Topic: Lattice point problems and distribution of values of quadratic forms February 1 at IAS

Presenter: Friedrich Goetze, University of Bielefeld

Topic: Super-Resolution in Time-Reversal Acoustics February 5

Presenter: Hongkai Zhao, University of California, Irvine

Abstract: In time-reversal acoustics a signal is recorded by an array of transducers, time-reversed and then re-transmitted into the medium. The re-transmitted signal propagates back through the same medium and refocuses on the source. The possibility of refocusing by time reversal has many important applications in medicine, geophysics, non-destructive testing, underwater acoustics, wireless communications, etc. In a homogeneous medium, the refocusing resolution of the time-reversed signal is limited by diffraction. When the medium has random inhomogeneities the resolution of the refocused signal can in some circumstances beat the diffraction limit. This is super-resolution. We give a theoretical treatment of this phenomenon and use numerical simulations to confirm the theory. This is a joint work with P. Blomgren and G. Papanicolaou.

Topic: Elliptic genera of singular varieties February 6

Presenter: A. Libgober, Chicago Circle

Topic: Quantum lattice systems at intermediate temperatures February 7

Presenter: Daniel Ueltschi, Princeton University

Topic: Reeb chords and symplectic geometry February 8

Presenter: Klaus Mohnke, Stanford University

Abstract: Using Gromov's construction of holomorphic disks with boundary on a Lagrangian submanifold I will prove that for each Legendrian knot in the standard contact three sphere and any corresponding contact one form there exists a Reeb orbit starting and ending on the knot. I will also discuss other situations in which one can derive the existence of such Reeb chords.

Topic: Title: p-adic L-functions of elliptic curves at supersingular primes February 8 at IAS

Presenter: Robert Pollack, Harvard University

Abstract: The p-adic L-function of an elliptic curve at an ordinary prime has finitely many zeroes all encoded in a single polynomial. This polynomial has great conjectural arithmetic importance via the Main Conjecture. The supersingular case is very different as the L-series is known to have infinitely zeroes. This talk will attempt to shed some light on the arithmetic nature of this situation.

Topic: Ricci curvature, minimal volumes, and Seiberg-Witten theory February 9

Presenter: Claude LeBrun, SUNY Stony Brook

Topic: A problem on differential forms coming from economics February 12

Presenter: Louis Nirenberg, Courant Institute

Topic: TBA February 12

Presenter: Terry Lyons, University of Oxford

Topic: Jet schemes of locally complete intersection canonical singularities February 13

Presenter: M. Mustata, University of California at Berkeley

Topic: What's (Genuinely) New in Constrained Optimization February 13

Presenter: Margarent Wright, Bell Laboratories, Lucent Technologies, Murray Hill, New Jersey

Abstract: Methods for finding the best value of a function are relatively easy to motivate and explain when there are no restrictions on the variables. Once constraints are added, however, the situation is much less clearcut. Solution techniques and convergence analysis can become so nonintuitive and so complicated that it is difficult to determine the connections, if any, between an apparently new approach and previous suggestions. We shall examine some of the most popular ideas today for treating constrained optimization problems, with special attention to novelty and related properties. This will be a fairly general talk (for non-experts in optimization).

Topic: Capacity of Quantum Channels February 14

Presenter: Mary Beth Ruskai, University of Massachusetts, Lowell

Topic: TBA February 14

Presenter: J. Arthur, University of Toronto and the Institute for Advanced Study

Topic: Variational problems from quantum field theory: February 15

The Chern-Simons-Higgs model

Presenter: Juergen Jost, Max Planck Institute, Leipzig

Topic: TBA February 19

Presenter: Paul Barford, Wisconsin University

Topic: Branched covers of the projective line and the Chow ring of the moduli February 20

space of curves

Presenter: R. Vakil, MIT

Topic: Higher-period ordered phases on the Bethe lattice February 21

Presenter: James Freericks, Georgetown University

Topic: On the smooth ergodic theory of some examples of parabolic flows February 21

Presenter: Giovanni Forni, Princeton University

Date: Wednesday, February 21, 2001, Time: 4:00 p.m., Location: Fine Hall 314

Abstract: We will present recent results on the behaviour of ergodic averages of smooth functions for two examples of `parabolic' conservative flows: generic area-preserving flows (with saddle-like singularities) on higher genus surfaces and horocycle flows on (compact) surfaces of constant negative curvature. We prove that the deviation of ergodic averages from the leading behaviour determined by the ergodic theorem exhibits a power-law decay controlled by invariant distributions. In the case of flows on higher genus surfaces this result was part of a series of conjectures by M.Kontsevich and A.Zorich. The proofs are based on the analysis of the hyperbolicity properties of the appropriate `renormalization' dynamics, related to the Teichmuller flow on the moduli space in the case of flows on higher genus surfaces and to the geodesic flow in the case of horocycle flows.

Topic: TBA February 23

Presenter: Gary Jensen, Washington University in St. Louis

Topic: TBA February 26

Presenter: Shadi Tahvildar-Zadeh, Rutgers University

Topic: Stochastic Optimization Problems in Finance February 26

Presenter: Ronnie Sircar, ORFE, Princeton University

Topic: TBA March 5

Presenter: Walter Strauss, Brown University

Topic: TBA March 5

Presenter: Jan Hesthaven, Brown University

Topic: TBA March 9

Presenter: Tian-Jun Li, Princeton University

Topic: TBA March 12

Presenter: Mei-Chi Shaw, University of Notre Dame

Topic: TBA March 12

Presenter: Rich Mclaughlin, University of North Carolina

Topic: TBA March 26

Presenter: Linda Rothschild, University of California-San Diego

Topic: Stochastic Growth Models on Lattices and Trees March 26

Presenter: Thomas Liggett, University of California, Los Angeles

Abstract: For the past thirty years, probabilists have studied a number of stochastic growth models that were motivated by problems in physics and biology. One of the most important of these is known as the contact process -- growth occurs as the result of "contact" with existing individuals. Such models often exhibit phase transitions, and this is the feature that leads to most of our interest in them. Until a decade ago, the contact process was studied almost exclusively on Euclidean lattices, leading to a rather complete theory in that context. Since then, it has been discovered that the behavior of the process can be quite different on exponentially growing structures such as homogeneous trees. In particular, the phase structure is richer than it is in the lattice case. In this lecture, I will briefly describe the most important results about the contact process on Z^d, and then the contrasting results for the process on a tree. I will then discuss a variant of the contact process on a tree that has the appealing property that the critical value for the phase transition can be computed explicitly. One of the ingredients in the computation is a collection of combinatorial identities satisfied by the d-ary Catalan numbers.

Topic: TBA March 27

Presenter: J. Starr, MIT

Topic: Some mathematical challenges from materials science March 28

Presenter: J. Taylor, Rutgers University

Topic: TBA March 30

Presenter: Vincent Moncrief, Yale University

Topic: TBA April 2

Presenter: Steve Wainger, University of Wisconsin

Topic: TBA April 2

Presenter: Eric Vanden-Eijnden, CIMS, New York University

Topic: Basic facts about wavelets that the cognoscenti are sure they know April 3

but I have doubts about this

Presenter: Guido Weiss, Washington University

Topic: TBA April 6

Presenter: Daniel Pollack, University of Washington