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: Escher, and Symmetry December 1

Presenter: John Conway, Princeton University

Abstract: It will be about the mathematics involved in the work of the Dutch graphic artist M.C. Escher.

Topic: Nonabelian additive number theory December 2

Presenter: Melvyn Nathanson, CUNY

Abstract: A central problem in combinatorial additive number theory is to understand the structure of sumsets hA, where A is a set of integers and hA is the set of all sums of h elements of A. This talk will be a survey of results and open problems about the asymptotic behavior of sumsets in abelian and nonabelian structures.

Topic: Universality in 2D Ising Model December 2

Presenter: Haru Pinson, Institute for Advanced Studies

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, Institute for Advanced Studies

Topic: Transverse intersection of foliations in 3 manifolds December 9

Presenter: Takashi Tsuboi, Tokyo University

Abstract: We are interested in knowing whether the transverse intersection of two foliations is unique. The dynamics of several flows, such as the Anosov flows, give rise to multi-foliations, hence the uniqueness of the intersection of two foliations implies that the flow is determined (up to parametrization) by the associated foliations. We will discuss the uniqueness question for several pairs of foliations. In particular, I will explain a joint work with Shigenori MATSUMOTO that the transverse intersection is unique for the Anosov foliations of the suspensions of hyperbolic toral automorphisms, however, the transverse intersection is not unique for the Anosov foliations of the unit tangent bundles over hyperbolic surfaces.

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: Analysis of the non-linear $\overline\partial$ operator December 10

Presenter: Igor Rodnianski, Princeton University

Topic: Introduction to Symplectic Field Theory December 14

Presenter: Yakov Eliashberg, Princeton University

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.

Topic: 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.