Topic: Anderson Localization: Results, Conjectures, and Open Problems October 21

Presenter: Werner Kirsch, University of Bochum

Cakes & Party in Fine Hall Common Room at 3 p.m. October 21

Title: Deus ex Machina: From Packing Planes to Quantum Computers

Presenter: N.J.A. Sloane, ATT Research Time: 4 - 4:45 p.m.

Title: The Symmetries of Things

Presenter: John H. Conway, Princeton University Time: 5 - 5:45 p.m.

Room: Fine 314

Date: Wednesday, October 21, 1998

Topic: Geometric Algorithims and Random Walks October 22

Presenter: Miklos Simonovits, Mathematical Institute of the Hungarian

Academy of Sciences

Abstract: In the talk I will consider high dimensional convex bodies given by oracles. It is natural to try to calculate

precisely or approximately) geometric characteristics of such convex bodies, like their volume or their diameter.

Calculating volume is also connected strongly with uniform point generation in a convex body, integration, ... The basic

methods rely heavily on the theory of random walks.) I will survey various problems and results connected to:

(a) the impossibility of calculating the volume of a high dimensional convex body efficiently, using deterministic algorithms.

(b) the possibility of this by randomized algoriths. (The first result in this field, a breakthrough, was a randomized

approximation algorithm of Dyer, Frieze and Kannan. The best volume algorithm today is that of Kannan, Lovasz and

myself, providing a good estimate, using roughly O(n^5) oracle questions.

(c) randomized algorithms for diameter do not work. Diameter cannot be estimated well, even if we use randomization.

Some of the results are joint with Laszlo Lovasz, some with Kannan and Lovasz, and some with Brieden, Gritzmann,

Kannan, Klee and Lovasz; and I intend also to speak about many further results of ours and others.

Topic: On some heuristic and rigorous asymptotic formulas in the October 22

theory of disordered systems

Presenter: L. Pastur, University VII, Paris

Topic: Euler-Poincare pairings and elliptic representations October 22

of Weyl groups and p-adic groups

Presenter: Mark Reeder, Boston College

Abstract: Schneider and Stuhler have defined a pairing EP between representations of a p-adic group G, that reflects the

geometry of elliptic conjugacy classes in G. We define more elementary pairings for representations of Weyl groups W

and component groups of centralizers, and show how all these pairings are related to one another. This leads on the one

hand to explicit calculations of EP, and on the other hand, to new results about Springer representations of W.

Topic: Monopoles and the relation between 4-manifold invariants October 22

Presenter: Paul Feehan, Institute for Advanced Studies

Topic: The construction of global surfaces of section in three-dimensional October 22

dynamical systems via first order elliptic systems

Presenter: Helmut Hofer, Courant Institute, NYU

Topic: On fine properties of eigen values of analytic matrix functions

Presenter: Michael Goldstein, University of Toronto

Topic: Towards a Siege-Weil formula in exceptional groups October 22

Presenter: Wee Teck Gan, Princeton University and IAS

Topic: Counting gradient flow lines and the Seiberg-Witten October 23

Invariant of 3-manifolds

Presenter: Yi-Jen Lee, Princeton University

Topic: Derived categories and functors II October 23 Math Building - IAS

Presenter: Alexander Kirillov, Institute for Advanced Studies

Topic: On the action of the symmetric group on the selected-type partition lattices October 26 Math Building - IAS

Presenter: Dmitry Kozlov, Institute for Advanced Studies

Abstract: In the first half of the talk I will outline from scratch the principal objects of study and tools of topological

combinatorics, such as the nerve functor, the Goresky-MacPherson theorem about the cohomology groups of the

complement of a subspace arrangement, various combinatorial techniques and some aspects of the group actions on

posets.

After that, I will present an example of a computation of the Betti numbers of a combinatorially defined cell complex C.

C is the quotient of X - the order complex of a partition lattice (or a selected-type sublattice) - by the action of the

symmetric group. The partition lattice is the intersection lattice of the braid arrangement and its order complex is important

in the computation of the cohomology groups of the complement of the braid arrangement and also appears in Vassiliev's

work on knot invariants. One interesting feature of the Betti numbers of C is that they measure the multiplicity of the trivial

character in the induced representation of the symmetric group on the homology groups of X. If time permits, I will discuss similar problems, where the constant sheaf is replaced by an arbitrary cellular sheaf.

Topic: Introduction to D-modules I October 26 Math Building - IAS

Presenter: Sergey Arkhipov, Institute for Advanced Studies

Topic: Critical metrics for the determinant of the laplacian October 26

Presenter: Kate Okikiolu, University of California San Diego

Topic: Interacting Particle Approximation for Nonlocal Nonlinear October 26

Evolution Problems

Presenter: Wojbor A. Woyczynski, Center for Stochastic and Chaotic Processes in Science and Technology, Case

Western Reserve University

Abstract: I will discuss an interacting particle system approximation (known as the "propagation of chaos problem") for a

class of integrodifferential equations of evolution type with the fractal anomalous diffusion and nonlocal nonlinear term.

The work is motivation by the problems of modeling growing semiconductor interfaces.

Topic: Towards a parametrization of the l-adic representations of October 27

the local Galois group

Presenter: Volker Heiermann, Institute for Advanced Studies

Topic: The Unruh Effect October 28

Presenter: Jakob Yngvason, Physics Dept., University of Vienna

Topic: Geometric flows of parabolic type October 28

Presenter: H. Mete Soner; PACM and CEOR Princeton

Abstract: Essential behavior of solutions to a large class of parabolic equations can be captured their singular set. In

models for phase separation the singular set is a domain wall, in the Ginzburg-Landau model for superconductivity or in

liquid crystals, the defect set has codimension two. There are applications to hydrodynamic limit of interacting particle

models as well.

In this talk, I will outline the "recent" weak theories for the evolution of these singular sets and use them to develop an

asymptotic theory for a class of reaction diffusion equations. Related topics are: viscosity solutions of Crandall, Evans

and Lions, geometric flows of Almgren and Taylor, and level set theory of Evans-Spruck and Chen-Giga-Goto.

Topic: A family of combinatorial determinants October 29

Presenter: Herb Wilf, University of Pennsylvania

Abstract: We evaluate a family of combinatorial determinants in simple closed form. The family includes, for example, the

nxn matrix whose (i,j) entry is the number of representations of the integer i as a sum of j squares, and many others.

Topic: Spectra of Markov operators on some countable subgroups of the October 29

"$ax+b$"-group

Presenter: Alain Valette, University of NeufChatel

Abstract: Paraphrasing M. Kac, Gromov asked "Can you hear the shape of a group?"; i.e., given a Cayley graph

associated with a finitely generated group $\Gamma$, which information can one extract from the spectrum of the

adjacency operator acting on $\ell^{2}(\Gamma)$? In the first part of the talk, we survey results on this inverse spectral

problem.

Since there are relatively few exact computations of such spectra, we address in the second part the direct spectral

problem for the subgroup $\Gamma_{n}$ of the $ax+b$ group, generated by translation by $1$ and dilation by $n$.

Using C*-algebraic techniques, we present computations both for the directed and undirected Cayley graphs of

$\Gamma_{n}$. In the directed case, one of the computations depends on the Generalized Riemann Hypothesis (actually

on Artin's conjecture).

Topic: Reformulations of surgery conjecture: surfaces in October 29

topological 4-manifolds

Presenter: Slava Krushkal, Institute for Advanced Studies

Topic: Recent development on compact Homogenous space October 30

Presenter: Zhuang-dan Guan, Princeton University

Topic: Reflection on the history of PDE November 5

Presenter: Felix Browder, Rutgers University

Topic: Functions of bounded higher variation

Presenter: Robert Jerrard, University of Illinois, Urbana

Topic: The Dirichlet problem for the subLaplacian November 9

Presenter: Luca Capogna

Abstract: Consider the operator L obtained as a sum of squares of vector fields satisfying Hormander's finite rank

condition. In a joint work with N. Garofalo and D-M Nhieu we studied the dirichlet problem Lu=0, u=g on the boundary

(g continuous or in Lp), for a smooth domain D. Assuming the analogue of the Poincare outer ball condition and a

generalization of Jerison and Kenig's NTA properties we show that the Green function is Lipschitz up to the boundary and

that there is a Poisson Kernel and a representation formula. We also prove reverse Holder estimates for the Poisson

Kernel and consequently that the harmonic measure and the surface measure are mutually absolutely continuous.

Examples of domains satisfying the required properties have been constructed.

Topic: On the Stability of positive Molecular Ions November 11

Presenter: Rafael Benguria, Catholic University, Santiago, Chile

Topic: Transfer by Markovian Flows November 11

Presenter: Leonid Koralov, Institute for Advanced Studies

Topic: Hecke algebras and weights of Markov traces November 12

Presenter: R. Orellana, University of California, San Diego

Topic: TBA November 12

Presenter: C. LeBrun, SUNY at Stony Brook

Topic: Divisibility of class numbers and sieve techniques November 12

Presenter: Etienne Fouvry, Universite d'Orsay

Topic: Dynamical Systems

Dates: January 29, 30, & 31, 1999

Presenters: D. Dolgopyat, University of California, Berkley; G. Forni, Princeton University; V. Kaloshin, Princeton

University; Y. Katznelson, Stanford University; D. Kosygin, NY University, Courant Institute; I. Krichever, Columbia

University; M. Lyubich, SUNY Stony Brook; G. Margulis, Yale University; J. Milnor, SUNY Stony Brook; D. Ornstein,

Stanford University; M. Shub, IBM, T.J. Watson Research Labs; J. Smillie, Cornell University; W. Veech, Rice University;

J. Xia, Northwestern University

For more info or to register contact: I.Sinai or J. Mather at dona@princeton.edu or L. Neuwirth at lpn@ccr-p.ida.org

(609)279-6231.