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

Title: Existence of solutions for the vortex sheet problem. March 8

Speaker: Zhouping Xin, Courant Institute, New York University and

Chinese University of Hong Kong

Topic: Elliptic Yang-Mills equation March 8

Presenter: Gang Tian, M.I.T.

Abstract: The Yang-Mills equation has played a very important role in the study of geometry and topology in the last few decades. Its regularity theory is crucial to applications. In this talk, I will give a brief tour of recent progress on regularity theory of the Yang-Mills equation on Riemannian manifolds. Some geometric applications and open problems will be also discussed.

Topic: Adhesion Dynamics and Random Walks March 9

Presenter: Toufic Suidan, Princeton University

Abstract: Consider N equally spaced point masses on the unit interval of the real line; each point mass is given a random initial velocity. The interparticle interaction is one dimensional gravity and binary collisions of particles are perfectly inelastic. We will be interested in the statistics of the mass aggregation process in the continuum limit. It turns out that this aggregation process is not gradual; it is abrupt and occurs at a nonrandom time. We also comment on the long time behavior of the ballistic case for which gravity is set to zero. These problems can be understood in terms of statistical properties of random walks; several of these properties will be discussed.

Topic: Soliton stability and blowup in modified KdV with critical nonlinearity March 9

Presenter: Frank Merle, Departement de Mathematiques, Ecole Normale

Topic: Floer homology and homology cobordism invariants March 9

Presenter: Kim Froyshev, Harvard University

Title: "Hodge Theory and Algebraic Cycles" March 10

Speaker: Matthew Kerr, Princeton University

Abstract: We demonstrate the dependence of rational equivalence upon the field of definition of a subvariety with a very concrete, cute example. This talk should be of special interest to anyone who would like to see geometric motivation for the Beilinson conjectures, though I think it will be accessible and fun for anyone who knows Abel's theorem.

Title: Eulerian Digraph Immersion March 10

Speaker: Thor Johnson, Princeton University

Abstract: This talk will discuss recent work in developing a theory for eulerian digraphs similar to that for undirected graphs found in Robertson and Seymour's Graph Minors series. Instead of "minor" the natural containment relation when studying eulerian digraphs is immersion. After defining immersion, tree-decompositions and path-decompositionsfor eulerian digraphs will be discussed. Many of the basic properties of these decompositions for the class of undirected graphs hold for eulerian digraphs as well. In particular, having no tree-decomposition of small width is equivalent to containing a certain type of grid. I will briefly discuss how the structure theorem of Graph Minors appears to hold for eulerian digraphs. The potential applications of such a theorem include the well-quasi ordering of eulerian digraphs under immersion and a polynomial-time algorithm for the k arc-disjoint linkages problem.

Topic: Existence results for some fully non-linear elliptic equations March 10

on Riemannian manifolds

Presenter: Jeff Viaclovsky, University of Texas and M.I.T.

Topic: Stochastic Navier Stokes Equations and Wiener Chaos March 16

Presenter: B.L. Rozovskii, University of Southern California, Los Angeles

Abstract: In this talk we are concerned with fluid dynamics described by stochastic flows of diffeomorphisms. Stochastic Euler and Navier-Stokes equations will be derived from the conservation laws of mass and momentum. Well-posedness of these equations shall be discussed. A Wiener chaos expansion of the velocity field will be presented and formulas for the statistical moments of this field will be derived.

Topic: TBA March 20

Presenter: Lev Kapitanski, Kansas State University

Title: On Internet-related scaling phenomena, and what they March 20

tell us about the Internet

Speaker: Walter Willinger, A&T Labs-Research

Abstract: Compared to the Public Switched Telephone Network, the Internet is a prime example of a truly large-scale complex system. To illustrate how various aspects of the Internet's complexity are directly reflected in the nature of the traffic that it carries, we discuss some of the recently observed scaling phenomena in measured Internet traffic (e.g., self-similarity, multifractal scaling), and comment on the few things that they can tell us and on the many things that they may tell us (in due time) about the Internet.

Topic: The Kirillov conjecture March 21

Presenter: M. Baruch, University of California at Santa Cruz

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

Presenter: Jacques Fejoz, Northwestern University

Topic: TBA March 23

Presenter: Steve Zelditch, John Hopkins University

Date: Thursday, March 23, 2000, Time: 4:30, Location: Fine 314

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: Embedded minimal tori and applications March 24

Presenter: Tobias Colding, New York University

Topic: TBA March 29

Presenter: R. Stanton, Ohio State University

Topic: TBA March 30

Presenter: Ilya Ustilovsky, New York University

Topic: TBA March 31

Presenter: Yu Yuan, University of Texas

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

of isolated singularities

Presenter: Yang Boazhong, M.I.T.

Topic: TBA 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: 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