Topic: The Notorious Piston and Other Problems in March 10

Nonequilibrium Statistical Mechanics

Presenter: Joel Lebowitz, Rutgers University

Topic: Some problems in the theory of trigonometric series March 10

Presenter: Sergei V. Konyagin, University of North Carolina and

Moscow State University

Abstract: A natural way to represent a periodic function is a trigonometric series. But whether that series represents the function adequately depends on its convergence, or divergence, properties. We propose to present selected results and problems on one-dimensional trigonometric series. The following questions will be discussed.

1. Convergence of trigonometric Fourier series almost everywhere.

2. The almost everywhere order of growth of the sequence of partial sums of Fourier series.

3. How can a rearrangement of Fourier series improve its convergence properties?

4. (If time permits.) Representation of functions by general trigonometric series.

Topic: Braid Groups and Branched Coverings: Beyond the Spherical Case March 11

Presenter: David Goldberg, Princeton University

Note: Pizza will be provided

Topic: Choosability for Ax=y March 11

Presenter: Matt Devos, Princeton University

Abstract: Let F be a finite field with p^c elements and let A be an n x n matrix over F. We are interested in solving the

equation Ax=y for column vectors x and y with certain coordinate-wise restrictions. In particular, for each i we will

restrict the ith coordinate of x to be in some set Xi and the ith coordinate of y to be in some set Yi. For an integer k, when

is it true that for every set of restrictions with |Xi| = k+1 and |Yi| = p^c - k, there exists a solution to Ax=y meeting these

requirements? Clearly if det(A) is nonzero then A has this property for k = p^c - 1. The permanent lemma of Noga Alon

proves that if perm(A) is nonzero then A has this property for k = 1. We will present a theorem which generalizes both of

these facts, and then apply it to prove a "choosability" generalization of Jaeger's 4-flow and 8-flow theorems.

Topic: Semi-invariants of Quivers and Klyachko's Saturation Problem March 11

Presenter: Harm Derksen, MIT

Abstract: For a quiver without oriented cycles, we consider the ring of semi-invariants of all representations of that quiver

of a fixed dimension. Our main result is that the semi-invariants constructed by Schofield always generate the

semi-invariant ring. Other results of Schofield now imply that the set of weights of the semi-invariants is given by linear

inequalities, and, in particular, this set is saturated. Applied to the triple flag quiver, our result gives a short proof of results

of Klyachko and Knutson-Tao about the set of nonzero Littlewood-Richardson coefficients.

Topic: Exotic smooth structures on 3(CP^2)#n(-CP^2) March 11

Presenter: Bahn Doug Park, Princeton University

Topic: On the distribution of spacings between quadratic residues, March 11

(work of Kurlberg and Rudnick)

Presenter: Wilhelm Schlag, Princeton University

Topic: Non-vanishing of quadratic Dirichlet L-functions at s=1/2 March 11

Presenter: Kannan Soundararaja, Princeton University

Topic: The mathematics of financial risk management March 12

Presenter: Luis Seco, University of Toronto

Topic: Incompressible flows of an ideal fluid with unbounded vorticity March 12

Presenter: Mikhail Vishik, University of Texas, Austin

Topic: Choosability with separation March 18

Presenter: Jan Kratochvil, Charles University, Prague

Abstract: List colorings and choosability of graphs are variants of coloring problems that became popular and thoroughly

studied in the last decade. In this talk I will report on joint work with Zs. Tuza and M. Voigt. We consider a variant of

choosability when the lists assigned to adjacent vertices are required to be "farther apart", namely to have intersection

of small size. This restriction has an interesting impact on the choosability of the graphs in question. For instance, it is now

commonly accepted that planar graphs are 4-colorable, while not every planar graph is 4-choosable. One of our results

shows that for planar graphs, if the lists assigned to adjacent vertices have intersections of size at most one, list size 4

again guarantees the existence of a proper list coloring. Other results I will present give asymptotically tight bounds on

choosability in terms of maximum degree.

Topic: The mathematics of financial risk management March 22

Presenter: Luis Seco, University of Toronto

Topic: Localization of Eigen Functions of Quasi-Periodic Equations March 22

Presenter: Michael Goldstein, University of Toronto

Topic: The mathematics of financial risk management March 23

Presenter: Luis Seco, University of Toronto

Topic: Diophantine, algebraic, deformation properties and patterns for power series March 23

Presenter: Dinesh Thakur, University of Arizona

Topic: The mathematics of financial risk management March 24

Presenter: Luis Seco, University of Toronto

Topic: Dissipation through dispersion March 24

Presenter: Avy Soffer, Rutgers University

Topic: Analysis and Spectral Theory on Graphs and Symplectic Geometry March 24

Presenter: Sergei Novikov, University of Maryland at College Park and

Landau Institute for Theoretical Physics

Topic: The mathematics of financial risk management March 25

Presenter: Luis Seco, University of Toronto

Topic: Statistical properties of weak Gibbs measures for certain March 25

nonhyperbolic systems

Presenter: Michiko Yuri, Sapporo University

Abstract (see attached)

Topic: Finite type of Donaldson polynomials, and the structure of Floer March 25

homology groups

Presenter: Kim Froyshov, Harvard University

Topic: The mathematics of financial risk management March 26

Presenter: Luis Seco, University of Toronto

Topic: The degree counting formulas for scalar curvature equation on S^n March 29

Presenter: Chang-Shou Lin, Chung-Cheng University, Taiwan

Date: March 29, 30 and April 1, 1999

For complete details see IAS homepage

Topic: On the rank of elliptic curves April 29

Presenter: Joseph Silverman, Brown University