Topic: Symmetrized random permutations and random matrices November 29

Presenter: Jinho Baik, Princeton University/IAS

Abstract : Recently, asymptotic statistics of the longest increasing subsequence of a random permutation (Ulam's problem) turns out to have a connection with random GUE matrix. After quick review, we consider symmetrized random permutations to obtain connections with GOE, GSE random matrices, and discuss related topics such as random involutions and certain asymmetric random walk. Analytic issue of the problem is a double scaling limit of certain Toeplitz/Hankel determinants. (Joint work with Eric Rains.)

Topic: Closing the gap in electromagnetic simulations November 29

Presenter: Bjorn Engquist, UCLA

Topic: Introduction to Symplectic Field Theory November 30

Presenter: Yakov Eliashberg, Princeton University

Topic: Congruences of Neron model for tori and the Artin conductor November 30

Presenter: J. Yu, Princeton University

Topic: Constructive criteria for locatization in random operators December 1

Presenter: Michael Aizenman, Princeton University

Topic: Geometry of the group of contact transformations December 1

Presenter: Yakov Eliashberg, Princeton University

Topic: Universality in 2D Ising Model December 2

Presenter: Haru Pinson, IAS

Date: Thursday, December 2, 1999

Time: 2:30 p.m.

Location: Fine 110

Topic: Introduction to Symplectic Field Theory December 2

Presenter: Yakov Eliashberg, Princeton University

Topic: An ergodic interpretation of high-dimensional helicities and applications December 2

Presenter: Tristan Riviere, CNRS, Paris and Courant Institute, NYU

Location: Rutgers, Hill Center, Room 705, tea is available in the 7th floor lounge 3:30 p.m.

Title: Homeomorphisms and simple loops on surfaces December 2

Presenter: Feng Luo, Rutgers University

Topic: Higher Regularity for Globally Area Minimizing Foliations December 3

Presenter: Penny Smith, Lehigh University

Topic: Propositional Proof Complexity December 7

Presenter: Alexander A Razborov, Princeton University

Topic: Derivation of the Euler equation from Quantum mechanics December 7

Presenter: Horng-Tzer Yau, Courant Institute

Topic: The eigenvalue problem and the saturation conjecture December 7

Presenter: William Fulton, University of Michigan

Topic: Smooth dynamics and new theoretical ideas in December 8

nonequilibrium statistical mechancis

Presenter: David Ruelle, I.H.E.S.

Topic: Universality in 2D Ising Model December 9

Presenter: Haru Pinson, IAS

Topic: Introduction to Symplectic Field Theory December 9

Presenter: Yakov Eliashberg, Princeton University

Title: Planar Polygons and Special Lagrangians in Calabi-Yau Manifolds December 9

Presenter: Ciprian S. Borcea, Rider University

Abstract: The possible configurations, up to orintation-preserving isometry, for a planar $n$-gon with prescribed length for each of its edges, make-up a compact space, which is, in general, a smooth, orientable manifold of dimension $(n-3)$.Its topological type varies according a chamber structure for admissible edge-length-vectors, and can be investigated by means of Morse theory, geometric invariant theory, symplectic and toric geometry.

In adequate coordinates, the defining equations are algebraic, and yield families of complex projective varieties whose real points are the above configuration spaces. In particular, a construction used by Darboux for quadrilaterals, leads, in arbitrary dimension, to Calabi-Yau varieties. The singularities of the latter are away from the real locus, and resolutions to Calabi-Yau manifolds will contain identifiable types of special Lagrangians.

A conjecture of Strominger, Yau, and Zaslow suggests that myrror symmetry for pairs of Calabi-Yau manifolds corresponds geometrically to a duality of fibrations in special Lagrangian tori, and indeed, we do find special Lagrangian tori at appropriate points in our family.

A different, yet related complexification, and thus other examples of special Lagrangian tori on Calabi-Yau manifolds, can be obtained from the non-Euclidean scenario. We investigate in more detail the families of K3 surfaces and Calabi-Yau threefolds associated to configuration spaces of pentagons and hexagons.

Topic: TBA December 14

Presenter: Karen Smith, University of Michigan

Topic: Mathematical problems of superfluids December 16

Presenter: Fabrice Bethuel, University of Paris 6

Location: Rutgers, Hill Center, Room 705, tea is available in the 7th floor lounge 3:30 p.m.

Title: TBA December 16

Presenter: Paul Feehan, Ohio State University

Saturday, December 18, 1999

Fine Hall

11:00 Coffee, Common Room

11:30 Victor Guillemin "The Strong Szego Limit Theorem"

1:30 Sergiu Klainerman "PDE as a unified subject"

2:30 Chris Sogge "Global estimates for the wave equation"

3:30 Alice Chang "Linking the Zeta functional determinant to problems in PDE"

All are welcome! To help the organizers, please e-mail conf99@math.princeton.edu before December 9, 1999 if you are

planning to attend.