

Discrete Mathematics Seminar  
Topic:  Optical Networks and Konig's Theorem  
Presenter:  Peter Winkler, Bell Labs  
Date:  Wednesday, April 9, 2003, Time: 2:15 p.m., Location: Fine Hall 224  
Abstract:  Technology keeps changing in the optical communications world, but somehow Konig's Theorem  to the effect that the edgechromatic number of a bipartite graph is its maximum degree  is always in the picture. We'll give four examples of problems which arose at Lucent, all related to both ends of the title, capped off by an ambitious conjecture. The work is joint in various combinations with April Rasala (MIT) and with Bell Labs colleagues Penny Haxell, Gordon Wilfong and Lisa Zhang.  
Department Colloquium  
Topic:  Universality for mathematical and physical systems  
Presenter:  Percy Deift, New York University  
Date:  Wednesday, April 9, 2003, Time: 4:30 p.m., Location: Fine Hall 314  
Abstract:  All physical systems in equilibrium
obey the laws of thermodynamics. In other words, whatever the precise nature
of the interaction between the atoms and molecules at the microscopic level,
at the macroscopic level, physical systems exhibit universal behavior in the
sense that they are all governed by the same laws and formulae of
thermodynamics. The speaker will recount some recent history of universality ideas in physics starting with Wigner's model for the scattering of neutrons off large nuclei and show how these ideas have led mathematicians to investigate universal behavior for a variety of mathematical systems. This is true not only for systems which have a physical origin, but also for systems which arise in a purely mathematical context such as the Riemann hypothesis, and a version of the card game solitaire called patience sorting. 

Cohomology of Groups  
Topic:  Cohomology and representations of finite group schemes Part II  
Presenter:  Julia Pevtsova, Institute for Advanced Study  
Date:  Thursday, April 10, 2003, Time: 3:00 p.m., Location: Fine Hall 801  
Abstract:  See abstract from April 8, 2003  
Joint Institute for Advanced Study /Princeton University/ Rutgers University Number Theory Seminar  
Topic:  Automorphic Distributions and Summation Formulas  
Presenter:  Stephen Miller, Rutgers University  
Date:  Thursday, April 10, 2003, Time: 4:15 p.m., Location: Hill Center 705 (Rutgers University)  
Abstract:  The talk will center on the analysis of the distributional boundary values of automorphic forms, and some applications of this theory to GL(3,Z)\GL(3,R). Foremost among these is a formula ala Poisson/Voronoi for sums weighted by the Fourier coefficients/Hecke eigenvalues of automorphic forms. This can be used to demonstrate cancellation in such sums, and was an ingredient of the recent sharp estimate of SarnakWatson for L_4 norms of Laplace eigenfunctions. I plan to discuss the problem of finding cancellation in sums of the form a_{n,1} exp(2 pi i n alpha), where alpha is irrational. (joint work with Wilfried Schmid).  
Geometric Analysis Seminar  
Topic:  A Bernstein problem for special Lagrangian equations  
Presenter:  Yu Yuan, University of Washington  
Date:  Friday, April 11, 2003, Time: 3:00 p.m., Location: Fine Hall 314  
Abstract:  In this talk, we derive a Bernstein type result for the special Lagrangian equation, namely, any global convex solution must be quadratic. In terms of minimal surfaces, the result says that any global minimal Lagrangian graph with convex potential must be a hyperplane.  


PACM Colloquium  
Topic:  Elastic strain in epitaxial thin films  
Presenter:  Russel Caflisch, University of California at Los Angeles  
Date:  Monday, April 14, 2003, Time: 4:00 p.m., Location: Fine Hall 214  
Abstract:  In an epitaxial thin films the lattice properties of the film are determined by those of the underlying substrate. A mismatch between the lattice spacing of the substrate and film will introduce a strain into the film, which can significantly influence the material structure and properties. This talk will describe analysis and computation for strain in an epitaxial film with harmonic interatomic potentials and intrinsic surface stress. The resulting force field at a step and the interactions between steps will be described. Generalizations to epitaxial wires and particles will be presented.  
Mathematical Physics Seminar  
Topic:  An extension of the HarishChandra (ItzyksonZuber) formula to nonunitary symmetries  
Presenter:  Edouard Brezin, Lab. Physique Theorique, Ecole Normale Superieure  
Date:  Tuesday, April 15, 2003, Time: 4:30 p.m., Location: Jadwin A06  
Abstract:  The ItzyksonZuber formula plays a central role in matrix models. It is used for chains of matrices, random scatterers (H=H_0+V, V random), etc. For the unitary group, the formula is WKB exact. For nonunitary groups (GOE, GSE, ...) there is a semiclassical expansion which, surprisingly, terminates after a finite number of terms in some cases of interest.  
Discrete Mathematics Seminar  
Topic:  Coloring Powers of Hamilton Cycles from Random Lists  
Presenter:  Michael Krivelevich, Tel Aviv University  
Date:  Wednesday, April 16, 2003, Time: 2:15 p.m., Location: Fine Hall 224  
Abstract:  View abstract  
Department Colloquium  
Topic:  The entropy formula for the Ricci flow and its geometric applications  
Presenter:  Grisha Perelman, St. Petersburg  
Date:  Wednesday, April 16, 2003, Time: 4:30 p.m., Location: Fine Hall 314  
Ergodic Theory and Statistical Analysis Seminar  
Topic:  A spectral gap property for measures;applications to the Anderson model  
Presenter:  Carol Shubin, California State University Northridge  
Date:  Thursday, April 17, 2003, Time: 2:00 p.m., Location: Fine Hall 214  
Abstract:  We discuss products of random matrices as they arise from studying the discrete Anderson model on the strip. We obtain a quantitative bound of the largest Lyapunov exponent. This was joint work with T. Wolff and R. Vakilian. We discuss extensions of this work by T. Wolff, first to $PSL(2,\R)$ and then more generally to noncompact semisimple Lie groups.  
Cohomology of Groups  
Topic:  On nilpotent ideals in the cohomology ring of a group  
Presenter:  Jonathan Pakianathan, University of Rochester  
Date:  Thursday, April 17, 2003, Time: 3:00 p.m., Location: Fine Hall 801  
Topology Seminar  
Topic:  Fixity and Group Actions  
Presenter:  Alejandro Adem, University of Wisconsen  
Date:  Thursday, April 17, 2003, Time: 4:30 p.m., Location: Fine Hall 314  
Abstract:  In this talk I will discuss recent work on constructing free group actions on products of spheres. This makes use of the notion of fixity of representations, homotopy theory and propagation of group actions. In particular we show that for p>3, every rank two pgroup acts freely and smoothly on a product of two spheres.  
Joint Princeton / IAS / Rutgers Number Theory Seminar  
Topic:  An arithmetic theta function  
Presenter:  Stephen Kudla, University of Maryland  
Date:  Thursday, April 17, 2003, Time: 4:15 p.m., Location: Fine Hall 322  
Abstract:  The arithmetic theta function is a modular form of weight 3/2 valued in the arithmetic Chow group of the arithmetic surface attached to a Shimura curve of Q. This function can be used to define a theta lift from modular forms of weight 3/2 to the elements of the arithmetic Chow group. A conjectural analogue of a result of Waldspurger gives a characterization of the nonvanishing of this arithmetic theta lift in terms of (i) local obstructions and (ii) the nonvanishishing of the central derivative of the Lfunction. This result is proved in some cases.  
Geometric Analysis Seminar  
Topic:  A general Liouville type theorem for some conformally invariant fully nonlinear equations  
Presenter:  Aobing Li, Rutgers University  
Date:  Friday, April 18, 2003, Time: 3:00 p.m., Location: Fine Hall 314  
Abstract:  In this talk, I will talk about some general Liouville type theorem for some conformally invariant fully nonlinear equations on the Euclidean space, i.e., we classified all the classical positive solutions of these equations. I will also present a Liouville type theorem for the same equation but on the upper half plane with the boundary condition. These are the joint works with Yanyan Li.  


Analysis Seminar  
Topic:  From Hilbert's variational principle to Einstein's equations as a well posed initial value problem  
Presenter:  James York, Cornell University  
Date:  Monday, April 21, 2003, Time: 4:00 p.m., Location: Fine Hall 314  
PACM Colloquium  
Topic:  Questions and models associated with the deliberate release of biological agents and their consequences  
Presenter:  Carlos CastilloChavez, Cornell University  
Date:  Monday, April 21, 2003, Time: 4:00 p.m., Location: Fine Hall 214  
Abstract:  The talk will include two intertwined
parts. One will deal with the 'transmission dynamics of behaviors" and
the second with the spread of epidemics on various topologies. The concept of
(a fixed) core group was introduced in epidemiology by Hethcote and Yorke
(1984) in the context of gonorrhea dynamics. Hadeler and CastilloChavez
(1995) and Huang and CastilloChavez (2002) have shown that core group
dynamics (in nonstructured and structured populations) have important
implications on disease transmission and control. We use these results as the
starting point for the development of simple models for the dynamics of drug
use (ecstasy), collaborative learning and ideologically driven behaviors
(fanaticism).
The results point out to the tremendous impact that "invading" small subpopulations of individuals with strong behaviors can have on the establishment of drug cultures, fanatic ideologies or good learning environments. The models developed naturally support subcritical bifurcations with troublesome implications for disease dynamics and control (CastilloChavez and Baojun Song, 2003). Intertwined with the first topic, I will discuss the spread of diseases on different topologies. I will address some issues that are relevant including recent efforts to define worstcase scenarios or to model epidemics on masstransportation systems (Gerardo Chowell et al. 2003 and CastilloChavez and Baojun, 2003). 

Algebraic Geometry Seminar  
Topic:  Spaces of rational curves on Fano hypersurfaces  
Presenter:  Jason Starr, MIT  
Date:  Tuesday, April 22, 2003, Time: 4:30 p.m., Location: Fine Hall 322  
Abstract:  I will discuss two methods for giving lower bounds on the Kodaira dimensions of spaces of rational curves on Fano hypersurfaces. The motivation comes from the open problem of finding a Fano variety X which is not unirational. The approach, suggested by Kollár, is to find an X which contains no rational surface passing through a very general point of X. The first step is to show that the varieties parametrizing rational curves on X are themselves not uniruled, e.g. the varieties parametrizing rational curves on X have nonnegative Kodaira dimension. Part of this research is joint work with A. J. de Jong.  
Department Colloquium  
Topic:  Stationary Determinantal Processes (Fermionic Lattice Gases)  
Presenter:  Russell Lyons, Indiana University  
Date:  Wednesday, April 23, 2003, Time: 4:30 p.m., Location: Fine Hall 314  
Abstract  Eigenvalues of random matrices arise in various areas of physics and mathematics. The moststudied such probability measures have a determinantal form. Several people have studied other specific determinantal processes, as well as a general theory. We shall discuss the general theory of stationary random fields on integer lattices that are defined via minors of multidimensional Toeplitz matrices. Explicit examples include combinatorial models, finitely dependent processes, and renewal processes in one dimension. Among the interesting properties of these processes, we focus mainly on whether they have a phase transition analogous to that which occurs in statistical mechanics. We describe necessary and sufficient conditions for the existence of such a phase transition and give several examples to illustrate the theorem. This is joint work with Jeff Steif.  
Ergodic Theory and Statistical Analysis Seminar  
Topic:  Diffusive and Coalescing Flows  
Presenter:  Yves Lejan, Université ParisSud  
Date:  Thursday, April 24, 2003, Time: 2:00 p.m., Location: Fine Hall 214  
Abstract  Coalescence and stickyness are introduced in a simple exemple. Then the compressible Kraichnan model for turbulent advection motivates new developments in the theory of flows driven by sochastic differential equations. It appears that some of these flows cannot be generated by a gaussian noise.  
Joint Institute for Advanced Study /Princeton University/ Rutgers University NonLinear Analysis Seminar  
Topic:  On the time evolution and steady states for inelastic Boltzmann equations  
Presenter:  Irene Gamba, University of Texas at Austin  
Date:  Thursday, April 24, 2003, Time: 4:00 p.m., Location: Fine Hall 214  
Abstract:  Kinetic models for inelastic
collisions provide an approach to understanding regimes of rapid
granular flows, both for cooling and diffusive states. Stochastic simulations
and experimental measurements indicate these models admite steady states
described by nonclassical probabilities with overpopulated tails with respect
to Gaussian behavior. We rigourusly prove that that is the case for some
Boltzmann type equations.
In the first part of the lecture we look at a short survey of related work from the last two years on homogeneous inelastic Boltzmann models. In the second part we shall consider the homogeneous inelastic Boltzmann equation for hard spheres with a diffusive term representing driven granular flows by a random background acceleration. We show of existence and uniqueness of strong solutions with all moment bounded, to the initial value problem. In addition we show the existence of stationary solutions which are pointwise bounded below by $C \exp(rv^b)$, with $r$ depending on the energy bounds and b depending on the rate of collisions to cross section and the forcing term and $b=3/2$. Finally, we present rigourous results on tail decay for solutions of inelastic Boltzmann equation for hard spheres with forcing terms corresponding to diffusive, friction and shear flow, separately. This work is partly in collaboration with C. Villani, A. Bobylev and V. Panferov. 

Joint Institute for Advanced Study /Princeton University/ Rutgers University Number Theory Seminar  
Topic:  Are motivic Lfunctions rational?  
Presenter:  Michael Larsen, Indiana  
Date:  Thursday, April 24, 2003, Time: 4:15 p.m., Location: Fine Hall 322  
Geometric Analysis Seminar  
Topic:  TBA  
Presenter:  Xiaodong Wang, MIT  
Date:  Friday, April 25, 2003, Time: 3:00 p.m., Location: Fine Hall 314  


PACM Colloquium  
Topic:  On the time evolution and steady states for inelastic Boltzmann equations  
Presenter:  Irene Gamba, University of Texas at Austin  
Date:  Monday, April 28, 2003, Time: 4:00 p.m., Location: Fine Hall 214  
Algebraic Geometry Seminar  
Topic:  Near by fundamental group of Mumford Tate curves  
Presenter:  Tomohide Terasoma, Institute for Advanced Study  
Date:  Tuesday, April 29, 2003, Time: 4:30 p.m., Location: Fine Hall 322  
Abstract:  We will study a problem of R.Hain. The main result says that the period of the arithmetic mapping class group can be written using multiple zeta values. A similar Galois theoretic result was obtained by IharaNakamura.  
Department Colloquium  
Topic:  TBA  
Presenter:  S.R.Srinivasa Varadhan, New York University  
Date:  Wednesday, April 30, 2003, Time: 4:30 p.m., Location: Fine Hall 314  
Joint Institute for Advanced Study /Princeton University/ Rutgers University Number Theory Seminar  
Topic:  Counting number fields of bounded discrminant  
Presenter:  Jordan Ellenberg, Princeton University  
Date:  Thursday, May 1, 2003, Time: 4:15 p.m., Location: Fine Hall 322  
Topology Seminar *** Please note  rescheduled from April 3, 2003  
Topic:  One parameter families of CalabiYau threefolds  
Presenter:  John Morgan, Columbia University  
Date:  Thursday, May 1, 2003, Time: 4:30 p.m., Location: Fine Hall 314  
Abstract:  There are lots of examples of oneparameter families of CalabiYau threefolds occurring as hypersurfaces or complete intersections in toric varieties. We study the resulting variations of Hodge structure from these families and compare the results to all possible variations and to various conjectures arising out of mirror symmetry conjectures.  


Analysis Seminar  
Topic:  TBA  
Presenter:  Alex Iosevich, University of Missouri at Columbia  
Date:  Monday, May 5, 2003, Time: 4:00 p.m., Location: Fine Hall 314  
Department Colloquium  
Topic:  The lost proof of Loewner's theorem  
Presenter:  Barry Simon, Caltech  
Date:  Wednesday, May 7, 2003, Time: 4:30 p.m., Location: Fine Hall 314  
Abstract:  A realvalued function, F, on an interval (a,b) is called matrix monotone if F(A) < F(B) whenever A and B are finite matrices of the same order with eigenvalues in (a,b) and A < B. In 1934, Loewner proved the remarkable theorem that F is matrix monotone if and only if F is real analytic with continuations to the upper and lower half planes so that Im F > 0 in the upper half plane. This deep theorem has evoked enormous interest over the years and a number of alternate proofs. There is a lovely 1954 proof that seems to have been "lost" in that the proof is not mentioned in various books and review article presentations of the subject, and I have found no references to the proof since 1960. The proof uses continued fractions. I'll provide background on the subject and then discuss the lost proof and a variant of that proof which I've found, which avoids the need for estimates, and proves a stronger theorem.  
Mathematical Physics Seminar *** Please note special date and time  
Topic:  A Canonical Factorization for Meromorphic Herglotz Functions on the Disk and a Proof of the Jacobi Matrix P2 Sum Rule on One Foot  
Presenter:  Barry Simon, Caltech  
Date:  Thursday, May 8, 2003, Time: 2:00 p.m., Location: Jadwin A06  
Abstract:  Last year Killip and Simon provided a complete description of the spectral measure associated to Jacobi matrices with L2 potentials. I will present a simple proof of their result that relies on two elements: an analysis of the general form of meromorphic Herglotz functions on the disk and the upper semicontinuity of the entropy. I'll begin by describing the general issue of the spectral and inverse spectral problems for Jacobi matrices, the significance of the P2 sum rule, then the canonical factorization and then the proof of the P2 sum rule.  
Joint Institute for Advanced Study /Princeton University/ Rutgers University Number Theory Seminar  
Topic:  Small gaps between primes  
Presenter:  Dan Goldston, San Jose State University  
Date:  Thursday, May 8, 2003, Time: 4:15 p.m., Location: Fine Hall 322  
Abstract:  This talk will discuss the main new idea behind the proof that there are infinitely many primes much closer together than the average spacing between primes, and how this idea was discovered. A sketch of the proof will be given. This is joint work with C. Yalcin Yildirim.  
Joint Institute for Advanced Study /Princeton University/ Rutgers University Number Theory Seminar  
*** Please note special day and time ***  
Topic:  Recent Developments Related to Prime Gaps  
Presenter:  Dan Goldston, San Jose State University  
Date:  Friday, May 9, 2003, Time: 2:00 p.m., Location: Fine Hall 322  
Abstract:  This talk will discuss improvements in the method for detecting small gaps between primes made by a number of people in the last two months, and problems that still need to be examined.  


Algebraic Geometry Seminar  
Topic:  TBA  
Presenter:  B. Guralnick  
Date:  Tuesday, May 13, 2003, Time: 4:30 p.m., Location: Fine Hall 322  