Tepper Haimo Award, the ICIAM Su Buchin Prize and the ETH/SIAM Peter Henrici Peter Kronheimer and Tom Mrowka Prize for research in applied analysis Gilbert Strang and mathematics education worldwide. Peter Shor was named one of Caltech’s “Distinguished Alumni.” Eric Lauga received the Andreas Acrivos Dissertation Award in Fluid Dynamics from the American Physical Society. Mark Behrens and Katrin Wehrheim both received Sloan Research Fellowships. Michel Goemans received a Guggenheim Fellowship in computer science. Victor Kaç and Tom Mrowka are newly elected members of the American Academy of Arts and Sciences. George Lusztig Victor Kaç received the Diploma of Academic Merit from the Romanian Academy. David Vogan has been appointed as the Robert Collins Distinguished Scholar. Peter Shor Associate Professors Martin Bazant and Alex Postnikov received tenure. Kiran Kedlaya was promoted to Associate Professor. Dan Kane ’07 was awarded the Bucsela Prize for outstanding MIT mathematics major. Dan also received the AMS-MAA- SIAM Frank and Brennie Morgan Prize for outstanding undergraduate research in Mark Behrens mathematics. Yaim Cooper ’07 received the AMITA Senior Academic Award. She was also runner-up for the Schafer Prize for Undergraduate Women in Mathematics. Graduate student Pavlo Pylyavskyy was selected for a Clay Liftoff Fellowship. For their outstanding George Lusztig research papers, Silvia Montarani and Luis Rademacher each received the Charles and Jennifer Johnson Prize. Possible future Ilya Elson, with Jason Burns and Teena mathematician Gerhardt as runners-up, received the Ilaria Seidel, Charles and Holly Housman Award for daughter of Excellence in Undergraduate Teaching. Paul Seidel and Graduate awards: Haynes Miller, Teena Michael Manapat received the Dean’s Ju-Lee Kim. Gerhardt, and Jason Burns. Education Award. Andrew Sutherland received an EECS Sprouls Award for an outstanding thesis in computer science. Staff member Kim Makara was awarded MIT’s Infinite Mile Award. Academic administrator Joanne Jonsson received the Dean’s Recognition Award. The UMO Project laboratory class creates “eureka!” moments for students Imagine a billiards table with no friction “The first thing to understand about these or spin. The ball is struck and hits the projects is that they are not well-defined,” sides in some sequence. What sequences Miller said. “Part of the challenge to the are theoretically possible? What if the students is to find an aspect of the problem table is triangular or pentagonal? that is interesting and approachable. So every time a team does a project it comes MIT students explored this scenario out differently.” recently through the Mathematics Project Laboratory. Projects are drawn from many mathemati- cal areas, including dynamical systems, Developed by Professors Michael Artin number theory, algebra, fluid mechanics, and Haynes Miller, the Mathematics asymptotic analysis, knot theory and Project Laboratory has no syllabus, no probability. Students choose from a The Undergraduate Mathematics Office, problem sets, and meets sporadically. selection of problems or design one one of the first offices for undergraduate Students, predominantly seniors, work of their own. During the semester, each administration at MIT and still one of in groups and select open-ended math- group of three students works on three the few Institute offices devoted solely to ematical questions to investigate. Experi- questions in which they design and run undergraduate education, was a revolu- ments are generally conducted on a experiments, analyze the results and tionary entity when Professor Arthur computer, but some students use old- present their findings to the class. Mattuck created it 30 years ago. Joanne fashioned paper and pencil. Jonsson and her colleagues, Debbie Bower, A recent project invited students to think Stephanie (Stevie) Gallarelli and Anna “I found that the class was an excellent through a mathematical model of water Ferrigno Ward now provide essential way to gain experience with working in a seeping through a sand bed.
Recommended publications
  • Meetings & Conferences of the AMS, Volume 48, Number 11

    Meetings & Conferences of the AMS, Volume 48, Number 11

    mtgs.qxp 10/30/01 1:55 PM Page 1415 Meetings & Conferences of the AMS IMPORTANT INFORMATION REGARDING MEETINGS PROGRAMS: AMS Sectional Meeting programs do not appear in the print version of the Notices. However, comprehensive and continually updated meeting and program information with links to the abstract for each talk can be found on the AMS website. See http://www.ams.org/meetings/. Programs and abstracts will continue to be displayed on the AMS website in the Meetings and Conferences section until about three weeks after the meeting is over. Final programs for Sectional Meetings will be archived on the AMS website in an electronic issue of the Notices as noted below for each meeting. Groups and Covering Spaces in Algebraic Geometry, Michael Irvine, California Fried, University of California Irvine, and Helmut Voelklein, University of California Irvine University of Florida. Harmonic Analyses and Partial Differential Equations, November 10–11, 2001 Gustavo Ponce, University of California Santa Barbara, and Gigliola Staffilani, Brown University and Stanford Meeting #972 University. Western Section Harmonic Analysis and Complex Analysis, Xiaojun Huang, Associate secretary: Bernard Russo Rutgers University, and Song-Ying Li, University of Cali- Announcement issue of Notices: September 2001 fornia Irvine. Program first available on AMS website: September 27, Operator Spaces, Operator Algebras, and Applications, 2001 Marius Junge, University of Illinois, Urbana-Champaign, Program issue of electronic Notices: December 2001 and Timur Oikhberg, University of Texas and University Issue of Abstracts: Volume 22, Issue 4 of California Irvine. Deadlines Partial Differential Equations and Applications, Edriss S. Titi, For organizers: Expired University of California Irvine.
  • TWAS Fellowships Worldwide

    TWAS Fellowships Worldwide

    CDC Round Table, ICTP April 2016 With science and engineering, countries can address challenges in agriculture, climate, health TWAS’s and energy. guiding principles 2 Food security Challenges Water quality for a Energy security new era Biodiversity loss Infectious diseases Climate change 3 A Globally, 81 nations fall troubling into the category of S&T- gap lagging countries. 48 are classified as Least Developed Countries. 4 The role of TWAS The day-to-day work of TWAS is focused in two critical areas: •Improving research infrastructure •Building a corps of PhD scholars 5 TWAS Research Grants 2,202 grants awarded to individuals and research groups (1986-2015) 6 TWAS’ AIM: to train 1000 PhD students by 2017 Training PhD-level scientists: •Researchers and university-level educators •Future leaders for science policy, business and international cooperation Rapidly growing opportunities P BRAZIL A K I N D I CA I RI A S AF TH T SOU A N M KENYA EX ICO C H I MALAYSIA N A IRAN THAILAND TWAS Fellowships Worldwide NRF, South Africa - newly on board 650+ fellowships per year PhD fellowships +460 Postdoctoral fellowships +150 Visiting researchers/professors + 45 17 Programme Partners BRAZIL: CNPq - National Council MALAYSIA: UPM – Universiti for Scientific and Technological Putra Malaysia WorldwideDevelopment CHINA: CAS - Chinese Academy of KENYA: icipe – International Sciences Centre for Insect Physiology and Ecology INDIA: CSIR - Council of Scientific MEXICO: CONACYT– National & Industrial Research Council on Science and Technology PAKISTAN: CEMB – National INDIA: DBT - Department of Centre of Excellence in Molecular Biotechnology Biology PAKISTAN: ICCBS – International Centre for Chemical and INDIA: IACS - Indian Association Biological Sciences for the Cultivation of Science PAKISTAN: CIIT – COMSATS Institute of Information INDIA: S.N.
  • Pterossauros Nasciam Sem a Capacidade De Voar

    Pterossauros Nasciam Sem a Capacidade De Voar

    NOTAS 1 Pterossauros nasciam sem a capacidade de voar Os filhotes de pterossauros, répteis ala- dos já extintos, contemporâneos dos dinossauros, rompiam seus ovos prontos para andar, mas não para bater asas e ga- nhar os ares. Assim que nasciam, os ossos Ovos fossilizados da cintura estavam formados. Isso permi- do pterossauro Hamipterus tia que eles se apoiassem sobre as patas tianshanensis e traseiras e dessem os primeiros passos. reconstituição Porém, a estrutura óssea que dá suporte artística da espécie aos movimentos do músculo peitoral, essencial para sustentar o voo, ainda não estava totalmente constituída. Os recém- -nascidos também não tinham todos os dentes, limitação que provavelmente os impedia de se alimentar sozinhos. Para sobreviver até que os ossos de apoio das asas e os dentes estivessem completos, os filhotes tinham de permanecer um bom tempo sob o cuidado dos pais. Esse cenário, sobre o desenvolvimento embrio- nário e os primeiros movimentos, ainda tímidos, dos filhotes de pterossauros, é sugerido em um estudo feito por paleon- tólogos brasileiros e chineses (Science, 1º de dezembro). “O descompasso entre o desenvolvimento dos ossos da cintura e os da musculatura peitoral indica que os pterossauros não conseguiam voar ao nascer”, comenta o paleontólogo Ale- xander Kellner, do Museu Nacional da Universidade Federal do Rio de Janeiro (UFRJ), um dos autores do trabalho. Com o auxílio de imagens de tomografia com- putadorizada, o grupo analisou o interior de 16 ovos de pterossauros da espécie Hamipterus tianshanensis, que viveu há cerca de 120 milhões de anos na bacia de Turpan-Hami, no noroeste da China.
  • I. Overview of Activities, April, 2005-March, 2006 …

    I. Overview of Activities, April, 2005-March, 2006 …

    MATHEMATICAL SCIENCES RESEARCH INSTITUTE ANNUAL REPORT FOR 2005-2006 I. Overview of Activities, April, 2005-March, 2006 …......……………………. 2 Innovations ………………………………………………………..... 2 Scientific Highlights …..…………………………………………… 4 MSRI Experiences ….……………………………………………… 6 II. Programs …………………………………………………………………….. 13 III. Workshops ……………………………………………………………………. 17 IV. Postdoctoral Fellows …………………………………………………………. 19 Papers by Postdoctoral Fellows …………………………………… 21 V. Mathematics Education and Awareness …...………………………………. 23 VI. Industrial Participation ...…………………………………………………… 26 VII. Future Programs …………………………………………………………….. 28 VIII. Collaborations ………………………………………………………………… 30 IX. Papers Reported by Members ………………………………………………. 35 X. Appendix - Final Reports ……………………………………………………. 45 Programs Workshops Summer Graduate Workshops MSRI Network Conferences MATHEMATICAL SCIENCES RESEARCH INSTITUTE ANNUAL REPORT FOR 2005-2006 I. Overview of Activities, April, 2005-March, 2006 This annual report covers MSRI projects and activities that have been concluded since the submission of the last report in May, 2005. This includes the Spring, 2005 semester programs, the 2005 summer graduate workshops, the Fall, 2005 programs and the January and February workshops of Spring, 2006. This report does not contain fiscal or demographic data. Those data will be submitted in the Fall, 2006 final report covering the completed fiscal 2006 year, based on audited financial reports. This report begins with a discussion of MSRI innovations undertaken this year, followed by highlights
  • Mirror Symmetry for Honeycombs

    Mirror Symmetry for Honeycombs

    TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 373, Number 1, January 2020, Pages 71–107 https://doi.org/10.1090/tran/7909 Article electronically published on September 10, 2019 MIRROR SYMMETRY FOR HONEYCOMBS BENJAMIN GAMMAGE AND DAVID NADLER Abstract. We prove a homological mirror symmetry equivalence between the A-brane category of the pair of pants, computed as a wrapped microlocal sheaf category, and the B-brane category of its mirror LG model, understood as a category of matrix factorizations. The equivalence improves upon prior results in two ways: it intertwines evident affine Weyl group symmetries on both sides, and it exhibits the relation of wrapped microlocal sheaves along different types of Lagrangian skeleta for the same hypersurface. The equivalence proceeds through the construction of a combinatorial realization of the A-model via arboreal singularities. The constructions here represent the start of a program to generalize to higher dimensions many of the structures which have appeared in topological approaches to Fukaya categories of surfaces. Contents 1. Introduction 71 2. Combinatorial A-model 78 3. Mirror symmetry 95 4. Symplectic geometry 100 Acknowledgments 106 References 106 1. Introduction This paper fits into the framework of homological mirror symmetry, as introduced in [23] and expanded in [19, 20, 22]. The formulation of interest to us relates the A-model of a hypersurface X in a toric variety to the mirror Landau-Ginzburg B- model of a toric variety X∨ equipped with superpotential W ∨ ∈O(X∨). Following Mikhalkin [27], a distinguished “atomic” case is when the hypersurface is the pair of pants ∗ n ∼ ∗ 1 n Pn−1 = {z1 + ···+ zn +1=0}⊂(C ) = T (S ) n+1 with mirror Landau-Ginzburg model (A ,z1 ···zn+1).
  • Soliton Model

    Soliton Model

    On long time dynamic and singularity formation of NLS MASSACHTS ITTUTE by OF TECHNOLOGY Chenjie Fan AUG 0 12017 B.S., Peking University (2012) LIBRARIES Submitted to the Department of Mathematics ARCHIVES in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY June 2017 @ Massachusetts Institute of Technology 2017. All rights reserved. Signature redacted Author ............................................ Department of Mathematics May 3rd, 2017 Certified by. Signature redacted ... Gigliola Staffilani LAbby Rockefeller Mauze Professor Thesis Supervisor Accepted by... Signature redacted .................. William Minicozzi Chairman, Department Committee on Graduate Theses 2 On long time dynamic and singularity formation of NLS by Chenjie Fan Submitted to the Department of Mathematics on May 3rd, 2017, in partial fulfillment of the requirements for the degree of Doctor of Philosophy Abstract In this thesis, we investigate the long time behavior of focusing mass critical nonlinear Schr6dinger equation (NLS). We will focus on the singularity formation and long time asymptotics. To be specific, there are two parts in the thesis. In the first part, we give a construction of log-log blow up solutions which blow up at m prescribed points simultaneously. In the second part, we show weak convergence to ground state for certain radial blow up solutions to NLS at well chosen time sequence. We also include a lecture note on concentration compactness. Concentration compactness is one of the main tool we use in the second part of the thesis. Thesis Supervisor: Gigliola Staffilani Title: Abby Rockefeller Mauze Professor 3 I Acknowledgments I am very fortunate to work with my advisor, Gigliola Staffilani.
  • Clay Mathematics Institute 2005 James A

    Clay Mathematics Institute 2005 James A

    Contents Clay Mathematics Institute 2005 James A. Carlson Letter from the President 2 The Prize Problems The Millennium Prize Problems 3 Recognizing Achievement 2005 Clay Research Awards 4 CMI Researchers Summary of 2005 6 Workshops & Conferences CMI Programs & Research Activities Student Programs Collected Works James Arthur Archive 9 Raoul Bott Library CMI Profile Interview with Research Fellow 10 Maria Chudnovsky Feature Article Can Biology Lead to New Theorems? 13 by Bernd Sturmfels CMI Summer Schools Summary 14 Ricci Flow, 3–Manifolds, and Geometry 15 at MSRI Program Overview CMI Senior Scholars Program 17 Institute News Euclid and His Heritage Meeting 18 Appointments & Honors 20 CMI Publications Selected Articles by Research Fellows 27 Books & Videos 28 About CMI Profile of Bow Street Staff 30 CMI Activities 2006 Institute Calendar 32 2005 Euclid: www.claymath.org/euclid James Arthur Collected Works: www.claymath.org/cw/arthur Hanoi Institute of Mathematics: www.math.ac.vn Ramanujan Society: www.ramanujanmathsociety.org $.* $MBZ.BUIFNBUJDT*OTUJUVUF ".4 "NFSJDBO.BUIFNBUJDBM4PDJFUZ In addition to major,0O"VHVTU BUUIFTFDPOE*OUFSOBUJPOBM$POHSFTTPG.BUIFNBUJDJBOT ongoing activities such as JO1BSJT %BWJE)JMCFSUEFMJWFSFEIJTGBNPVTMFDUVSFJOXIJDIIFEFTDSJCFE the summer schools,UXFOUZUISFFQSPCMFNTUIBUXFSFUPQMBZBOJOnVFOUJBMSPMFJONBUIFNBUJDBM the Institute undertakes a 5IF.JMMFOOJVN1SJ[F1SPCMFNT SFTFBSDI"DFOUVSZMBUFS PO.BZ BUBNFFUJOHBUUIF$PMMÒHFEF number of smaller'SBODF UIF$MBZ.BUIFNBUJDT*OTUJUVUF $.* BOOPVODFEUIFDSFBUJPOPGB special projects
  • Floer Homology, Gauge Theory, and Low-Dimensional Topology

    Floer Homology, Gauge Theory, and Low-Dimensional Topology

    Floer Homology, Gauge Theory, and Low-Dimensional Topology Clay Mathematics Proceedings Volume 5 Floer Homology, Gauge Theory, and Low-Dimensional Topology Proceedings of the Clay Mathematics Institute 2004 Summer School Alfréd Rényi Institute of Mathematics Budapest, Hungary June 5–26, 2004 David A. Ellwood Peter S. Ozsváth András I. Stipsicz Zoltán Szabó Editors American Mathematical Society Clay Mathematics Institute 2000 Mathematics Subject Classification. Primary 57R17, 57R55, 57R57, 57R58, 53D05, 53D40, 57M27, 14J26. The cover illustrates a Kinoshita-Terasaka knot (a knot with trivial Alexander polyno- mial), and two Kauffman states. These states represent the two generators of the Heegaard Floer homology of the knot in its topmost filtration level. The fact that these elements are homologically non-trivial can be used to show that the Seifert genus of this knot is two, a result first proved by David Gabai. Library of Congress Cataloging-in-Publication Data Clay Mathematics Institute. Summer School (2004 : Budapest, Hungary) Floer homology, gauge theory, and low-dimensional topology : proceedings of the Clay Mathe- matics Institute 2004 Summer School, Alfr´ed R´enyi Institute of Mathematics, Budapest, Hungary, June 5–26, 2004 / David A. Ellwood ...[et al.], editors. p. cm. — (Clay mathematics proceedings, ISSN 1534-6455 ; v. 5) ISBN 0-8218-3845-8 (alk. paper) 1. Low-dimensional topology—Congresses. 2. Symplectic geometry—Congresses. 3. Homol- ogy theory—Congresses. 4. Gauge fields (Physics)—Congresses. I. Ellwood, D. (David), 1966– II. Title. III. Series. QA612.14.C55 2004 514.22—dc22 2006042815 Copying and reprinting. Material in this book may be reproduced by any means for educa- tional and scientific purposes without fee or permission with the exception of reproduction by ser- vices that collect fees for delivery of documents and provided that the customary acknowledgment of the source is given.
  • AFFINE HECKE ALGEBRAS and THEIR GRADED VERSION 0.1. Let

    AFFINE HECKE ALGEBRAS and THEIR GRADED VERSION 0.1. Let

    JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY Volume 2, Number 3, July 1989 AFFINE HECKE ALGEBRAS AND THEIR GRADED VERSION GEORGE LUSZTIG Dedicated to Sir Michael Atiyah on his sixtieth birthday INTRODUCTION 0.1. Let Hvo be an affine Hecke algebra with parameter Vo E C* assumed to be of infinite order. (The basis elements ~ E Hvo corresponding to simple reflections s satisfy (~+ 1)(Ts - v~C(s») = 0, where c(s) EN depend on s and are subject only to c(s) = c(s') whenever s, Sf are conjugate in the affine Weyl group.) Such Hecke algebras appear naturally in the representation theory of semisimple p-adic groups, and understanding their representation theory is a question of considerable interest. Consider the "special case" where c(s) is independent of s and the coroots generate a direct summand. In this "special case," the question above has been studied in [I] and a classification of the simple modules was obtained. The approach of [1] was based on equivariant K-theory. This approach can be attempted in the general case (some indications are given in [5, 0.3]), but there appear to be some serious difficulties in carrying it out. 0.2. On the other hand, in [5] we introduced some algebras H,o' depending on a parameter roE C , which are graded analogues of Hvo . The graded algebras H '0 are in many respects simpler than Hvo' and in [5] the representation theory of H,o is studied using equivariant homology. Moreover, we can make the machinery of intersection cohomology work for us in the study of H '0 ' while in the K-theory context of Hvo it is not clear how to do this.
  • Prizes and Awards Session

    Prizes and Awards Session

    PRIZES AND AWARDS SESSION Wednesday, July 12, 2021 9:00 AM EDT 2021 SIAM Annual Meeting July 19 – 23, 2021 Held in Virtual Format 1 Table of Contents AWM-SIAM Sonia Kovalevsky Lecture ................................................................................................... 3 George B. Dantzig Prize ............................................................................................................................. 5 George Pólya Prize for Mathematical Exposition .................................................................................... 7 George Pólya Prize in Applied Combinatorics ......................................................................................... 8 I.E. Block Community Lecture .................................................................................................................. 9 John von Neumann Prize ......................................................................................................................... 11 Lagrange Prize in Continuous Optimization .......................................................................................... 13 Ralph E. Kleinman Prize .......................................................................................................................... 15 SIAM Prize for Distinguished Service to the Profession ....................................................................... 17 SIAM Student Paper Prizes ....................................................................................................................
  • CV Updated: August 16, 2021

    CV Updated: August 16, 2021

    http://yufeizhao.com [email protected] MIT Department of Mathematics Yufei Zhao 77 Massachusetts Ave, Room 2-271 Cambridge, MA 02139, USA Department of Mathematics, Massachusetts Institute of Technology Cambridge, MA Assistant Professor of Mathematics 2017— Class of 1956 Career Development Assistant Professor 2018—2021 Previous and Visiting Academic Positions Department of Mathematics, Stanford University Stanford, CA Visiting Assistant Professor Spring 2020 Simons Institute for the Theory of Computing, UC Berkeley Berkeley, CA Simons-Berkeley Research Fellow Spring 2017 New College, University of Oxford Oxford, UK Esmée Fairbairn Junior Research Fellow in Mathematics 2015—2017 Education Massachusetts Institute of Technology Cambridge, MA Ph.D. Mathematics. Advisor: Jacob Fox 2011—2015 University of Cambridge Cambridge, UK M.A.St. Mathematics with Distinction 2010—2011 Massachusetts Institute of Technology Cambridge, MA S.B. Mathematics, with minor in Economics 2006—2010 S.B. Computer Science and Engineering Selected Awards and Honors NSF CAREER award, 2021 MIT UROP Outstanding Mentor Award for Faculty, 2020 MIT First Year Advisor Award—Innovative Seminar, 2019 Sloan Research Fellowship, 2019 MIT Future of Science award, 2018 SIAM Dénes König Prize, 2018 Johnson Prize, MIT Mathematics Department, 2015 Microsoft Research PhD Fellowship, 2013–2015 Morgan Prize Honorable Mention, 2011 Gates Cambridge Scholarship, 2010–2011 MIT Jon A. Bucsela Prize in Mathematics, 2010 Putnam Math Competition: Three-time Putnam Fellow (top five rank) 2006, 2008,
  • From Stein to Weinstein and Back. Symplectic Geometry of Affine

    From Stein to Weinstein and Back. Symplectic Geometry of Affine

    BULLETIN (New Series) OF THE AMERICAN MATHEMATICAL SOCIETY Volume 52, Number 3, July 2015, Pages 521–530 S 0273-0979(2015)01487-4 Article electronically published on February 19, 2015 From Stein to Weinstein and back. Symplectic geometry of affine complex manifolds, by Kai Cieliebak and Yakov Eliashberg, AMS Colloquium Publications, vol. 59, American Mathematical Society, Providence, RI, 2012, xii+364 pp., ISBN 978- 0-8218-8533-8, hardcover, US $78. The book under review [5] is a landmark piece of work that establishes a fun- damental bridge between complex geometry and symplectic geometry. It is both a research monograph of the deepest kind and a panoramic companion to the two fields. The main characters are, respectively, Stein manifolds on the complex side and Weinstein manifolds on the symplectic side. The connection between the two is established by studying the corresponding geometric structures up to homotopy, or deformation, a context in which the h-principle plays a fundamental role. Stein manifolds are fundamental objects in complex analysis of several variables and in complex geometry. There are several equivalent definitions, but the most intuitive one is the following: they are the complex manifolds that admit a proper holomorphic embedding in some Cn (they are in particular noncompact). Stein manifolds can be thought of as being a far-reaching generalization of domains of holomorphy in Cn. Other important classes of examples are noncompact Riemann surfaces and complements of hyperplane sections of smooth algebraic manifolds. The latter are actually examples of affine (algebraic) manifolds, meaning that they are described by polynomial equations in Cn.