Current info: http://www.math.princeton.edu/~web/seminar.html

Topic: Waves in Nonlinear Periodic Structures March 22

Presenter: Michael I. Weinstein, Bell Laboratories

Topic: New solutions of the vacuum Einstein equations March 22

Presenter: R. Schoen, Stanford University

Abstract: This talk will give a brief introduction to the Cauchy problem for the vacuum Einstein equations. We will describe new constructions of Cauchy data which produce asymptotically flat solutions with particularly simple asymptotic behavior. For example, we will explain why solutions which are identical with a Kerr solution in a neighborhood of spatial infinity are dense in a natural topology on the space of initial data.

Topic: On Log Canonical Thresholds of Reducible Plane Curves March 23

Consisting of Three Components - Presenter: T. Kuwata, Tokyo Denki

Time: 11 a.m., Location: Fine 601

Topic: Unirationality of cubic hypersurfaces - Presenter: J. Kollár, Princeton University

Time: 1:30 p.m., Location 1201

Topic: Birationality, characterization of $P^n$ and applications - Presenter: Y. Kachi, The John Hopkins University

Time: 3 p.m., Location 1201

Topic: Equivariant compactifications of vector groups - Presenter: Y. Tschinekl, Princeton University

Time: 4:30 p.m., Location: Fine 1201

Topic: Global secular dynamics in the planar three-body problem March 23

Presenter: Jacques Fejoz, Northwestern University

Date: Thursday, March 23, 2000, Time: 2:30 p.m., Location: Fine 110

Topic: Ample line bundles on symplectic manifolds and their almost March 23

holomorphic sections

Presenter: Steve Zelditch, John Hopkins University

Abstract: The space H^0(M, L^N) of holomorphic sections of powers of an ample line bundle over a compact Kahler manifold has a generalization to almost-complex symplectic manifolds. We study the limits as N tends to infinity of the probabilities that the sections do various things. The main theme is that in an asymptotic sense, almost holomorphic sections behave very much like holomorphic ones, hence like homogeneous polynomials of degree N.

Topic: Complex Monge-Ampere equation and Ricci curvature March 23

Presenter: Gang Tian, M.I.T. & Princeton University

Topic: Global Rough Solutions for Nonlinear Wave Equations

Presenter: M. Keel, Cal Tech

Topic: Random Walks and the Gittins Index March 24

Presenter: Peter Winkler, Bell Labs

Abstract: Let $G$ be a fixed finite graph with a distinguished target node, and suppose that two tokens reside initially at nodes $x$ and $y$ of $G$. At each tick of a clock you may select either token, which then takes a uniformly random step to a neighboring node. Your object is to get one token to the target in minimum expected time. Say "$x>y$" if your correct strategy begins with selecting the token at $x$. If $x>y$ and $y>z$, is $x>z$?

Topic: Covering lattice points by subspaces March 24

Presenter: Gergely Harcos, Princeton University

Abstract: I shall find tight estimates for the minimum number of proper subspaces needed to cover all lattice points in an

n-dimensional convex body C, symmetric about the origin 0. This problem arised in connection with the higher

dimensional Littlewood-Offord problem. Apart from some auxiliary results in number theory the pigeon-hole principle will

be the only tool utilized in the talk. Joint work with I. Barany, J. Pach and G. Tardos.

Topic: Embedded minimal tori and applications March 24

Presenter: Tobias Colding, New York University

Topic: The Vlasov-Maxwell System March 27

Presenter: Robert Glassey, Indiana University

Abstract: The Vlasov-Maxwell equations are the equations of motion for a collisionless plasma: a high temperature, low density ionized gas in which electromagnetic forces dominate collisional effects. In this lecture we will probe the major open question: does the initial-value problem have a smooth global solution for smooth data of unrestricted size? That is, are there shocks in collisionless plasmas? Partial answers and known results will be surveyed, including weak solutions, solutions with small data, the resolution of the large-data problem in two space dimensions and classical vs. relativistic formulations.

Topic: Mechanisms Underlying Realistic Response in a March 27

Model of the Visual Cortex

Presenter: Mike Shelley, Courant Institute, New York University

Abstract: What might be the cortical mechanisms underlying neuronal responses in the primary visual cortex V1, such as orientation selectivity, diversity in its degree, and Simple/Complex cell behaviors. I will discuss a minimal, but realistic, neuronal network model of a V1 input layer. In an inhibitorily dominated regime, the network dynamics yields orientation selectivity, dynamics, response diversity, and Simple behaviors, in qualitative agreement with experiment. A mathematical analysis of data, and of reduced "coarse-grained" network models, reveal some of the underlying network mechanisms. Tea will be served at 3:45 p.m. in 204 Fine Hall

Topic: Modularity of Q-curves March 28

Presenter: Jordan Ellenberg, Princeton University

Topic: TBA March 29

Presenter: R. Stanton, Ohio State University

Topic: Contact structures on the boundaries of subcritical Stein domains March 30

Presenter: Ilya Ustilovsky, New York University

Topic: Constructing representations of a matroid. March 31

Presenter: Jim Geelen, University of Waterloo

Abstract: ``For $M$ is a matroid that is not representable over a finite field {\bf F}, we consider the problem of finding a short certificate that $M$ is not representable over {\bf F}$.'' The purpose of this talk is to explain the previous sentence and to present partial results toward the solution of the problem. This is joint work with James Oxley, Dirk Vertigan, and Geoff Whittle.

Topic: A priori estimates for two classes of fully nonlinear March 31

equations without convexity

Presenter: Yu Yuan, University of Texas

Abstract: (I) We derive an a priori estimate for the fully nonlinear elliptic equations with convex level sets. We do not need any convexity assumption for the proof of two dimensional case, as the classical result indicates. This is a joint work with L. A. Caffarelli. (II) We also derive an a priori estimate in dimension three for the special Lagrangian equations, which fail both the usual convexity condition and the assumption in (I).

Topic: Uniqueness of tangent connections of Yang-Mills March 31

connections of isolated singularities

Presenter: Yang Boazhong, M.I.T.

Topic: Discrete analogues of the spherical maximal function April 3

Presenter: Stephen Wainger, University of Wisconson

Topic: TBA April 3

Presenter: Mark Gross, University of Warwick

Topic: Random Colorings of a Cayley Tree April 5

Presenter: Peter Winkler, Bell Labs

Abstract: Probability measures on the space of proper colorings of a Cayley tree (that is, an infinite regular connected graph with no cycles) are of interest not only in combinatorics but also in statistical physics, as states of the antiferromagnetic Potts model at zero temperature, on the ``Bethe lattice''. We concentrate on a particularly nice class of such measures which remain invariant under parity-preserving automorphisms of the tree. Using branching random walks, we determine when more than one such measure exists. This talk (on joint work with Graham Brightwell, of the London School of Economics) will provide, we hope, a helpful glimpse into the rapidly expanding intersection of combinatorics and statistical physics.

Topic: TBA April 10

Presenter: Hart Smith, University of Washington

Topic: TBA April 11

Presenter: Sándor Kovács, Chicago

Topic: Some Insights of Computational Complexity Theory April 12

Presenter: Avi Wigderson, I.A.S. & Hebrew University, Jerusalem

Abstract: Computational complexity theory has been one of the most exciting fields of scientific research over the last few decades. This research studies the power of feasible computation, and is guided by a few clear and focused questions, deeply motivated on scientific, practical and philosophical grounds, like the P vs NP problem, and the questions on the power of randomized and quantum computation. While these problems are far from resolved, Complexity Theory was able to offer fresh rigorous definitions to some central notions which naturally (or less so) arise from these questions, and unveil many rich and beautiful connections between them. In this general survey, I would like to probe some of the unique features and insights of the complexity theory viewpoint. This will be done by considering how (and why) notions which intrigued people for centuries or even millenia (like Knowledge, Randomness, Cryptography, Learning, Proof, and naturally, Computation), reveal new dimensions, and are suprisingly linked together, when viewed from our special Computational Complexity glasses.

Topic: Strong form of Poincare duality April 13

Presenter: Edgar Brown, Brandeis University

Topic: TBA April 17

Presenter: Jim Colliander, UC Berkley

Topic: TBA April 19

Presenter: N. Higson, Pennsylvania State University

Topic: TBA April 20

Presenter: Casim Abbas, University of Pennsylvania

Topic: TBA April 24

Presenter: Chris Sogge, John Hopkins University

Topic: "New" geometry and topology of orbifolds April 27

Presenter: Y. B. Ruan, University of Wisconsin at Madison