SEMINARS
Updated: 10-15-2008
 OCTOBER 2008 Statistical Mechanics Seminar Topic: Heat conduction and Non-Equilibrium 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 Non-Equilibrium 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 "non-commutative harmonic analysis": understanding very general mathematical problems (particularly of geometry or analysis) in the presence of a (non-commutative) 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 Harish-Chandra, 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 K-theory). 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 l-colorings 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 3-colorings is achieved by a semi-complete biparite graph. This is joint work with Po-Shen Loh and Benny Sudakov. Number Theory Seminar ***Please note special location Topic: Dynamical Mordell-Lang problems Presenter: Thomas J. Tucker, Rochester Date: Thursday, October 16, 2008, Time: 4:30 p.m., Location: IAS West Building Lecture Hall Abstract: The Mordell-Lang 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 non-fillable. 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 three-sphere Presenter: Fernando Coda Marques, IMPA-Brazil 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 path-connectedness of the space of positive scalar curvature metrics on the three-sphere. 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 p-adic and \ell-adic 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 Manin-Mumford conjecture (about the closure of any set of torsion points in an abelian variety), the Andr\'e-Oort conjecure (about the closure of any set of CM-points 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 $O(\sqrt d m^{d-1})$ vertices of $G_1$ so that no topologically nontrivial cycles remain. This improves an $O(d^{\log_2 (3/2)}m^{d-1})$ 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 Langlands--Rapoport conjectures for Shimura varieties of Hodge type Presenter: A. Vasiu, Binghampton University Date: Thursday, October 30, 2008, Time: 4:30 p.m., Location: IAS S-101 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 level-m symplectic similitude structures for all m prime to p. Deep conjectures of Tate and Langlands--Rapoport pertain to points of N with values in an algebraic closure of the field with p elements. We report on the proof of the Langlands--Rapoport 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 F-valued 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: Spectral-element 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 spectral-element 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 spectral-element 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 Serre-type 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 three-dimensional 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 representation-theoretic 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 Serre-type 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: Jih-Hsin, 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 2-D 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 2-D 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: Pierre-Louis 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, non-equilibrium 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, non-equilibrium 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 Rankin-Selberg $L$-function. As an application, we also give an analytic proof' of the Gross-Zagier formula without computing the local intersection numbers at finite primes. This is a joint work with Jan Bruinier. Topology Seminar Topic: Minimal intersection and self-intersection 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 Z-module 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 non-empty boundary, one can use this presentation to prove it is possible to compute the minimal number of self-intersection 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 nano-fluidic 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 coarse-graining to bridge the large gap in timescales and length scales, coupling between disparate methods such as molecular dynamics and Navier-Stokes 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 Event-Driven Molecular Dynamics (SEDMD) [A. Donev and A. L. Garcia and B. J. Alder, J. Comp. Phys., 227(4), 2644-2665, 2008], polymers are modeled as chains of hard spheres and the solvent is modeled using a dense-fluid generalization of the Direct Simulation Monte Carlo (DSMC) method [Phys. Rev. Lett., 101, 075902, 2008]. Even with all of the speedup compared to brute-force MD the algorithm is still time-consuming 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 lower-resolution continuum model elsewhere. I will present a hybrid method that couples an explicit fluctuating compressible Navier-Stokes solver with the particle method. The coupling is flux-based and generalizes previous work [J. B. Bell and A. L. Garcia and S. A. Williams, SIAM Multiscale Modeling and Simulation, 6, 1256-1280, 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 Bose-Einstein 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 Gross-Pitaevskii equation. In the lecture recent results concerning the appearance and disappearance of vortex lattices in rapidly rotating Bose-Einstein 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 cap-and-trade 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 cap-and-trade CO2 emissions scheme, comparing the results of cap-and-trade 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 non-trivial "local-to-global" 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 "pseudo-reductive 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 Borel-Serre 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 pseudo-reductive groups, and the rest of the talk will show how it is used to establish the finiteness of the local-to-global 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 k-isomorphism class of a projective k-variety is determined (up to "finite ambiguity") by its k_v-isomorphism 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 Sophia-Antipolis 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