SEMINARS
Updated: 10-1-2008
 OCTOBER 2008 Department Colloquium Topic: The geometry and topology of arithmetic hyperbolic 3-manifolds Presenter: Alan Reid, University of Texas Date: Wednesday, October 1, 2008, Time: 4:30 p.m., Location: Fine Hall 314 Abstract: This talk will discuss recent advances in regards to some of the main open problems about hyperbolic 3-manifolds in the context of arithmetic hyperbolic 3-manifolds. Graduate Seminar Topic: The Composition Problem in Measure Spaces Presenter: Philip J. Isett, Princeton University Date: Thursday, October 2, 2008, Time: 12:30 p.m., Location: Fine Hall 314 Abstract: Let X,Y be measurable spaces and \eta : X \to Y be a measurable function. Under what conditions on \eta is the composition with f : Y \to C a well defined operation when f is only specified almost everywhere? Does composition with \eta induce a map between L^p spaces ? I will show how one generally would answer these questions , give an algebraic prespective on the problem(and on measure spaces in general), and give a complete solution when the map\eta is multipilication on the p-adic integers. Number Theory Seminar Topic: Asymptotics for special derivatives of L-series Presenter: Nicolas Templier, Universite Montpellier II, France and Institute for Advanced Study Date: Thursday, October 2, 2008, Time: 4:30 p.m., Location: IAS S -101 Abstract: In a first part, we shall prove a quantitative nonvanishing result conjectured by Ph.Michel and A.Venkatesh which concerns the special derivatives occuring in the Gross-Zagier formula. Our method relies on two classical equidistribution Theorems in arithmetic geometry. In a second part, we shall explain how to refine these results with methods from analytic number theory. We shall emphasize on the new aspects of this analytic approach which may hopefully be used in other contexts. Topology Seminar Topic: Almost minimal laminations and the connectivity of ending lamination space Presenter: David Gabai, Princeton University Date: Thursday, October 2, 2008, Time: 4:30 p.m., Location: Fine Hall 314 Abstract: We show that if S is a finite type hyperbolic surface which is not the 3 or 4-holed sphere or 1-holed torus, then the Ending lamination space of S is connected, locally path connected and cyclic. Using Klarrich's theorem this implies that the boundary of a curve complex associated to any such space is connected, locally path connected and cyclic. Differential Geometry and Geometric Analysis Seminar Topic: A new example with positive sectional curvature Presenter: Wolfgang Ziller, University of Pennsylvania Date: Friday, October 3, 2008, Time: 3:00 p.m., Location: Fine Hall 314 Abstract: I will discuss the construction of a new example with positive sectional curvature on a 7-dimensional manifold homeomorphic to the unit tangent bundle of the 4-sphere. The metric is of Kaluza Klein type on an orbifold principle bundle over the 4-sphere and is closely related to the geometry of self dual Einstein and 3- Sasakian metrics. Analysis Seminar Topic: A Hyperbolic Free-Boundary Problem for 3D Compressible Euler Flow in Physical Vacuum Presenter: Steve Shkoller, University of California, Davis Date: Monday, October 6, 2008, Time: 4:00 p.m., Location: Fine Hall 110 Abstract: We prove well-posedness for compressible flow with free-boundary in physical vacuum, modeled by the 3D compressible Euler equations. The vanishing of the density at the vacuum boundary induces degenerate hyperbolic equations that become characteristic, requiring a separate analysis of time, normal, and tangential derivatives to handle the manifest 1/2-derivative loss. Unfortunately, the methods for incompressible flow do not work for the degenerate compressible regime; a priori nonlinear estimates are obtained using the geometric structure of the Euler equations, and an existence theory is developed using a novel approximation scheme employing an artificial phase. The result is in collaboration with Coutand and Lindblad. Geometry, Representation Theory, and Moduli Seminar Topic: Local Gromov-Witten Invariants of Spin Curves Presenter: Junho Lee, UCF Date: Monday, October 6, 2008, Time: 4:00 p.m., Location: Fine Hall 314 Abstract: See http://www.math.princeton.edu/~rahulp/08lee.pdf PACM Colloquium Topic: Structure Determination through Eigenvectors of Sparse Operators Presenter: Amit Singer, PACM & Mathematics, Princeton University Date: Monday, October 6, 2008, Time: 4:00 p.m., Location: Fine Hall 214 Abstract: In many applications, the main goal is to obtain a global low dimensional representation of the data, given some local noisy geometric constraints. In this talk we will show how the problems listed below can be efficiently solved by constructing suitable operators on their data and computing a few eigenvectors of sparse matrices corresponding to the data operators. * Cryo Electron Microscopy for protein structuring: reconstructing the three-dimensional structure of a molecule from projection images taken at random unknown orientations (unlike classical tomography, where orientations are known). * NMR spectroscopy for protein structuring: finding the global positioning of all hydrogen atoms in a molecule from their local distances. Distances between neighboring hydrogen atoms are estimated from the spectral lines corresponding to the short ranged spin-spin interaction. * Sensor networks: finding the global positioning from noisy local distances. Joint work with Ronald Coifman, Yoel Shkolnisky (Yale Applied Math) and Fred Sigworth (Yale School of Medicine). Algebraic Geometry Seminar Topic: A Torelli theorem over finite fields Presenter: Yuri Tschinkel, New York University Date: Tuesday, October 7, 2008, Time: 4:30 p.m., Location: Fine Hall 322 Abstract: I will discuss a set-theoretic analog of the classical Torelli theorem for curves. Statistical Mechanics Seminar Topic: On models of random permutations and their relation to Bose-Einstein condensation Presenter: Daniel Ueltschi, Warwick University Date: Wednesday, October 8, 2008, Time: 2:00 p.m., Location: Jadwin 343 Abstract: The first half of the talk will be devoted to probabilistic models of "spatial" random permutations, that involve points in R^d. Permutations are weighed according to the length of the jumps. The main question deals with the occurrence of infinite cycles. The second part of the talk will be devoted to the quantum Bose gas in the path-integral representation. Models of interacting spatial permutations are expected to shed light on the effects of the interactions on the Bose-Einstein condensation. Graduate Seminar Topic: GRH and polynomial-time primality testing Presenter: Jacob Tsimerman, Princeton University Date: Thursday, October 9, 2008, Time: 12:30 p.m., Location: Fine Hall 314 Abstract: For a long time, a famous open problem was to figure out whether a number was prime quickly (in polynomial time). It's interesting to see how under the generalized riemann hypothesis, the problem becomes completely straightforward. I will introduce the relevant concept and present the simple proof. During the second half, I will present a provably polynomial time test, without reliance on GRH. If time permits, I will say some more about L-functions and their application to computing. Discrete Mathematics Seminar Topic: Directed graphs without short cycles Presenter: Jacob Fox, Princeton University Date: Thursday, October 9, 2008, Time: 2:15 p.m., Location: Fine Hall 224 Abstract: In a directed graph G, a feedback arc set is a collection of edges whose deletion makes G acyclic. Extending a result of Chudnovsky, Seymour, and Sullivan, we give an upper bound on the size of the minimum feedback arc set in digraphs without short directed cycles. Our result can be also used to answer a question of Yuster concerning cycles of almost given length in digraphs. This is joint work with Peter Keevash and Benny Sudakov. Number Theory Seminar Topic: Gross--Schoen cycles and triple product L-series Presenter: Shou-Wu Zhang, Columbia University Date: Thursday, October 9, 2008, Time: 4:30 p.m., Location: Fine Hall 214 Differential Geometry and Geometric Analysis Seminar Topic: The volume of a differentiable stack Presenter: Alan Weinstein, UC Berkeley Date: Friday, October 10, 2008, Time: 3:00 p.m., Location: Fine Hall 314 Abstract: We extend to the setting of Lie groupoids the notion of the cardinality of a finite groupoid (a rational number, equal to the Euler characteristic of the correspondingdiscrete orbifold). Since this quantity is an invariant under equivalence of groupoids, we call it the volume of the associatedstack rather than of the groupoid itself. Since there is no natural measure in the smooth case like the counting measure in the discrete case, we need extra data to define the volume. This data has the form of an invariant section of a naturalline bundle over the stack. Sections of a square root of this line bundle constitute an intrinsic Hilbert space'' of the stack. The talk will not require prior knowledge of groupoids or stacks. Analysis Seminar Topic: Multi-parameter Carnot-Carathéadory balls Presenter: Brian Street, University of Toronto Date: Monday, October 13, 2008, Time: 4:00 p.m., Location: Fine Hall 110 Abstract: We discuss multi-parameter Carnot-Carathéadory balls. In particular, we discuss questions motivated by multi-parameter singular integrals. These results generalize results due to Nagel, Stein, and Wainger in the single parameter setting. Geometry, Representation Theory, and Moduli Seminar Topic: TBA Presenter: A. Caldararu, Wisconsin Date: Monday, October 13, 2008, Time: 4:00 p.m., Location: Fine Hall 314 PACM Colloquium Topic: Simulations of 5-D Plasma Turbulence in Fusion Energy Devices Presenter: Greg Hammett, Princeton Plasma Physics Lab Date: Monday, October 13, 2008, Time: 4:00 p.m., Location: Fine Hall 214 Abstract: This talk will start with a brief status report on magnetic fusion energy research. One of the key challenges in fusion has been the occurrence of fine-scale turbulent fluctuations, which cause plasma to leak out of a magnetic trap, so we would like to be able to predict and reduce this turbulence. A major advance in this field has been the recent development of codes for comprehensive 5-D gyrokinetic simulations of microturbulence in the core region of fusion devices. These simulations have been made feasible by significant advances not only in raw computer power, but also in asymptotic simplification of the problem formulation, and in algorithmic development. Remaining challenges and some opportunities for contributions from applied and computational mathematics will be described. Algebraic Geometry Seminar Topic: TBA Presenter: Florin Ambro, Romanian Academy of Sciences/ Johns Hopkins Date: Tuesday, October 14, 2008, Time: 4:30 p.m., Location: Fine Hall 322 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. 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: TBA Presenter: Sam Ruth, Princeton University Date: Thursday, October 16, 2008, Time: 12:30 p.m., Location: Fine Hall 314 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 Topic: Dynamical Mordell-Lang problems Presenter: Thomas J. Tucker, Rochester Date: Thursday, October 16, 2008, Time: 4:30 p.m., Location: IAS S -101 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. 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: TBA Presenter: Frans Oort, University of Utrecht/ Columbia University Date: Tuesday, October 21, 2008, Time: 4:30 p.m., Location: Fine Hall 322 Statistical Mechanics Seminar Topic: Resonances in chaotic systems Presenter: Giovanni Gallavotti, University of Rome/Rutgers Date: Wednesday, October 22, 2008, Time: 2:00 p.m., Location: Jadwin 343 Abstract: In chaotic systems resonances are often called "synchronizations". In simple cases the phenomenon can be analytically studied: I consider two simple identical Anosov special flows and discuss their synchronization at small coupling. Department Colloquium Topic: TBA Presenter: Frans Oort, University of Utrecht/ Columbia University Date: Wednesday, October 22, 2008, Time: 4:30 p.m., Location: Fine Hall 314 Graduate Seminar Topic: TBA Presenter: Vivek Shende, Princeton University Date: Thursday, October 23, 2008, Time: 12:30 p.m., Location: Fine Hall 314 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: TBA Presenter: Jih-Hsin, Academica Sinica Taipei Date: Friday, November 7, 2008, Time: 3:00 p.m., Location: Fine Hall 314 Analysis Seminar Topic: TBA Presenter: Sijue Wu, University of Michigan, Ann Arbor Date: Monday, November 10, 2008, Time: 4:00 p.m., Location: Fine Hall 110 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. 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 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: Compressive Optical Imaging Presenter: Rebecca Willett, Electrical Engineering, Duke University Date: Monday, December 1, 2008, Time: 4:00 p.m., Location: Fine Hall 214 Abstract: Recent work in the emerging field of compressed sensing indicates that, when feasible, judicious selection of the type of image transformation induced by imaging systems may dramatically improve our ability to perform reconstruction, even when the number of measurements is small relative to the size and resolution of the final image. The basic idea of compressed sensing is that when an image is very sparse (i.e. zero-valued at most locations) or highly compressible in some basis, relatively few incoherent observations suffice to reconstruct the most significant non-zero basis coefficients. These theoretical results have profound implications for the design of new imaging systems, particularly when physical and economical limitations require that these systems be as small, mechanically robust, and inexpensive as possible. In this talk I will describe the primary theory underlying compressed sensing and discuss some of the key mathematical challenges associated with its application to practical imaging systems. In particular, I will explore several novel imaging system designs based on compressed sensing, including compressive coded aperture and hyperspectral imagers, and examine the interplay between compressed sensing theory and the practical physical constraints which must be considered to effectively exploit this theory. 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 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