Annual Report 2005 - Fields Institute - University of Toronto

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Andre Henriques (MIT) Computation of torus-equivariant complex oriented cohomology theories of flag varieties Michael Hopkins (MIT) The work of Jack Morava Po Hu (Wayne State) On algebraic analogues of string topology Mikhail Kapranov (Yale) Floer homology for ind-schemes Nitu Kitchloo (San Diego) Buildings for Kac-Moody groups Igor Kriz (Michigan) Conformal field theory, Grothendieck-Teichmueller theory and other structures Jacob Lurie (MIT) Elliptic cohomology and derived algebraic geometry James McClure (Purdue) The intersection pairing for PL chains, with applications to string topology Goro Nishida (Kyoto) Steenrod algebra, Dickson invariants and the automorphism groups of the additive group law Charles Rezk (UIUC) On Dyer-Lash of algebras of operations on Morava E-Theory Eric Sharpe (UIUC) D-branes and derived categories Andrew Stacey (NTNU, Trondheim) A Construction of a Dirac operator on loop space Stephan Stolz (Notre Dame) Elliptic cohomology via conformal field theories? Dennis Sullivan (SUNY Stony Brook) Chain level Gromov-Witten theory T h e m a t i c P r o g r a m s Hirotaka Tamanoi (UC Santa Cruz) Decomposition of orbifold mapping spaces and geometric Hecke operators Constantin Teleman (Cambridge) Twistings in Gromov-Witten theory Takeshi Torii (Fukuoka, Japan) Degeneration of formal groups and generalized Chern characters David Ben-Zvi (Texas) The Geometric Langlands Program Workshop on Mirror Symmetry November 19–23, 2004 Held at Perimeter Institute Organizing Committee: Denis Auroux (MIT), Mark Gross (Warwick), Kentaro Hori (Toronto) and Noriko Yui (Queen’s) This workshop brought together leading mathematicians and theoretical physicists. The talks focused on various recent developments in the field of mirror symmetry, from both the mathematical and physical points of view, and provided a broad panorama of the current state of the art. Additional funding for the workshop was provided by the Connaught fund, and by the NSF through a grant in support of the program. The mathematical aspects of mirror symmetry that the workshop focused on included the Strominger-Yau-Zaslow conjecture, the Kontsevich homological mirror symmetry conjecture, number-theoretic aspects (arithmetic and motives), and generalized Kähler geometry and T-duality. In addition, recent developments such as (0,2) mirror symmetry and (0,2) correlation functions, flux backgrounds, affine structures, etc., were discussed. The talks on the theoretical physics side of mirror symmetry covered topics on topological sigma models, matrix factorizations, T-duality for holomorphic non-commutative tori, the Hori–Vafa conjecture, etc. This workshop was the third or fourth concerning mirror symmetry held in Canada in the last four years. It was undoubtedly the biggest one in terms of number of participants, and also the broadest from the scientific point of view. It brought together leading mathematicians and theoretical physicists from all over the world for five days, to Fields Institute 2005 ANNUAL REPORT 22
study and discuss the recent developments in mirror symmetry. The notion of mirror symmetry originated in string theory, but it has exploded onto the mathematical scene. Most notably, many recent developments in Algebraic Geometry, Symplectic Geometry, Number Theory and Lie Algebras have been inspired by mirror symmetry and string theory. The workshop offered opportunities for mathematicians to exchange ideas and discuss problems surrounding mirror symmetry face to face with theoretical physicists. Perimeter Institute’s new award-winning building provided a wonderful stage for the workshop. All talks were presented in the main auditorium equipped with state of the art high tech gadgets. Many mathematicians opted for blackboards for their presentations! There was plenty of time for participants to discuss mathematics and physics in informal settings; in particular, the “Bistro” on the fourth floor not only supplied lunches and refreshments, but also big blackboards! Congratulations go to Perimeter Institute for creating such an inspiring atmosphere. Speakers: Allan Adams (Harvard) Towards (0,2) mirror symmetry Denis Auroux (MIT) Homological mirror symmetry for Fano surfaces Victor Batyrev (Universität Tübingen) Cohomology groups in mirror symmetry Andrei Caldararu (Pennsylvania) Hochschild structures: an algebraic geometer’s point of view Xenia de la Ossa (Oxford) The arithmetic of Calabi-Yau manifolds Kenji Fukaya (Kyoto) Counting open Riemann surface with Lagrangian boundary condition and perturvative Chern-Simons gauge theory Mark Gross (Warwick) Affine structures, mirror symmetry, and K3 surfaces Marco Gualtieri (Fields) Generalized Kähler geometry and T-duality Anton Kapustin (Caltech) Topological sigma-models and generalized complex geometry T h e m a t i c P r o g r a m s Sheldon Katz (Illinois at Urbana-Champaign) (0,2) correlation functions Albrecht Klemm (Wisconsin at Madison) Higher genus amplitudes on compact Calabi-Yau and threshold corrections Naichung Conan Leung (Minnesota) G 2 geometry and mirror triality Grigory Mikhalkin (Toronto) Complex, real and tropical curves David R. Morrison (Duke) Strominger-Yau-Zaslow revisited Yong-Geun Oh (Wisconsin at Madison) The [FOOO]-obstruction cycle and Landau-Ginzburg potential Tony Pantev (Pennsylvania) T-duality for holomorphic non-commutative tori Rolf Schimmrigk (Kennesaw State) Arithmetic varieties from string theory and D-branes Bernd Siebert (Universitaet Freiburg) Affine geometry of degeneration limits and mirror symmetry Jan Stienstra (Utrecht) Motives and strings Helena Verrill (Louisiana State) The Picard-Fuchs equation of the A n family of Calabi-Yau varieties Johannes Walcher (IAS Princeton) Matrix factorizations: stability and mirror symmetry Noriko Yui (Queen’s) Certain non-rigid Calabi–Yau threefolds over Q and their modularity Ilia Zharkov (Harvard) Kähler affine structures and the affine Calabi conjecture Fields Institute 2005 ANNUAL REPORT 23
Page 1 and 2: Fields Institute 2005 ANNUAL REPORT
Page 3 and 4: Institute Profile 2 Message from th
Page 5 and 6: departments in universities and col
Page 7 and 8: major fund-raising campaign that wo
Page 9 and 10: postdoctoral fellows, the institute
Page 11 and 12: The Geometry of String Theory: Sept
Page 13 and 14: There were two additional associate
Page 15 and 16: Course on Symplectic Geometry and T
Page 17 and 18: Andrew Neitzke (Harvard) Elements o
Page 19 and 20: Student and auditor feedback about
Page 21 and 22: string theory. Nigel Hitchin himsel
Page 23: The conference featured reports of
Page 27 and 28: Takuya Okuda (Caltech) Calabi-Yau c
Page 29 and 30: workshop, Thursday was devoted to a
Page 31 and 32: Other issues center around various
Page 33 and 34: Thinking of this problem in terms o
Page 35 and 36: tiveness of Quantum Physics in Math
Page 37 and 38: Lectures DISTINGUISHED LECTURE SERI
Page 39 and 40: the pair on an equal footing. In th
Page 41 and 42: outstanding question in this field
Page 43 and 44: etween mathematics, statistics, and
Page 45 and 46: distinguished long-term visitors, C
Page 47 and 48: Achim Kempf of the University of Wa
Page 49 and 50: THE NATIONAL PROGRAM ON COMPLEX DAT
Page 51 and 52: Hugh Chipman disciplines, some comm
Page 53 and 54: MITACS, NPCDS, the Sustainable Fore
Page 55 and 56: Bo Song (Clemso) Visualization of f
Page 57 and 58: Michael Joswig (TU Berlin) Convex h
Page 59 and 60: Norbert Lütkenhaus (Erlangen) Quan
Page 61 and 62: Career: Some Remarks. On August 7,
Page 63 and 64: Jeremy Quastel and Tom Salisbury Ne
Page 65 and 66: the property (T) in 2001.) The work
Page 67 and 68: This conference brought together ma
Page 69 and 70: Many speakers reported on recent pr
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Combinatorics workshop participants
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Workshop participants Each of the i
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Workshop participants Speakers: Ran
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Bruce Allison their work, discuss n
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Poster participants talks, each of
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Workshop on Mathematical Programmin
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University) presented recent result
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volume are Rajendra Bhatia (India),
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SEMINARS Algebraic Combinatorics Se
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Geometry and Model Theory Seminar S
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ments. All of the results obtained
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Vladimir Vinogradov (Ohio) On “co
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parameters - for example, in the ca
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Winter 2004 Meeting of the Canadian
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Special Sessions: Automatic Sequenc
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meeting introduced an Industry/Acad
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The workshop was attended by approx
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tri-annually. MOPTA 05 will be held
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Lowell Aronoff (Cannex Financial Ex
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Kuznetsov, he models each firm usin
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ment returns. The object of the res
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Camp participants Math Camp Program
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This Fields-sponsored symposium was
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Fields Institute Fellows The honour
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Fields Institute Communications Ser
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BARBARA LEE KEYFITZ Director TOM SA
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Scientific Advisory Panel 2004-2005
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and of the Board of Directors of th
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Industrial Advisory Board The Indus
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students at the University of Ottaw
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and graduate students are involved
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F i n a n c i a l S t a t e m e n t
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Fields Institute 2005 ANNUAL REPORT
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Annual Report 2005 - Fields Institute - University of Toronto

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