Topic: Integrability and selection in non-linear interface dynamics December 9

Presenter: Mark Mineev-Weinstein, Los Alamos National Laboratory

Topic: Combinatorics, representations, and vector bundles on flag varieties December 9

Presenter: Arun Ram, Princeton University

Abstract: History has taught us that the geometry of the flag variety can (and should) be used to understand the

representations of semisimple Lie groups. In recent work with H. Pittie we have reversed the picture and shown how we

can use representation theory and some recent combinatorial techniques of P. Littelmann to attack geometric problems!

I will describe this combinatorics and explain how and why this combinatorics yields very precise information both for

representation theory and for the geometry of flag varieties.

Topic: Percolation and Collision December 10

Presenter: Peter Winkler, Bell Labs

Abstract: Suppose two tokens are taking simple random walks on the same (finite, connected, undirected) graph G. A

"schedule demon" (left over from a 1990 asynchronous distributed computing problem) wishes to push them as far as

possible along their pre-ordained paths without a collision, just by exercising the privilege of deciding at each moment

which token moves next.

The "clairvoyant demon" conjecture says that if the demon is not unlucky and the graph is sufficiently complex, and he

knows where the tokens are going infinitely far into the future, then he can keep them apart forever. This conjecture

remains open.

The "fickle" demon cannot see the future but has a more powerful feature: she can take moves back. Both problems can

be formulated rather neatly as dependent percolation problems. We show why standard percolation methods fail here

but, at least for the fickle demon, a novel approach does the trick. (Our approach is quite different from the independent

proof presented by Bela Bollobas at IAS on Nov 16, joint work with Paul Balister and Alan Stacey.)

Topic: On the differential equations satisfied by weighted orbital integrals December 10

Presenter; W. Hoffmann, Institute for Advanced Studies

Abstract: Weighted orbital integrals are certain tempered distributions on reductive groups over local fields appearing on

the geometric side of the Arthur-Selberg trace formula. For the groundfield of real numbers, they satisfy a system of

differential equations, which was used to determine explicitly their Fourier transforms in the case of rank one. The study of

these differential equations in higher rank reveals a new combinatorial structure connected with root systems. In the talk I

will review the general properties of weighted orbital integrals and the associated invariant distributions, the differential

equations and some results pointing toward a general formula for the Fourier transforms.

Topic: Principal G-bundles over T^2 and T^3 December 10

Presenter: John Morgan, Columbia University

Topic: Intersecting a curve with algebraic subgroups of a multiplicative group December 10

Presenter: Enrico Bombieri, Institute for Advanced Study

Topic: Differentiability of Lipschitz functions on metric measure spaces December 11

Presenter: Jeff Cheeger, Courant Institue

Topic: An Exact Mass Formula for Orthogonal Groups December 11

Presenter: Jonathan Hanke, Princeton University

Topic: The hunt for the Bellman function: Control theory December 14

methods in harmonic analysis.

Presenter: Sergei Treil, Michigan State

Topic: Controlling Dispersive Chaos December 14

Presenter: Paul Kolodner, Bell Laboratories, Lucent Technologies, Inc.

Abstract: Amid the recent enthusiasm for applying new techniques of nonlinear dynamics to the control of chaos, it has

been recognized that control of spatially-extended systems which exhibit erratic behavior is an important and unsolved

problem. In this talk, I will describe a convection experiment in which this goal has been achieved. ``Dispersive chaos'' is

a state observed in experiments on oscillatory convection in binary fluids in a narrow, quasi-one-dimensional, annular

geometry. This state which is characterized by the erratic appearance and abrupt decay of spatially-localized bursts of

traveling waves. In numerical simulations of this system based on the complex Ginzburg-Landau equation, my

collaborators and I have been able to suppress dispersive chaos by applying a spatially-inhomogeneous stress parameter

which is computed from the phase of the complex state variable. We have also implemented such spatial feedback in an

actual convection experiment by adjusting the voltages applied to 24 small heaters arranged along the circumference of the

lower plate of the convection cell. The applied stress-parameter profile is computed from the complex amplitude of the

convection pattern as derived from shadowgraph images. With the right feedback algorithm, we can suppress chaos

near onset and make measurements of the unstable branch of the bifurcation diagram.

Topic: Geometric Eisenstein Series December 15

Speaker: Dennis Gaitsgory, Harvard University and IAS

Topic: A hypergraph version of Dirac's theorem December 17

Presenter: Endre Szemeredi, Rutgers University

Abstract: If in a 3-uniform hypergraph on n vertices, every edge is in at least n/2 hyperedges (triangles), then the

hypergraph contains a Hamiltonian cycle of triangles. Maybe the methods used in the proof are of some interest. (Joint

work with A. Rucinski and V. Rodl.)

Topic: Random products of matrices, sharp ergodic theorems, and distributing

points uniformly on measure spaces

Presenter: Yehuda Shalom, Princeton University

Topic: Toric varieties and nilpotent orbits December 17

Presenter: W. Graham, IAS and University of Georgia

Abstract: One of the most important constructions in Lie theory is the Springer resolution of the nilpotent variety. This

talk will discuss a construction of an analogue for the universal cover of the regular nilpotent orbit, which makes use of

toric varieties. We will also discuss analogues for other orbit covers.

Topic: TBA December 17

Presenter: Yanyan Li, Rutgers University

Topic: TBA December 17

Presenter: Tamas Hausel, Institute for Advanced Studies

Topic: On recent progress on the Kakeya conjecture and related problems December 21

Presenter: Terence Tao, UCLA

Topic: On spectral multipliers for sub-laplacians on solvable Lie groups January 25

Presenter: Detlef Muller, University of Kiel