race problem

Presenter: Kevin Ford, University of South Carolina

Topic: Mellin transform techniques for elliptic layer potentials on polygons November 6

Presenter: Irina Mitrea, Institute for Advanced Study

Topic: Twist, kinks, and drag: whirling elastica November 6

Presenter: Tom Powers, Brown University

Topic: The Theta Body and Partitionable Graphs November 7

Presenter: Bruce Shepherd, Lucent Technologies

Topic: Algebro-geometric isomonodromic deformations and variation of the November 7

mirror map

Presenter: Charles Doran, Columbia University

Abstract: Variation of the string-theoretic mirror map in families motivates an investigation of the Picard-Fuchs differential equation of a pencil under deformation. Such variations define special algebraic solutions to isomonodromic deformation equations. Explicit Painleve VI solutions coming from elliptic pencils are determined. The method is generalized, yielding a topological characterization of a large class of "pullback" solutions coming from specially parametrized Hurwitz curves.

Topic: Arithmetic progressions of length four November 8

Presenter: T. Gowers, Cambridge University and Princeton University

Abstract: The famous theorem of Szemer\'edi, proving a conjecture of Erd\"os and Tur\'an from 1936, asserts that for every $\delta>0$ and every natural number $k$ there exists an $N$ such that every subset $A\subset\{1,2,\dots,N\}$ of cardinality at least $\delta N$ contains an arithmetic progression of length $k$. When $k=2$ this assertion is trivial. The case $k=3$ was proved by Roth in 1953 using the circle method. The case $k=4$ is much harder (for reasons that can be made quite explicit) and was not solved until 1969, when Szemer\'edi found a highly ingenious combinatorial argument, which over the next few years he was able to extend to progressions of arbitrary length. In 1977, Furstenberg discovered a completely different and more conceptual argument using ergodic theory, which led to many extensions of the original theorem. Both these proofs ignored Roth's method, and indeed there are very serious obstacles to extending this method to progressions of length greater than three, as I shall demonstrate. However, it can be done, and this will be the main topic of the talk. One of the main advantages of the new approach to the theorem is that it gives very greatly improved bounds for the dependence of $N$ on $k$ and $\delta$. Another is that the proof is much more closely related to results in additive number theory and may eventually lead to the solution of problems in that area.

Topic: Bernoulli Convolutions and K-Partitions with Intermediate Values of November 9

Conditional Entropies

Presenter: Elon Lindenstrauss, Institute for Advanced Study (joint work with Yuval Peres and Wilhelm Schlag)

Abstract: In my talk I will describe how one can use the theory of Bernoulli convolutions to study certain linear realizations of a Bernoulli process on two symbols as a real valued stationery process, which we show have trivial left and right tails. This work was motivated by a question suggested to us by Ya. Sinai regarding the possible values of the entropy of $ K $-partitions, which we answer for the case of Bernoulli measure preserving systems. Time permitting, I will also discuss related new results regarding Bernoulli convolutions and more general projected measures in the symbolic context.

Topic: Monochromatic Unit Fractions November 9

Presenter: E. Croot, Berkeley University

Abstract: We will outline the proof of a general theorem on unit fractions, which has the following corollary:

There exists a constant $b>0$ (effective and computable) such that for any $r$-coloring of the natural numbers $\geq 2$, there exits a monochromatic set $S \subset [2,b^r]$ such that $$\sum_{n \in S} {1 \over n} = 1. $$ In fact, we will show that $b$ may be taken to be $e^{167000}$, for $r$ sufficiently large, and we note that $b$ cannot be taken to be smaller than $e$, since the integers in $[2,e^{(1-\epsilon)r}]$ can be partitioned into $r$ subsets such that the sum of the reciprocals of the numbers in each subset is just under $1$.

Topic: P. A. Smith theory and duality November 8

Presenter: Bernhard Hanke, University of Munich/Notre Dame

Topic: Minimal graphs in R^3 over unbounded domains November 10

Presenter: Joel Spruck, Johns Hopkins University

Topic: TBA November 13

Presenter: Peter Bunge, Geosciences, Princeton University

Topic: Dependent Random Selections and the Balog-Szemeredi Theorem November 14

Presenter: Tim Gowers, University of Cambridge

Topic: TBA November 15

Presenter: Oded Schramm, Microsoft Research and Wiezmann Institute

Topic: Induction theorems in algebra and topology November 16

Presenter: J. Grodal, Institute for Advanced Study

Topic: Sharp Sobolev-Poincare inequalities on compact Riemannian manifold November 17

Presenter: Emmanuel Hebey, Universite de Cergy-Pontoise

Topic: TBA November 20

Presenter: Haim Brezis, Université de Paris VI and Rutgers University

Topic: Is M_{g,n} a Mori dream space (mod p)? November 21

Presenter: Sean Keel, University of Texas

Topic: The PCT theorem and local observables November 21

Presenter: Jakob Yngvason, University of Vienna

Topic: The monodromy matrix, the adiabatic WKB method and the spectrum November 22

of quasi-periodic operators on the real line

Presenter: Frederic Klopp, University of Paris

Topic: TBA November 22

Presenter: A. Eskin, University of Chicago

Topic: Harmonic analysis on the infinite symmetric group November 27

Presenter: Alexei Borodin, University of Pennsylvania

Topic: Non-uniform structures in granular and gas-solid flows November 27

Presenter: Sankaran Sundaresan, Chemical Engineering, Princeton University

Topic: TBA November 29

Presenter: H. Hofer, Courant Institute and Princeton University

Topic: TBA November 30

Presenter: V. Shokurov, Johns Hopkins University

Topic: TBA December 1

Presenter: Wang Guo-Fang, Max Planck Institute

Topic: TBA December 4

Presenter: Salvatore Torquato, Chemistry, Princeton University

Topic: The moduli space of cubic surfaces is complex hyperbolic December 5

Presenter: Jim Carlson, University of Utah

Topic: TBA December 8

Presenter: Claude Le Brun, SUNY Stony Brook

Topic: Coherent and Dissipative Electronic Transport in Aperiodic Media December 12

Presenter: Jean V. Bellissard, Universite Paul Sabatier, Toulouse, France and Institut Universitaire de France