

OCTOBER 2008 


Statistical Mechanics Seminar 
Topic: 
Heat conduction and NonEquilibrium Statistical Mechanics: some considerations 
Presenter: 
Federico Bonetto, Georgia Tech 
Date: 
Wednesday, October 15, 2008, Time: 2:00 p.m., Location: Jadwin 343 
Abstract: 
I will present some standard models of NonEquilibrium Statistical Mechanics focusing mainly on heat conduction. I'll discuss their origin and significance and present some of the available analytical and numerical results. The talk will be at an introductory level. 


Analysis Seminar ***Please note special time and date 
Topic: 
A general unique continuation theorem for the Einstein equations 
Presenter: 
Spyridon Alexakis, MIT 
Date: 
Wednesday, October 15, 2008, Time: 3:30 p.m., Location: Fine Hall 110 
Abstract: 
I will discuss a unique continuation result for the vacuum Einstein equations across bifurcate horizons. The main result uses
a recent Carleman estimate of Ionescu and Klainerman, together with some geometric gauge constructions. More broadly I will indicate how Carleman estimates for the wave operator can be used to derive unique continuation for the Einstein equations. 


Department Colloquium 
Topic: 
Unitary representations of simple Lie groups 
Presenter: 
David Vogan, MIT 
Date: 
Wednesday, October 15, 2008, Time: 4:30 p.m., Location: Fine Hall 314 
Abstract: 
By 1950, work of Gelfand and others had led to a general program for "noncommutative harmonic analysis": understanding very general mathematical problems (particularly of geometry or analysis) in the presence of a (noncommutative) symmetry group G. A first step in that program is classification of unitary representations  that is, the realizations of G as automorphisms of a Hilbert space. Despite tremendous advances from the work of HarishChandra, Langlands, and others, completing this first step is still some distance away. Since functional analysis is not as fashionable now as it was in 1950, I'll explain some of the ways that Gelfand's problem can be related to algebraic geometry (particularly to equivariant Ktheory). I'll also discuss the (closely related) question of whether computers may be able to help solve these problems. 


Graduate Seminar 
Topic: 
Ergodic Theory 
Presenter: 
Sam Ruth, Princeton University 
Date: 
Thursday, October 16, 2008, Time: 12:30 p.m., Location: Fine Hall 314 
Abstract: 
I will be discussing two basic invariants of ergodic theory, entropy and ergodicity, through the problems they were invented to solve. This talk will be heavy on examples and low on rigour. 


Discrete Mathematics Seminar 
Topic: 
The Maximum Number of Colorings of Graphs of Given Order and Size 
Presenter: 
Oleg Pikhurko, Carnegie Mellon University 
Date: 
Thursday, October 16, 2008, Time: 2:15 p.m., Location: Fine Hall 224 
Abstract: 
Wilf asked in the 1980s about f(n,m,l), the maximum number of lcolorings that a graph with n vertices and m edges can have. We essentially solve this problem for l=3, in particular proving, for all large n, the conjecture of Lazebnik (1989) that if m\le n^2/4 then the maximum number of 3colorings is achieved by a semicomplete biparite graph. This is joint work with PoShen Loh and Benny Sudakov. 


Number Theory Seminar ***Please note special location 
Topic: 
Dynamical MordellLang problems 
Presenter: 
Thomas J. Tucker, Rochester 
Date: 
Thursday, October 16, 2008, Time: 4:30 p.m., Location: IAS West Building Lecture Hall 
Abstract: 
The MordellLang conjecture, proved by Faltings and Vojta, states that a finitely generated subgroup of a semiabelian variety intersects any subvariety of that semiabelian variety in a union of finitely many translates of subgroups. It seems natural to ask if such a theorem holds when the finitely generated subgroup is replaced by a finitely generated semigroup of morphisms of a general variety; for example, one might take a semigroup of endomorphisms of a semiabelian variety. We will prove that this is true in many cases when the semigroup is cyclic and also give counterexamples in the more general case, some simple and some more complicated. 


Topology Seminar 
Topic: 
Khovanov homology, open books, and tight contact structures 
Presenter: 
John Baldwin, Princeton University 
Date: 
Thursday, October 16, 2008, Time: 4:30 p.m., Location: Fine Hall 314 
Abstract: 
I will discuss a construction modeled on Khovanov homology which associates to a surface, S, and a product of Dehn twists, Phi, a group Kh(S,Phi). The group Kh(S,Phi) may sometimes be used to determine whether the contact structure compatible with the open book (S,Phi) is tight or nonfillable. This construction generalizes the relationship between the reduced Khovanov homology of a link and the Heegaard Floer homology of its branched double cover. 


Differential Geometry and Geometric Analysis Seminar 
Topic: 
The space of positive scalar curvature metrics on the threesphere 
Presenter: 
Fernando Coda Marques, IMPABrazil 
Date: 
Friday, October 17, 2008, Time: 3:00 p.m., Location: Fine Hall 314 
Abstract: 
In this talk we will discuss a proof of the pathconnectedness of the space of positive scalar curvature metrics on the threesphere. The proof uses the Ricci flow with surgery and the connected sum construction of Gromov and Lawson. The work of Perelman on Hamilton's Ricci flow is fundamental. 


Analysis Seminar 
Topic: 
TBA 
Presenter: 
Gustav Holzegel, Princeton University 
Date: 
Monday, October 20, 2008, Time: 4:00 p.m., Location: Fine Hall 110 


Geometry, Representation Theory, and Moduli Seminar 
Topic: 
The chiral superstring measure and modular forms 
Presenter: 
S. Grushevsky, Princeton University 
Date: 
Monday, October 20, 2008, Time: 4:00 p.m., Location: Fine Hall 314 


PACM Colloquium 
Topic: 
Group representation patterns in digital signal processing 
Presenter: 
Shamgar Gurevich, Mathematics, University of California, Berkeley and Ronny Hadani, Mathematics, University of Chicago 
Date: 
Monday, October 20, 2008, Time: 4:00 p.m., Location: Fine Hall 214 
Abstract: 
In the lecture we will explain how various fundamental structures from group representation theory appear naturally in the context of discrete harmonic analysis and can be applied to solve concrete problems from digital signal processing. We will begin the lecture by describing our solution to the problem of finding a canonical orthonormal basis of eigenfunctions of the discrete Fourier transform (DFT). Then we will explain how to generalize the construction to obtain a larger collection of functions that we call "The oscillator dictionary." Functions in the oscillator dictionary admit many interesting properties, in particular, we will explain several of these properties which arise in the context of problems of current interest in areas such as communication and radar. Joint work with Nir Sochen (Tel Aviv). 


Algebraic Geometry Seminar 
Topic: 
Leaves in moduli spaces in characteristic p 
Presenter: 
Frans Oort, University of Utrecht/ Columbia University 
Date: 
Tuesday, October 21, 2008, Time: 4:30 p.m., Location: Fine Hall 322 
Abstract: 
We try to understand the geometry of the moduli space of polarized abelian varieties in characteristic p. E.g. the phenomenon that Hecke orbits blow up and down in a rather unpredictable way. Choose a point x, corresponding to a polarized abelian variety. We study C(x) consisting of all moduli points of polarized abelian varieties which have the same padic and \elladic invariants. This turns out to be a locally closed subset. We discuss properties of these sets, which form a foliation of the related Newton polygon stratum. We give several applications. 


Statistical Mechanics Seminar 
Topic: 
Thermostats: equivalence and thermodynamic limit 
Presenter: 
Giovanni Gallavotti, University of Rome/Rutgers 
Date: 
Wednesday, October 22, 2008, Time: 2:00 p.m., Location: Jadwin 343 
Abstract: 
An ongoing question is whether the isokinetic, isoenergetic or other thermostat models are acceptable as model of thermostats in nonequilibrium statistical mechanics as opposed to thermostats which are made of infinite Hamiltonian systems in thermal equilibrium. I will discuss the problem and the strict equivalence of the isokinetic, isoenergetic and Hamiltonian thermostats in the thermodynamic limit and the difference between the 1,2 dimensional systems and the 3 dimensional (or higher) ones. 


Department Colloquium 
Topic: 
Three conjectures in arithmetic geometry 
Presenter: 
Frans Oort, University of Utrecht/ Columbia University 
Date: 
Wednesday, October 22, 2008, Time: 4:30 p.m., Location: Fine Hall 314 
Abstract: 
We discuss the ManinMumford conjecture (about the closure of any set of torsion points in an abelian variety), the Andr\'eOort conjecure (about the closure of any set of CMpoints in a moduli space) and the Hecke Orbit Conjecture (about the closure of the Hecke orbit of a moduli point). These conjectures, on the borderline of geometry and arithmetic, seem to be (have been) solved. We explain the similarities. We will discuss the motivation for these conjectures, and in some cases we will say something about methods of proofs. 


Graduate Seminar 
Topic: 
TBA 
Presenter: 
Vivek Shende, Princeton University 
Date: 
Thursday, October 23, 2008, Time: 12:30 p.m., Location: Fine Hall 314 


Discrete Mathematics Seminar 
Topic: 
Eliminating cycles in the torus via isoperimetric inequalities 
Presenter: 
Noga Alon, Tel Aviv Unisersity and IAS 
Date: 
Thursday, October 23, 2008, Time: 2:15 p.m., Location: Fine Hall 224 
Abstract: 
Let $G_{\infty}=(C_m^d)_{\infty}$ denote the graph whose set of vertices is $\{1,\ldots ,m\}^d$, where two distinct vertices are adjacent iff they are either equal or adjacent in $C_m$ in each coordinate. Let $G_{1}=(C_m^d)_1$ denote the graph on the same set of vertices in which two vertices are adjacent iff they are adjacent in one coordinate in $C_m$ and equal in all others. Both graphs can be viewed as graphs of the $d$dimensional torus. We prove that one can delete $O(\sqrt d m^{d1})$ vertices of $G_1$ so that no topologically nontrivial cycles remain. This improves an $O(d^{\log_2 (3/2)}m^{d1})$ estimate of Bollob\'as, Kindler, Leader and O'Donnell. We also give a short proof of a result implicit in a recent paper of Raz: one can delete an $O(\sqrt d/m)$ fraction of the edges of $G_{\infty}$ so that no topologically nontrivial cycles remain in this graph. The technique also yields a short proof of a recent result of Kindler, O'Donnell, Rao and Wigderson; there is a subset of the continuous $d$dimensional torus of surface area $O(\sqrt d)$ that intersects all nontrivial cycles. All proofs are based on the same general idea: the consideration of random shifts of a body with small boundary and no nontrivial cycles, whose existence is proved by applying the isoperimetric inequality of Cheeger or its vertex or edge discrete analogues. Joint work with Bo'az Klartag. 


Special Geometry Seminar 
Topic: 
A compactification for the space of quadratic differentials 
Presenter: 
Kasra Rafi, University of Oklahoma 
Date: 
Friday, October 24, 2008, Time: 2:00 p.m., Location: Fine Hall 801 


Number Theory Seminar 
Topic: 
On the Tate and LanglandsRapoport conjectures for Shimura varieties of Hodge type 
Presenter: 
A. Vasiu, Binghampton University 
Date: 
Thursday, October 30, 2008, Time: 4:30 p.m., Location: IAS S101 
Abstract: 
Let p be a prime. Let F be an algebraic closure of the finite field F_p with p elements. An integral canonical model N of a Shimura variety Sh(G,X) of Hodge type is a regular, closed subscheme of a suitable pull back of the Mumford moduli tower M over Z_{(p)}. We recall that M parametrizes isomorphism classes of principally polarized abelian schemes over Z_{(p)}schemes which have a fixed relative dimension and which have levelm symplectic similitude structures for all m prime to p. Deep conjectures of Tate and LanglandsRapoport pertain to points of N with values in an algebraic closure of the field with p elements. We report on the proof of the LanglandsRapoport conjecture for those Sh(G,X) with the property that each simple factor of the adjoint Shimura pair (G^{ad},X^{ad}) has compact factors and it is not of D_n^{H} type. As a key ingredient we get an ad\'elic version of the Tate conjecture for many supersingular abelian varieties which are associated to Fvalued points of certain N. 


NOVEMBER 2008 


Analysis Seminar 
Topic: 
TBA 
Presenter: 
Hans Lindblad, University of California, San Diego 
Date: 
Monday, November 3, 2008, Time: 4:00 p.m., Location: Fine Hall 110 


PACM Colloquium 
Topic: 
Spectralelement and adjoint methods in computational seismology 
Presenter: 
Jeroen Tromp, PACM & Geosciences, Princeton University 
Date: 
Monday, November 3, 2008, Time: 4:00 p.m., Location: Fine Hall 214 
Abstract: 
We provide an introduction to the use of spectralelement and adjoint methods in seismology. Following a brief review of the basic equations that govern seismic wave propagation, we discuss how these equations may be solved numerically based upon the spectralelement method (SEM) to address the forward problem in seismology. Examples of synthetic seismograms calculated based upon the SEM are compared to data recorded by global and regional seismographic networks. We also discuss the challenge of using the remaining differences between the data and the synthetic seismograms to constrain better Earth models and source descriptions. This leads naturally to adjoint methods, which provide a practical approach to this formidable computational challenge and enables seismologists to tackle the inverse problem. 


Algebraic Geometry Seminar 
Topic: 
TBA 
Presenter: 
Harry Tamvakis, University of Maryland 
Date: 
Tuesday, November 4, 2008, Time: 4:30 p.m., Location: Fine Hall 322 


Statistical Mechanics Seminar 
Topic: 
Current large deviations in stochastic systems 
Presenter: 
Thierry Bodineau, Ecole Normale, Paris 
Date: 
Wednesday, November 5, 2008, Time: 2:00 p.m., Location: Jadwin 343 
Abstract: 
Using the hydrodynamic limit theory, we will review the large deviations of the heat current through a diffusive system maintained off equilibrium by two heat baths at unequal temperatures. In particular, we will discuss the occurrence of dynamical phase transitions which may occur for some models and the structure of the long range correlations in systems maintained off equilibrium. 


Department Colloquium 
Topic: 
Cremona transformations and homeomorphisms of topological surfaces 
Presenter: 
János Kollár, Princeton University 
Date: 
Wednesday, November 5, 2008, Time: 4:30 p.m., Location: Fine Hall 314 
Abstract: 
See http://www.math.princeton.edu/colloq/co_kollar.pdf 


Number Theory Seminar 
Topic: 
Weight Cycling and Serretype Conjectures 
Presenter: 
Florian Herzig, Northwestern University 
Date: 
Thursday, November 6, 2008, Time: 4:30 p.m., Location: Fine Hall 214 
Abstract: 
Suppose that rho is a threedimensional modular mod p Galois representation whose restriction to the decomposition groups at p is irreducible and generic. If rho is modular in some (Serre) weight, then a representationtheoretic argument shows that it also has to be modular in certain other weights (we can give a short list of possibilities). This goes back to an observation of Buzzard for GL_2. Previously we formulated a Serretype conjecture on the possible weights of rho. Under the assumption that the weights of rho are contained in the predicted weight set, we apply the above weight cycling argument to show that rho is modular in precisely all the nine predicted weights. This is joint work with Matthew Emerton and Toby Gee. 


Differential Geometry and Geometric Analysis Seminar 
Topic: 
The singular set of C^{1} smooth surfaces in the Heisenberg group 
Presenter: 
JihHsin, Academica Sinica Taipei 
Date: 
Friday, November 7, 2008, Time: 3:00 p.m., Location: Fine Hall 314 


Analysis Seminar 
Topic: 
Almost global wellposedness of the 2D full water wave problem 
Presenter: 
Sijue Wu, University of Michigan, Ann Arbor 
Date: 
Monday, November 10, 2008, Time: 4:00 p.m., Location: Fine Hall 110 
Abstract: 
We consider the problem of global in time existence and uniqueness of solutions of the 2D infinite depth full water wave equation. It is known that this equation has a solution for a time period $[0, T/\epsilon]$ for initial data of form $\epsilon\Psi$, where $T$ depends only on $\Psi$. We show that for such data there exists a unique solution for a time period $[0, e^{T/{\epsilon}}]$. This is achieved by better understandings of the nature of the nonlinearity of the full water wave equation. 


Geometry, Representation Theory, and Moduli Seminar 
Topic: 
TBA 
Presenter: 
X. Liu, Notre Dame 
Date: 
Monday, November 10, 2008, Time: 4:00 p.m., Location: Fine Hall 314 


PACM Colloquium 
Topic: 
TBA 
Presenter: 
PierreLouis Lions, College de France and Ecole Polytechnique 
Date: 
Monday, November 10, 2008, Time: 4:00 p.m., Location: Fine Hall 214 


Algebraic Geometry Seminar 
Topic: 
TBA 
Presenter: 
Osamu Fujino, Nagoya University 
Date: 
Tuesday, November 11, 2008, Time: 4:30 p.m., Location: Fine Hall 322 


Statistical Mechanics Seminar 
Topic: 
On quantum, stationary, nonequilibrium states 
Presenter: 
Michael Sigal, University of Toronto 
Date: 
Wednesday, November 12, 2008, Time: 2:00 p.m., Location: Jadwin 343 
Abstract: 
In this talk I will describe recent results on existence and dynamical stability of stationary, nonequilibrium states in certain models of quantum statistical mechanics. This is a joint work with Marco Merkli and Matthias Mueck. 


Department Colloquium 
Topic: 
TBA 
Presenter: 
Bao Châu Ngô, Institute for Advanced Study 
Date: 
Wednesday, November 12, 2008, Time: 4:30 p.m., Location: Fine Hall 314 


Number Theory Seminar 
Topic: 
Faltings' height of CM cycles and Derivative of $L$functions 
Presenter: 
Tonghai Yang, University of Wisconsin at Madison 
Date: 
Thursday, November 13, 2008, Time: 4:30 p.m., Location: Fine Hall 214 
Abstract: 
In this talk, we first describe a systematic way to construct `automorphic Green functions' for Kudla's special divisors on a Shimura variety of orthogonal type $(n, 2)$. We then give an explicit formula for their values at a CM cycle. This formula suggests a direct relation between the Faltings' height of these CM cycles with the central derivative of some RankinSelberg $L$function. As an application, we also give an `analytic proof' of the GrossZagier formula without computing the local intersection numbers at finite primes. This is a joint work with Jan Bruinier. 


Topology Seminar 
Topic: 
Minimal intersection and selfintersection of curves on surfaces 
Presenter: 
Moira Chas, SUNY Stony Brook 
Date: 
Thursday, November 13, 2008, Time: 4:30 p.m., Location: Fine Hall 314 
Abstract: 
Consider the set of free homotopy classes of directed closed curves on an oriented surface and denote by V the Zmodule generated by this set. Goldman discovered a Lie algebra structure on this module, obtained by combining the geometric intersection of curves with the usual loop product. Later on, Turaev found a Lie coalgebra structure on the quotient of V by the one dimensional subspace generated by the trivial loop. Moreover, the Goldman Lie bracket passes to this quotient and both operations satisfy the identities of a Lie bialgebra. This Lie bialgebra has a purely combinatorial presentation. When the surface has nonempty boundary, one can use this presentation to prove it is possible to compute the minimal number of selfintersection points of representatives of a free homotopy class A by means of Lie bialgebra in two different ways: firstly, counting (with multiplicity) the number of terms of the cobracket of powers of A and secondly, counting (with multiplicity) the number of terms of the bracket betweem different powers of A. From this Lie bialgebra structure one can recover the minimal intersection number of two free homotopy classes, provided that one of these classes contains a simple representative. The tools used to prove this result suggest that it would be possible to prove analogous results for the String bracket on certain closed three manifolds. Some of these results are joint work with Fabiana Krongold. 


Differential Geometry and Geometric Analysis Seminar 
Topic: 
TBA 
Presenter: 
Xiaodong Wang, Michigan State University 
Date: 
Friday, November 14, 2008, Time: 3:00 p.m., Location: Fine Hall 314 


PACM Colloquium 
Topic: 
Multiscale Methods for Hydrodynamics of Polymer Chains in Solution 
Presenter: 
Aleksandar Donev, Lawrence Livermore National Laboratory 
Date: 
Monday, November 17, 2008, Time: 4:00 p.m., Location: Fine Hall 214 
Abstract: 
The hydrodynamics of complex fluids, such as polymer solutions and colloidal suspensions, has attracted great interest due to recent advances in fabrication of micro and nanofluidic devices. I will first review recent advances in mesoscopic numerical methods for simulating the interaction between complex fluid flow and suspended macro molecules and structures. Computational issues at play include coarsegraining to bridge the large gap in timescales and length scales, coupling between disparate methods such as molecular dynamics and NavierStokes solvers, the inclusion of thermal fluctuations.
I will then present my recent work at LLNL to develop novel particle methods for modeling polymer chains in flow. Typically, Molecular Dynamics (MD) is used for the polymer chains, and the solvent is modeled with a mesoscopic method. In our algorithm, termed Stochastic EventDriven Molecular Dynamics (SEDMD) [A. Donev and A. L. Garcia and B. J. Alder, J. Comp. Phys., 227(4), 26442665, 2008], polymers are modeled as chains of hard spheres and the solvent is modeled using a densefluid generalization of the Direct Simulation Monte Carlo (DSMC) method [Phys. Rev. Lett., 101, 075902, 2008]. Even with all of the speedup compared to bruteforce MD the algorithm is still timeconsuming due to the large number of solvent particles necessary to fill the computational domain. It is natural to restrict the particle model only to regions close to a polymer chain and use a lowerresolution continuum model elsewhere. I will present a hybrid method that couples an explicit fluctuating compressible NavierStokes solver with the particle method. The coupling is fluxbased and generalizes previous work [J. B. Bell and A. L. Garcia and S. A. Williams, SIAM Multiscale Modeling and Simulation, 6, 12561280, 2008] to dense fluids as appropriate for polymer problems.
I will conclude with a look into the challenges of developing a simulation methodology capable of simulating macroscopic flows of complex fluids with atomistic fidelity. 


Algebraic Geometry Seminar 
Topic: 
TBA 
Presenter: 
Sabin Cautis, Rice University 
Date: 
Tuesday, November 18, 2008, Time: 4:30 p.m., Location: Fine Hall 322 


Statistical Mechanics Seminar 
Topic: 
Bosons in rapid rotation 
Presenter: 
Jakob Yngvason, University of Vienna 
Date: 
Wednesday, November 19, 2008, Time: 2:00 p.m., Location: Jadwin 343 
Abstract: 
One of the most remarkable manifestations of superfluidity in BoseEinstein condensates is the way the condensate responds to rotation. In a superfluid the rotation of the container confining the fluid leads to the formation of vortices with quantized circulation. This phenomenon can be studied through the solutions of a nonlinear Schrodinger equation, the GrossPitaevskii equation. In the lecture recent results concerning the appearance and disappearance of vortex lattices in rapidly rotating BoseEinstein condensates will be discussed. 


Department Colloquium 
Topic: 
TBA 
Presenter: 
Valery Alexeev, University of Georgia 
Date: 
Wednesday, November 19, 2008, Time: 4:30 p.m., Location: Fine Hall 314 


Topology Seminar 
Topic: 
TBA 
Presenter: 
Peter Ozsvath, Columbia University 
Date: 
Thursday, November 20, 2008, Time: 4:30 p.m., Location: Fine Hall 314 


Analysis Seminar 
Topic: 
TBA 
Presenter: 
Soonsik Kwon, Princeton University 
Date: 
Monday,November 24, 2008, Time: 4:00 p.m., Location: Fine Hall 110 


PACM Colloquium 
Topic: 
Emissions Market Models 
Presenter: 
René Carmona, PACM & ORFE, Princeton University 
Date: 
Monday, November 24, 2008, Time: 4:00 p.m., Location: Fine Hall 214 
Abstract: 
The main goal of the talk is to introduce a new capandtrade scheme design for the control and the reduction of atmospheric pollution. The tools developed for the purpose of the study are intended to help policy makers and regulators understand the pros and cons of the emissions markets at a quantitative level.
We propose a model for an economy where risk neutral firms produce goods to satisfy an inelastic demand and are endowed with permits by the regulator in order to offset their pollution at compliance time and avoid having to pay a penalty. Firms that can easily reduce emissions do so, while those for which it is harder buy permits from those firms anticipating that they will not need them, creating a financial market for pollution credits.
Our model captures most of the features of the European Union Emissions Trading Scheme. We show existence of an equilibrium and uniqueness of emissions credit prices. We also characterize the equilibrium prices of goods and the optimal production and trading strategies of the firms. We choose the electricity market in Texas to illustrate numerically the qualitative properties observed during the implementation of the first phase of the European Union capandtrade CO2 emissions scheme, comparing the results of capandtrade schemes to the Business As Usual benchmark. In particular, we confirm the presence of windfall profits criticized by the opponents of these markets. We also demonstrate the shortcomings of tax and subsidy alternatives. Finally we introduce a relative allocation scheme which, despite its ease of implementation, leads to smaller windfall profits than the standard scheme. 


Algebraic Geometry Seminar 
Topic: 
Finiteness theorems for algebraic groups over function fields 
Presenter: 
Brian Conrad, Stanford University 
Date: 
Tuesday, November 25, 2008, Time: 4:30 p.m., Location: Fine Hall 322 
Abstract: 
If X is a smooth variety over a global field k, G is an algebraic group over k equipped with an action on X, and x is a point in X(k) then it is natural to ask how the property of x' in X(k) being in the G(k)orbit of x compares with being in the G(k_v)orbit of x for all places v of k. In general there is a nontrivial "localtoglobal" obstruction space, but one can ask if it is finite. Even when G is semisimple, this finiteness problem leads to the consideration of the isotropy group G_x that is generally not connected or reductive (or even smooth when char(k) > 0). In the number field case the finiteness of these obstruction spaces was proved by Borel and Serre long ago, but their method used characteristic 0 in an essential way. Recently in joint work with Gabber and G. Prasad we have developed a theory of "pseudoreductive groups" which is a very useful tool to prove results for general affine algebraic groups in the function field case that were previously known only in the reductive case. In particular, this work makes it possible to prove the analogue of the BorelSerre finiteness result over function fields (away from char. 2 for now). The first part of the talk will explain a bit about the theory of pseudoreductive groups, and the rest of the talk will show how it is used to establish the finiteness of the localtoglobal obstruction spaces in the function field case (in char. > 2). If time permits we will also discuss an application to the problem of whether the kisomorphism class of a projective kvariety is determined (up to "finite ambiguity") by its k_visomorphism class for all places v of k (a problem solved by Mazur over number fields, once again making essential use of characteristic 0). 


DECEMBER 2008 


Analysis Seminar 
Topic: 
TBA 
Presenter: 
Alessio Figalli, Université de Nice SophiaAntipolis and Ecole Polytechnique 
Date: 
Monday, December 1, 2008, Time: 4:00 p.m., Location: Fine Hall 110 


PACM Colloquium 
Topic: 
TBA 
Presenter: 
Ingrid Daubechies, PACM,, Princeton University 
Date: 
Monday, December 1, 2008, Time: 4:00 p.m., Location: Fine Hall 214 


Algebraic Geometry Seminar 
Topic: 
TBA 
Presenter: 
Eduardo Esteves, Instituto de Matematica Pura e Aplicada 
Date: 
Tuesday, December 2, 2008, Time: 4:30 p.m., Location: Fine Hall 322 


Statistical Mechanics Seminar 
Topic: 
Local and Global Structure of Stationary States of Macroscopic Systems 
Presenter: 
Joel Lebowitz, Rutgers University 
Date: 
Wednesday, December 3, 2008, Time: 2:00 p.m., Location: Jadwin 343 
Abstract: 
The microscopic structure of a macroscopic system in a steady state is described locally, i.e. at a suitably scaled macroscopic point $x$, by a time invariant measure of the corresponding infinite system with translation invariant dynamics. This measure may be extremal, with good decay of correlations, or a superposition of extremal measures, with weights depending on $x$ (and possibly even on the way one scales).
I will illustrate the above by some exact results for 1D lattice systems with two types of particles (plus holes) evolving according to variants of the simple asymmetric exclusion process, in open or closed systems. Somewhat surprisingly, the spatially asymmetric local dynamics satisfy (in some cases) detailed balance with respect to a global Gibbs measure with long range pair interactions. 


Department Colloquium 
Topic: 
TBA 
Presenter: 
Bruce Kleiner, Yale University 
Date: 
Wednesday, December 3, 2008, Time: 4:30 p.m., Location: Fine Hall 314 


Topology Seminar 
Topic: 
TBA 
Presenter: 
Elisenda Grigsby, Columbia University 
Date: 
Thursday, December 4, 2008, Time: 4:30 p.m., Location: Fine Hall 314 


PACM Colloquium 
Topic: 
Computational Astrophysics and the Dynamics of Accretion Disks 
Presenter: 
James M. Stone, PACM & Astrophysical Sciences 
Date: 
Monday, December 8, 2008, Time: 4:00 p.m., Location: Fine Hall 214 
Abstract: 
he ever increasing performance of computer hardware and improvements to the accuracy of numerical algorithms are revolutionizing scientific research in many disciplines, but perhaps none more so than astrophysics. I will begin by describing why computation is crucial for the solution of a variety of problems at the forefront of research in astronomy and astrophysics, with particular emphasis on understanding accretion flows onto black holes. I will outline the challenge of developing, testing, and implementing numerical algorithms for the investigation of these problems. Finally, I will present results that demonstrate how computation can help us understand the basic physics of magnetized accretion disks. 


Geometry, Representation Theory, and Moduli Seminar 
Topic: 
TBA 
Presenter: 
K. Behrend, UBC 
Date: 
Monday, December 8, 2008, Time: 4:00 p.m., Location: Fine Hall 314 


Algebraic Geometry Seminar 
Topic: 
TBA 
Presenter: 
David Smyth, Harvard University 
Date: 
Tuesday, December 9, 2008, Time: 4:30 p.m., Location: Fine Hall 322 


Department Colloquium 
Topic: 
TBA 
Presenter: 
Kai Behrend, University of British Columbia 
Date: 
Wednesday, December 10, 2008, Time: 4:30 p.m., Location: Fine Hall 314 



