SEMINARS
Updated: 11-1-2006
   
   
NOVEMBER 2006
   
Institute for Advanced Study and Princeton University Number Theory Seminar
Topic: A Weyl-like bound for automorphic L-functions
Presenter: Jianya Liu, Shandong University, China
Date:  Thursday, November 2, 2006, Time: 4:30 p.m., Location: SH-101 at the Institute for Advanced Study
Abstract: A central problem in the theory of L-functions is to investigate their sizes on the critical line. The convexity bound, which follows from the Phragmen-Lindelof principle, is of little use in applications. Therefore much effort has been made to obtain subconvexity bounds for various L-functions, which have also been applied to give various equi-distribution results. In the classical case of the Riemann zeta-function, this convexity exponent is 1/4, and the classical subconvexity theorem of Weyl states that the 1/4 can be reduced to 1/6. In this talk, I will report a joint work with Yuk-Kam Lau and Yangbo Ye, in which we obtain a Weyl-like bound for Rankin-Selberg automorphic L-functions in the weight/eigenvalue aspect.
   
PACM Colloquium
Topic: Information Theory and Probability Estimation: From Shannon to Shakespeare via Laplace, Good, Turing, Hardy, Ramanujan, and Fisher
Presenter: Alon Orlitsky, ECE and CSE, University of California, San Diego
Date:  Monday, November 6, 2006, Time: 4:00 p.m., Location: Fine 214
Abstract:

Standard information-theoretic results show that data over small, typically binary, alphabets can be compressed to Shannon's entropy limit. Yet most practical sources, such as text, audio, or video, have essentially infinite support. Compressing such sources requires estimating probabilities of unlikely, even unseen, events, a problem considered by Laplace. Of existing estimators, an ingenious if cryptic one derived by Good and Turing while deciphering the Enigma code works best yet not optimally. Hardy and Ramanujan's celebrated results on the number of integer partitions yield an asymptotically optimal estimator that compresses arbitrary-alphabet data patterns to their entropy. The same approach generalizes Fisher's seminal work estimating the number of butterfly species and its extension authenticating a poem purportedly written by The Bard. The talk covers these topics and is self contained.

Joint work with Prasad Santhanam, Krishna Viswanathan, and Junan Zhang.


   
Analysis Seminar
Topic: A central limit theorem for convex sets
Presenter: Bo'az Klartag, Princeton University
Date:  Monday, November 6, 2006, Time: 4:00 p.m., Location: Fine 110
Abstract: Suppose X is a random vector, that is distributed uniformly in some n-dimensional convex set. It was conjectured that when the dimension n is very large, there exists a non-zero vector u, such that the distribution of the real random variable <X,u> is close to the gaussian distribution. A well-understood situation, is when X is distributed uniformly over the n-dimensional cube. In this case, <X,u> is approximately gaussian for, say, the vector u = (1,...,1) / sqrt(n), as follows from the classical central limit theorem. We prove the conjecture for a general convex set. Moreover, when the expectation of X is zero, and the covariance of X is the identity matrix, we show that for 'most' unit vectors u, the random variable <X,u> is distributed approximately according to the gaussian law. We argue that convexity - and perhaps geometry in general - may replace the role of independence in certain aspects of the phenomenon represented by the central limit theorem.
   
Algebraic Geometry Seminar
Topic: Constructing Bridgeland Moduli Spaces with Mukai Flops
Presenter: Aaron Bertram, University of Utah
Date:  Tuesday, November 7, 2006, Time: 4:30 p.m., Location: Fine 322
Abstract: Bridgeland stability for K3 surfaces, inspired by the string theorists' pi-stability, is based on a novel generalization of the "classical" slope function d/r for vector bundles on a curve. Unlike the curve case, Bridgeland stability has built-in variation and wall-crossings, leading one to predict new birational models of the moduli spaces of degree-stable coherent sheaves on K3 surfaces. In this talk I'll discuss a strategy worked out jointly with Daniele Arcara to exploit the holomorphic symplectic structure of these moduli spaces to construct the new birational models "by hand" as Mukai flops.
   
Mathematical Physics Seminar
Topic: On the multifractal structure of the generalized eigenfunctions of certain sparse Schrödinger operators
Presenter: Frederic Klopp, Universite Paris-Nord
Date:  Tuesday, November 7, 2006, Time: 4:30 p.m., Location: Jadwin 343
Abstract: The talk is devoted to the study of the generalized eigenfunctions for certain Schrödinger operators with sparse potentials on the half-line. This study reduces to that of an ergodic matrix cocycle for which we develop an exact renormalization analysis based upon the monodromization procedure. The analysis results in a multi-fractal description of the solutions to the Schrödinger equation. As a consequence, we obtain a complete description of the set of ergodic parameters for which the Lyapunov exponent of the cocycle, hence, the modified Lyapunov exponent of the Schrödinger equation, exists and does not exist. It also gives a multi-fractal description of the generalized eigenfunctions of the operator. The talk is based on a joint work, which is in progress, with A. Fedotov (St Petersburg).
   
Operations Research and Financial Engineering Seminar
Topic:

Sato processes and the valuation of structured products

Presenter: Dilip Madan, Robert H. Smith School of Business
Date:  Tuesday, November 7, 2006, Time: 4:30 p.m., Location: E-219, E-Quad
Abstract: We report on the adequacy of using Sato processes to value equity structured products. An analysis of the variance of realized variance for Sato processes shows that these processes may be suited to option contracts on realized volatility. Nonlinear pricing principles based on hedging to acceptability are outlined for the purpose of pricing structured transactions. It is shown that typically different products should be priced using different models. Pricing comparisons of Sato process prices with other standard models like Heston stochastic volatility, with and without jumps, VGSA, local volatility and local CGMY are also provided. Sato processes tend to over price cliquets relative to other models. They also maintain the value of long dated out-of-the-money realized variance options. (Joint work with Ernst Eberlein)
   
Discrete Mathematics Seminar
Topic: Inverse Littlewood-Offord theorems
Presenter: Van Vu, Rutgers University
Date:  Wednesday, November 8, 2006, Time: 2:15 p.m., Location: Fine 224
  See http://www.math.princeton.edu/~bsudakov/vu2006-fall.pdf
   
Geometry, Representation Theory, and Moduli Seminar
Topic: TBA
Presenter: J. Solomon, IAS
Date:  Wednesday, November 8, 2006, Time: 3:00 p.m., Location: Fine 214
   
Department Colloquium
Topic: Irrational triangular billiards
Presenter: Richard Schwartz, Brown University
Date:  Wednesday, November 8, 2006, Time: 4:30 p.m., Location: Fine 314
Abstract: It is an old and open problem whether or not every triangular shaped billiard table has a periodic billiard path. The answer is known to be yes for acute, right, and rational triangles but unknown in the obtuse irrational case. Over several years, Pat Hooper and I have developed a graphical user interface, called McBilliards, with a view towards resolving the triangular billiards problem. The huge experimental output from the progran illustrates the extreme and previously unexpected complexities of the problem. In my talk I will survey the experimental evidence from McBilliards and also explain some of our rigorous results which were inspired by the experiments.
   
Ergodic Theory and Statistical Mechanics Seminar
Topic: The distribution of visible lattice points and collision times in the periodic Lorentz gas
Presenter: J.Marklof, Bristol
Date:  Thursday, November 9, 2006, Time: 2:00 p.m., Location: Fine 401
Abstract:

I will discuss two closely related problems.
(1) Take integer lattice points in a large ball of radius R and project them onto the unit sphere S centered at x. It is well known that the sequence of projected points becomes uniformly distributed on S as R becomes large. I will show that, for every fixed x, the statistical correlation functions of this sequence have limiting distributions with some remarkable properties. The proof uses Ratner's classification of ergodic measures invariant under unipotent flows.
(2) The periodic Lorentz gas describes a point particle moving in a periodic array of spherical scatterers of radius r. I'll explain why the probability for a particle to hit the first scatterer after a fixed time T has a limiting distribution in the small scatterer limt r->0 and discuss some of its properties. This particular question was raised by Sinai in the early 1980s.
This is joint work with A. Strombergsson.

   
Ergodic Theory and Statistical Mechanics Seminar
Topic: On non perturbative Anderson localization for random potentials with fast decaying correlations
Presenter: Michael Goldstein, University of Toronto
Date:  Thursday, November 9, 2006, Time: 3:30 p.m., Location: Fine 401
Abstract: See http://www.math.princeton.edu/~seminar/2006-07-sem/GoldsteinAbstract11-9-2006.pdf
   
Institute for Advanced Study and Princeton University Number Theory Seminar
Topic: Multiple Dirichlet series attached to Weyl groups
Presenter: Solomon Friedberg, Boston College
Date:  Thursday, November 9, 2006, Time: 4:30 p.m., Location: Fine Hall 214
Abstract: Weyl group multiple Dirichlet series are multiple Dirichlet series in several variables whose coefficients involve Gauss sums and also reflect the combinatorics of a given root system. The earliest examples came from Mellin transforms of metaplectic Eisenstein series and have been intensively studied over the last 20 years. These functions and their residues unify and generalize a number of examples which have been previously treated individually, often with applications to analytic number theory. In this lecture I give an account of some of the major research to date and the opportunities for the future.
   
Operations Research and Financial Engineering Seminar
Topic:

Inferences on the proportion of non-null effects in large-scale multiple comparisons

Presenter: Jiashun Jin, Perdue University
Date:  Thursday, November 9, 2006, Time: 4:30 p.m., Location: E-219, E-Quad
Abstract: The immediate need for effective massive data mining gives rise to a recent new field in statistics: large-scale multiple simultaneous testing or multiple comparisons. In such settings, one tests thousands or even millions of hypotheses simultaneously H1 , H2 , . . . , Hn , where associated with each hypothesis is a summary test statistic X1 , X2 , . . . , Xn . A problem of particular interest is to estimate the proportion of non-null effects, i.e., the proportion of hypotheses that are untrue. In this talk, we report some recent progress on estimating the proportion. We model each Xj as normally distributed with individual mean μj and individual variance σ2 j , where the parameters satisfy that (μj , σj ) = (0, 1) if Hj is true, and (μj , σj ) 1) otherwise. We show that, under natural identifiability conditions, universal oracle equivalence of the proportion can be constructed, which equals to the true proportion for any n and any set of parameters. The oracle naturally yields real estimators, which are uniformly consistent for the proportion over a wide class of situations. This talk is based on collaborated works with (alphabetically) Tony Cai, David Donoho, Mark Low, Jie Peng, and Pei Wang.
   
Topology Seminar
Topic: TBA
Presenter: Andras Stipsicz, Renyi Institute of Mathematics
Date:  Thursday, November 9, 2006, Time: 4:30 p.m., Location: Fine 314
   
Differential Geometry and Geometric Analysis Seminar
Topic: An L_p Affine Isoperimetric Inequality and Its Applications
Presenter: Gaoyong Zhang, Polytechnic University, NY
Date:  Friday, November 10, 2006, Time: 3:00 p.m., Location: Fine 314
Abstract: Affine surface areas of convex bodies will be defined by an integral geometric approach. An L_p affine isoperimetric inequality that is stronger than the classical isoperimetric inequality will be discussed. The affine isoperimetric inequality can be applied to establishing sharp affine Sobolev inequalities. This strengthens the equivalence of the isoperimetric inequality and the sharp Sobolev inequality.
   
Differential Geometry and Geometric Analysis Seminar *** Please note special time
Topic: High dimensional generalizations of Perelman's results and their applications
Presenter: Lei Ni, UCSD
Date:  Friday, November 10, 2006, Time: 4:00 p.m., Location: Fine 314
   
Analysis Seminar
Topic: Global existence for energy critical waves in 3-d domains
Presenter: Nicolas Burq, Paris 11
Date:  Monday, November 13, 2006, Time: 4:00 p.m., Location: Fine 110
Abstract: We prove that the quintic (critical) defocussing wave equation with Dirichlet boundary conditions in a 3-d bounded domain is globally well posed in energy space. The main ingredient of the proof is an (optimal) Strichartz inequality derived from some recent spectral projector estimates by Smith and Sogge and a precise study of the boundary value problem. (joint with G. Lebeau and F. Planchon)
   
PACM Colloquium
Topic: Denoising Color Images
Presenter: Yang Wang, Mathematics, Georgia Institute of Technology
Date:  Monday, November 13, 2006, Time: 4:00 p.m., Location: Fine 214
Abstract:

Natural color images captured by digital cameras often exhibit noticeable noise, particularly when the pictures are taken under low lighting or artificial lighting conditions. Traditional denoising techniques, which are often tested for removing artificial noise in monochromatic images, often do not work well for noisy color images.

In this talk, we present an overview of some of the traditional methods for denoising. We discuss a new strategy, which we call the cross-channel principle, that can be applied for very effective denoising of color images. In particular we show how this principle can be applied to the total variation denoising scheme and an ENO type denoising scheme.


   
Algebraic Geometry Seminar
Topic: Toric vector bundles and the resolution property
Presenter: Sam Payne, Stanford University; Clay Institute
Date:  Tuesday, November 14, 2006, Time: 4:30 p.m., Location: Fine 322
Abstract: Is every coherent sheaf on an algebraic variety the quotient of a locally free sheaf of finite rank? I will discuss an investigation of this question via equivariant vector bundles on toric varieties, and will give examples of complete (singular, nonprojective) toric threefolds with no nontrivial equivariant vector bundles of rank less than or equal to 3. It is not known whether these varieties have any nontrivial vector bundles at all.
   
Mathematical Physics Seminar
Topic: Many Bosons
Presenter: E. Trubowitz, ETH, Zurich
Date:  Tuesday, November 14, 2006, Time: 4:30 p.m., Location: Jadwin 343
   
Operations Research and Financial Engineering Seminar
Topic:

Roughing it up: Disentangling Continuous and Jump Components in Measuring, Modeling and Forecasting Asset Return Volatility

Presenter: Francis X. Diebold, University of Pennsylvania
Date:  Thursday, November 14, 2006, Time: 4:30 p.m., Location: E-219, E-Quad
   
Department Colloquium
Topic: TBA
Presenter: Mircea Mustaţă, University of Michigan; IAS
Date:  Wednesday, November 15, 2006, Time: 4:30 p.m., Location: Fine 314
   
Institute for Advanced Study and Princeton University Number Theory Seminar
Topic: Intersection complex on the Baily-Borel compactification of a Siegel modular variety
Presenter: Sophie Morel, IAS
Date:  Thursday, November 16, 2006, Time: 4:30 p.m., Location: Fine 214
Abstract: In this talk, I will explain how to compute the trace of a power of the Frobenius endomorphism on the intersection cohomology of the Baily-Borel compactification of a Siegel modular variety. The main tools are : - Kottwitz's calculation of the number of points of PEL Shimura varieties over finite fields; - a theorem of Pink about the direct image in the Baily-Borel compactification of a local system on a Shimura variety; - a new construction of the intermediate extension of a pure perverse sheaf as a weight truncation of the full direct image.
   
Topology Seminar
Topic: On triangulations of 3-manifolds
Presenter: William Jaco, IAS and Oklahoma State University
Date:  Thursday, November 16, 2006, Time: 4:30 p.m., Location: Fine 314
Abstract: We shall discuss work (mostly joint with Hyam Rubinstein) on triangulations of 3-manifolds. This includes the construction of minimal-vertex triangulations, including layered and efficient triangulations; and operations on triangulations, including crushing triangulations along normal surfaces and blow-ups of ideal triangulations. We shall also discuss triangulated Heegaard splittings and triangulated Dehn fillings. There are many, many open questions and interesting speculation on connections of these triangulations to the geometry of 3-manifolds.
   
Differential Geometry and Geometric Analysis Seminar
Topic: TBA
Presenter: Young-Heon Kim, University of Toronto
Date:  Friday, November 17, 2006, Time: 3:00 p.m., Location: Fine 314
   
Analysis Seminar
Topic: TBA
Presenter: Alexander Kiselev, University of Wisconsin
Date:  Monday, November 20, 2006, Time: 4:00 p.m., Location: Fine 110
   
PACM Colloquium
Topic: Faithful recovery of vector valued functions from incomplete data. Recolorization and art restoration
Presenter: Massimo Fornasier, PACM, Princeton University
Date:  Monday, November 20, 2006, Time: 4:00 p.m., Location: Fine 214
Abstract:

On March 11, 1944, the famous Eremitani's Church in Padua (Italy) was destroyed in an Allied bombing together with the inestimable frescoes by Andrea Mantegna et al. contained in the Ovetari Chapel. In the last 60 years, several attempts have been made to restore the fresco fragments by traditional methods, but without much success. We have developed a fast, robust, and efficient pattern recognition algorithm in order to map the original position and orientation of the fragments, based on comparisons with an old gray level image of the fresco prior to the damage. This innovative technique allowed for the partial reconstruction of the frescoes. Unfortunately, the surface covered by the fragments is only 77 m^2, while the original area was of several hundreds. This means that we can currently reconstruct only a fraction (less than 8%) of this inestimable artwork. In particular the original color of the blanks is not known. This begs the question of whether it is possible to estimate mathematically the original colors of the frescoes by making use of the potential information given by the available fragments and the gray level of the pictures taken before the damage. Can one estimate how faithful such restoration is?

In this talk we retrace the development of the recovery of the frescoes as an inspiring and challenging real-life problem for the development of new mathematical methods. We introduce two models for the recovery of vector valued functions from incomplete data, with applications to the fresco recolorization problem. The models are based on the minimization of a functional which is formed by the discrepancy with respect to the data and additional regularization constraints. The latter refer to joint sparsity measures with respect to frame expansions for the first functional and functional total variation for the second. We establish the relations between these two models. As a byproduct we develop the basis of a theory of fidelity in color recovery, which is a crucial issue in art restoration.

   
Algebraic Geometry Seminar
Topic: TBA
Presenter: Mircea Mustaţă, University of Michigan; IAS
Date:  Tuesday, November 21, 2006, Time: 4:30 p.m., Location: Fine 322
   
Mathematical Physics Seminar
Topic: Mean-Field and Classical Limit of Many-body Schroedinger Dynamics for Bosons
Presenter: Sandro Graffi, Univ. of Bologna
Date:  Tuesday, November 21, 2006, Time: 4:30 p.m., Location: Jadwin 343
Abstract: A new proof of the convergence of the N-particle Schroedinger dynamics for bosons towards the dynamics generated by the Hartree equation in the mean-field limit. For a restricted class of two-body interactions, we obtain convergence estimates uniform in h- bar, up to an exponentially small remainder. For h-bar = 0, the classical dynamics in the mean-field limit is given by the Vlasov equation. (Joint work with J.Froehlich and S.Schwarz.)
   
Discrete Mathematics Seminar
Topic: TBA
Presenter: Rados Radoicic, CUNY
Date:  Wednesday, November 22, 2006, Time: 2:15 p.m., Location: Fine 224
   
Special Analysis Seminar
Topic: TBA
Presenter: Fabrice Planchon, Paris 13
Date:  Wednesday, November 22, 2006, Time: 3:00 p.m., Location: Jadwin A07
   
PACM Colloquium
Topic: Inverse scattering in nuclear magnetic resonance
Presenter: Charles Epstein, Mathematics, University of Pennsylvania
Date:  Monday, November 27, 2006, Time: 4:00 p.m., Location: Fine 214
Abstract: Selective excitation is an essential ingredient of any application of nuclear magnetic resonance, e.g. MR-imaging or spectroscopy. I will explain how the problem of selective excitation of 2-level quantum systems leads directly to the classical inverse scattering problem for the 2x2 AKNS system. We discuss the analysis of the inverse scattering transform and the role of non-linearity. I then show how a viable numerical algorithm, based on the hard pulse approximation, allows for the practical and accurate solution of this problem.
   
Algebraic Geometry Seminar
Topic: TBA
Presenter: Brent Doran, Oxford University and IAS
Date:  Tuesday, November 28, 2006, Time: 4:30 p.m., Location: Fine 322
   
Topology Seminar *** Please note special date
Topic: On The Homeomorphism Problem: Classification of 3-manifolds
Presenter: William Jaco, IAS
Date:  Tuesday, November 28, 2006, Time: 4:30 p.m., Location: Fine 314
Abstract: While it may not be widely known, the Thurston Geometrization Conjecture gives a theoretical proof of the Homeomorphism Problem and, consequentially, that 3-manifolds can be classified. In the announcement of G. Perelman (and subsequent work by others), the Thurston Geometrization Conjecture has been claimed to be true. We shall give the steps to an algorithm that determines if two given 3-manifolds are homeomorphic (The Homeomorphism Problem). For 3-manifolds this is equivalent to the existence of a classification. Namely, a list of 3-manifolds can be constructed so that each 3-manifold appears on the list precisely once and given a 3-manifold it can be decided where it is placed on the list (Classification of 3-manifolds).
   
Operations Research and Financial Engineering Seminar
Topic: TBA
Presenter: Marcel Rindisbacher, University of Toronto
Date:  Tuesday, November 28, 2006, Time: 4:30 p.m., Location: E-219, E-Quad
   
Discrete Mathematics Seminar
Topic: Global connectivity from local conditions
Presenter: David Galvin, University of Pennsylvania
Date:  Wednesday, November 29, 2006, Time: 2:15 p.m., Location: Fine 224
  See http://www.math.princeton.edu/~bsudakov/galvin2006-fall.pdf
   
Department Colloquium
Topic: TBA
Presenter: Chris Skinner, Princeton University
Date:  Wednesday, November 29, 2006, Time: 4:30 p.m., Location: Fine 314
   
Ergodic Theory and Statistical Mechanics Seminar
Topic: On stochastic properties of billiards and on tagged particle diffusion in the 1d Rayleigh gas
Presenter: Peter Balint, Budapest University of Technology and Economics
Date:  Thursday, November 30, 2006, Time: 2:00 p.m., Location: Fine 401
Abstract: In this talk I would like to consider stochastic phenomena arising in various classical mechanical systems. The first part of the talk is meant to give an overview on some recent progress related to ergodic and statistical properties of hyperbolic billiards (joint works with Sebastien Gouezel, Pavel Bachurin and Imre Peter Toth). The second part describes some new observations on tagged particle diffusion in the 1d Rayleigh gas (joint result with Balint Toth and Imre Peter Toth).
   
Institute for Advanced Study and Princeton University Number Theory Seminar
Topic: TBA
Presenter: Roman Holowinsky, IAS
Date:  Thursday, November 30, 2006, Time: 4:30 p.m., Location: Fine 214
   
Topology Seminar
Topic: TBA
Presenter: Dillan Thurston, Columbia University and Barnard College
Date:  Thursday, November 30, 2006, Time: 4:30 p.m., Location: Fine 314
   
DECEMBER 2006
   
Differential Geometry and Geometric Analysis Seminar
Topic: TBA
Presenter: Mario Bonk, University of Michigan
Date:  Friday, December 1, 2006, Time: 3:00 p.m., Location: Fine 314
   
PACM Colloquium - Distinguished Lecture Series
Topic: Genomic Information: Biology and Medicine in the 21st Century
Presenter: Eric S. Lander, Broad Institute, Massachusetts Institute of Technology
Date:  Friday, December 1, 2006, Time: 8:00 p.m., Location:A02 McDonnell Hall
Abstract: The Human Genome Project was just an early step in a decades-long scientific program aimed at achieving a systematic and comprehensive view of biology and medicine. This program involves deep collaboration among biologists, chemists, physicians, engineers and -- importantly -- mathematicians and computer scientists. The lecture will describe current projects in genomic medicine, including comparative genomics, human genetics, cancer genetics and chemical biology. Along the way, it will highlight analytical issues that arise from the massive amounts of genomic information that are rapidly becoming available.
   
Analysis Seminar
Topic: TBA
Presenter: Natasa Pavlovic, Princeton University
Date:  Monday, December 4, 2006, Time: 4:00 p.m., Location: Fine 110
   
Algebraic Geometry Seminar
Topic: TBA
Presenter: Günter Harder, Max Planck Institut für Mathematik; IAS
Date:  Tuesday, December 5, 2006, Time: 4:30 p.m., Location: Fine 322
   
Operations Research and Financial Engineering Seminar
Topic: TBA
Presenter: Gordan Zitkovic, University of Texas
Date:  Tuesday, December 5, 2006, Time: 4:30 p.m., Location: E-219, E-Quad
   
Discrete Mathematics Seminar
Topic: TBA
Presenter: Tom Bohman, Carnegie Mellon University
Date:  Wednesday, December 6, 2006, Time: 2:15 p.m., Location: Fine 224
   
Geometry, Representation Theory, and Moduli Seminar
Topic: TBA
Presenter: M. Mirzakhani, Princeton University
Date:  Wednesday, December 6, 2006, Time: 3:00 p.m., Location: Fine 214
   
Department Colloquium
Topic: Blow ups of complex solutions of 3D-Navier-Stokes system and Renormalization Group Method.
Presenter: Yakov Sinai, Princeton University
Date:  Wednesday, December 6, 2006, Time: 4:30 p.m., Location: Fine 314
Abstract: In this talk I shall explain the following result of Dong Li and mine:there exists an open set in the space of 10-parameter families of initial conditions such that for each family from this set there are values of parameters such that the corresponding solution develops blow up in finite time.
   
Institute for Advanced Study and Princeton University Number Theory Seminar
Topic: Periods and relative trace formulas for GL(2) in the local setting
Presenter: Brooke Feigon, IAS
Date:  Thursday, December 7, 2006, Time: 4:30 p.m., Location: Fine Hall 214
   
Topology Seminar
Topic: On the contact class in Heegaard Floer homology
Presenter: William H. Kazez, University of Georgia
Date:  Thursday, December 7, 2006, Time: 4:30 p.m., Location: Fine 314
Abstract: In joint work with Ko Honda and Gordana Matic, we present an alternate description of the Ozsv\'ath-Szab\'o contact class in Heegaard Floer homology. Using this description, we prove that if a contact structure $(M,\xi)$ has an adapted open book decomposition whose page $S$ is a once-punctured torus, then the monodromy is right-veering if and only if the contact structure is tight.
   
Differential Geometry and Geometric Analysis Seminar
Topic: TBA
Presenter: Bruce Kleiner, Yale University
Date:  Friday, December 8, 2006, Time: 3:00 p.m., Location: Fine 314
   
Analysis Seminar
Topic: TBA
Presenter: Enno Lenzman, MIT
Date:  Monday, December 11, 2006, Time: 4:00 p.m., Location: Fine 110
   
Algebraic Geometry Seminar
Topic: TBA
Presenter: Brendan Hassett, Rice University
Date:  Tuesday, December 12, 2006, Time: 4:30 p.m., Location: Fine 322
   
Geometry, Representation Theory, and Moduli Seminar
Topic: TBA
Presenter: M. Aganagic, Berkeley
Date:  Wednesday, December 13, 2006, Time: 3:00 p.m., Location: Fine 214
   
Department Colloquium
Topic: Trees, elliptic operators, and K-theory for group C*-algebra
Presenter: Paul Baum, Penn State University
Date:  Wednesday, December 13, 2006, Time: 4:30 p.m., Location: Fine 314
Abstract: Let G be a locally compact Hausdorff second countable topological group. Examples are Lie groups, discrete groups, p-adic groups and adelic groups. The regular representation of G gives rise to a C* algebra known as the reduced C* algebra of G. Twenty five years ago P.Baum and A.Connes conjectured an answer to the problem of calculating the K-theory of this C* algebra. When true, this conjecture has corollaries in various branches of mathematics. Among these corollaries are the Novikov conjecture (topology) and the stable Gromov-Lawson-Rosenberg conjecture (differential geometry). In essence, the conjecture asserts that every element in the K-theory of the reduced C* algebra of G is the index of some G-equivariant elliptic operator, and that the only relations on these indices are the "obvious" index preserving relations. This is made precise by using the universal example for proper actions of G. In low dimensions this universal example is a tree. Due to the work of a number of mathematicians, the conjecture is now known to be true for certain classes of groups (e.g. connected Lie groups, discrete hyperbolic groups, discrete a-t-menable groups, algebraic p-adic groups, algebraic adelic groups). The search for a counter-example (to a somewhat generalized version of the conjecture) has led to some intriguing questions involving the expander graphs of Lubotzky-Sarnak and a random group (which probably exists) of Gromov. The talk is intended for a general mathematical audience. The basic definitions (C* algebra, K-theory etc) will be carefully stated in the talk.
   
Topology Seminar
Topic: TBA
Presenter: Saul Schleimer, Rutgers University
Date:  Thursday, December 14, 2006, Time: 4:30 p.m., Location: Fine 314