SEMINARS
Updated: 3-28-2007
   
MARCH 2007
   
Sato-Tate Seminar
Topic: Deformations with bilinear data
Presenter: Brian Conrad, University of Michigan and Columbia University
Date:  Wednesday, March 28, 2007, Time: 1:30 p.m., Location: Fine 314
   
Geometry, Representation Theory, and Moduli Seminar
Topic: TBA
Presenter: B. Eynard, CEA/Saclay
Date:  Wednesday, March 28, 2007, Time: 3:00 p.m., Location: Fine 214
   
Ergodic Theory and Statistical Mechanics Seminar
Topic: Regularity of solutions to the Navier-Stokes equations evolving from small initial data in a critical space
Presenter: Natasa Pavlovich, Princeton University
Date:  Thursday, March 29, 2007, Time: 2:00 p.m., Location: Fine 401
Abstract: In this talk we will present a joint work with Pierre Germain and Gigliola Staffilani on regularity of solutions to the Navier-Stokes equations evolving from small initial data in a critical space in R^n. More precisely, in 2001 H. Koch and D. Tataru proved the existence of global in time solutions to the incompressible Navier-Stokes equations in R^n corresponding to the initial data small enough in BMO^{-1}. We prove that under certain smallness condition on the initial data in BMO^{-1}, the solutions constructed by Koch and Tataru are more regular. As a consequence, we obtain a decay estimate in time for any space derivative, and space analyticity of the solution. Also as an application of our regularity theorem, we prove a regularity result for self-similar solutions.
   
Priuceton University and Institute for Advanced Study Number Theory Seminar
Topic: Local-global compatibility in p-adic Langlands for GL_2(Q)
Presenter: Matthew Emerton, Northwestern University
Date:  Thursday, March 29, 2007, Time: 4:30 p.m., Location: Fine 322
Abstract: In this talk I will explain some recent results on local-global compatibility for the action of GL_2 of the finite adeles on the p-adically completed cohomology of modular curves, as well as some applications of these results (e.g. to the Fontaine-Mazur conjecture). These results rely for their proof on the existence of a p-adic local Langlands correspondence, recently constructed by Colmez, and I will also spend some time describing Colmez's work.
   
Topology Seminar
Topic: Floer homology and surface decompositions
Presenter: Andras Juhasz, Princeton University
Date:  Thursday, March 29, 2007, Time: 4:30 p.m., Location: Fine 314
Abstract: We define an invariant of balanced sutured manifolds called sutured Floer homology. In this talk we give a formula that shows how this invariant changes under surface decompositions. Using our formula we can simplify the proofs of a result of Ozsvath and Szabo that link Floer homology detects the Thurston norm, and a theorem of Ni that knot Floer homology detects fibred knots. We also show that for a wide class of knots if the top term of knot Floer homology has rank < 4 then the knot complement admits a depth one taut foliation.
   
Columbia University and Princeton University Probability Day
Topic and Presenters:
Program
Date:  Friday, March 30, 2007, Time: 9:30 a.m.- registration, Location: Princeton University, Computer Science Building, Room CS 104
   
Differential Geometry and Geometric Analysis Seminar
Topic: TBA
Presenter: Simon Brendle, Stanford University
Date:  Friday, March 30, 2007, Time: 3:00 p.m., Location: Fine 314
   
APRIL 2007
   
Analysis Seminar *** Please note special time
Topic: Singularities and transport in viscoelastic fluids
Presenter: Becca Thomases, Courant Institute
Date:  Monday, April 2, 2007, Time: 2:30 p.m., Location: Fine 110
Abstract: Viscoelastic flow modeled by the Oldroyd-B equations will be discussed from an analytical and computational perspective. First I will present a local energy decay theorem which applies to a large class of hyperbolic systems including the Oldyoryd-B model. This decay theorem is used to prove that global smooth solutions exist for small initial data. While small solutions are global, the problem for large data is much more complicated. I will present recent computational work on the Oldroyd-B equations which indicates that the system develops singularities exponentially in time at hyperbolic stagnation points in the flow. The singularities arise in the stress field of the flow and the algebraic structure of these singularities depends critically on an important elasticity parameter, the Weissenberg number. A local approximation to the solution at the hyperbolic stagnation point is constructed and there is excellent agreement between the local solution and the simulations. In addition, past a critical Weissenberg number the flow pattern becomes quite sensitive to time periodic perturbations of the background forcing (or changes in initial data) and there is a transition from small scale local mixing around the stable and unstable manifolds to global mixing in the fluid.
   
PACM Colloquium
Topic: Simulation of Black Hole Collisions
Presenter: Frans Pretorius, Physics, University of Alberta
Date:  Monday, April 2, 2007, Time: 4:00 p.m., Location: Fine 214
Abstract: The collision of two black holes is thought to be one of the most energetic events in the universe, emitting in gravitational waves as much as 5-10% of the rest mass energy of the black holes. An international effort is presently underway to detect gravitational waves from black hole collisions and other cataclysmic events in the universe. The early success of the detectors will rely on the matched filtering technique to extract what are, by the time the waves reach earth, very weak distortions in the local geometry of space and time. In the case of binary black hole mergers, obtaining the predicted waveforms for use in the matched filters requires numerical solution of the merger process during the final stages of the collision. In this talk I will describe the computational challenges and techniques required to simulate black holes within the framework of Einstein's theory of general relativity, and present results form recent successful simulations of black hole coalescence.
   
Algebraic Geometry Seminar
Topic: Local systems and multiplier ideals
Presenter: Nero Budur, Notre Dame and IAS
Date:  Tuesday, April 3, 2007, Time: 4:30 p.m., Location: Fine 322
Abstract: One of the most versatile tools that measures the complexity of singularities is the multiplier ideal. Locally, the multiplier ideals are quite well-understood through different interpretations and connections with many local invariants of singularities. In this talk we show how spaces of unitary local systems of rank one provide natural settings for studying global invariants of singularities involving multiplier ideals.
   
Mathematical Physics Seminar
Topic: Laser-Atom Interaction: Ionization and Resonances for a model system
Presenter: Christian Stucchio, Rutgers University
Date:  Tuesday, April 3, 2007, Time: 4:30 p.m., Location: Jadwin 343
Abstract: The behavior of an atom in a radiation field is a topic of fundamental importance in atomic physics. Except for a few limiting regimes (radiation is small, radiation is slowly varying), very little is known rigorously about the the time-dependent behavior of the electron's wavefunction. present a new method for analyzing the problem, based on domain restriction using Dirichlet-to-Neumann boundary conditions. As an application, I show that ionization always occurs (regardless of the frequency, or field strength) in a common physical model. This is a joint work with O. Costin and J. L. Lebowitz.
   
Discrete Mathematics Seminar
Topic: TBA
Presenter: Endre Szemeredi, Rutgers University
Date:  Wednesday, April 4, 2007, Time: 2:15 p.m., Location: Fine 224
   
Department Colloquium
Topic: Langlands Correspondence for Loop Groups
Presenter: Edward Frenkel, UC Berkeley
Date:  Wednesday, April 4, 2007, Time: 4:30 p.m., Location: Fine 314
Abstract: The local Langlands correspondence relates representations of a reductive algebraic group over the p-adic field and representations of the Galois group of this field. If we replace F by the field C((t)) of complex (formal) Laurent power series, then the corresponding group becomes the (formal) loop group. It is natural to ask: is there an analogue of the Langlands correspondence in this case? It turns out that the answer is affirmative, and there is an interesting theory which may be viewed as both "geometrization" and "categorification" of the classical theory. I will explain the general set-up for this new theory and give some examples using representations of affine Kac-Moody algebras. I will also explain the connection to the global geometric Langlands correspondence.
   
Operations Research and Financial Engineering Seminar
Topic: Inverse problems in option pricing and random mixtures of martingales
Presenter: Rama Cont, Columbia University
Date:  Wednesday, April 4, 2007, Time: 4:30 p.m., Location: E-219, E-Quad
Abstract: The inverse problem of recovering an option pricing model (or martingale measure) from a set of given market prices of options, known in finance as the model calibration problem, has been treated in the literature either via inversion formulae applied to continuum data or by applying deterministic optimization methods to a (regularized) least squares formulation of the problem. These methods yield a single set of model parameters calibrated to market data and ignore the non uniqueness of the solution, which reflects {\it model uncertainty}. We propose a probabilistic construction to solve this problem: starting from a prior distribution on models and a set of observed option prices, we construct a random martingale measure, whose expectation yield an arbitrage-free pricing rule consistent with the observed option prices and whose dispersion properties can be used to quantify model uncertainty. We describe a Monte Carlo algorithm for computing prices under this rule and characterize the limit behavior of the algorithm, which is shown to possess a dual interpretation in terms of minimization of ``model uncertainty". This construction, which only involves a well-posed unconstrained minimization of a convex function, can be seen as a dynamic arbitrage-free version of Avellaneda et al.'s Weighted Monte Carlo algorithm applicable to a wide range of pricing models and products. Our approach yields a non-trivial posterior distribution, instead of a single price, for exotic options and allows to simulate from this posterior distribution. As an example, we compute the posterior distribution for a barrier option given a set of European calls and puts, in a stochastic volatility model with jumps.
   
Ergodic Theory and Statistical Mechanics Seminar
Topic: Baby-talk on Sato-Tate problem
Presenter: Nicholas Katz, Princeton University
Date:  Thursday, April 5, 2007, Time: 2:00 p.m., Location: Fine 401
   
Symplectic Geometry Seminar *** Please note special time and location
Topic: Symplectic 6-manifolds via tropical 3-manifolds: An informal introduction to torus fibrations of Calabi-Yau manifolds
Presenter: Ricardo Castano-Bernard, Kansas State University
Date:  Thursday, April 5, 2007, Time: 3:00 p.m., Location: Fine 601
Abstract: Tropical manifolds are manifolds which admit an integral affine structure away from a codimension two singular set. In mirror symmetry, such manifolds are expected to arise as Gromov-Hausdorff limits of degenerating families of Calabi-Yau manifolds. In this talk I will give a simple algorithm that produces symplectic 6-manifolds starting from tropical 3-manifolds.
   
Special Department Colloquium
Topic: Layered lattices
Presenter: Hendrik Lenstra, Mathematisch Instituut, Universiteit Leiden
Date:  Thursday, April 5, 2007, Time: 4:30 p.m., Location: Fine 314
Abstract: Lattice basis reduction algorithms can be used for solving systems of linear equations over the ring of integers. An analysis of this application suggests that it is more appropriately handled by means of a "layered lattice". This is a new notion of lattice, for which the length function takes values in an ordered vector space of dimension greater than one.
   
Operations Research and Financial Engineering Seminar
Topic:

Functional linear regression that's interpretable

Presenter: Gareth James, University of Southern California
Date:  Thursday, April 5, 2007, Time: 4:30 p.m., Location: E-219, E-Quad
Abstract: Regression models to relate a scalar Y to a functional predictor W(t) are becoming increasingly common. Work in this area has concentrated on estimating a coefficient function, beta(t), with Y related to W(t) through the integral of beta(t)W(t). Regions where beta(t) is not equal to 0 correspond to places where there is a relationship between W(t) and Y. Alternatively, points where beta(t) = 0 indicate no relationship. Hence, for interpretation purposes, it is desirable for a regression procedure to be capable of producing estimates of beta(t) that are exactly zero over certain regions and have simple structure, such as a piecewise constant or linear form, over the other regions. Unfortunately, most fitting procedures result in an estimate for beta(t) that is rarely exactly zero and has unnatural wiggles making the curve hard to interpret. In this talk I will introduce a new approach called Functional Linear Regression That's Interpretable. FLiRTI uses variable selection ideas, applied to various derivatives of beta(t), to produce estimates that are both interpretable, flexible and accurate. In addition one can prove non-asymptotic theoretical bounds on the estimation error which provide strong theoretical motivation for our approach. I will demonstrate FLiRTI on simulated and real world data sets. Time permitting, I will also discuss some extensions of FLiRTI.
   
Symplectic Geometry Seminar
Topic: Lagrangian 3-torus fibrations
Presenter: Ricardo Castano-Bernard, Kansas State University
Date:  Friday, April 6, 2007, Time: 2:00 p.m., Location: Fine 214
Abstract: In the paper "Topological Mirror Symmetry," Mark Gross developed a method to construct topological models of mirror pairs of Calabi-Yau manifolds. These models are equipped with SYZ-dual topological 3-torus fibrations. In this talk, we give a generalization of Gross' construction to the symplectic category. We shall explain how to modify topological fibrations to obtain Lagrangian fibrations giving rise to symplectic models of mirror pairs of Calabi-Yau 3-manifolds. These models are naturally associated to the conjectural tropical limits of degenerating families of CY's.
   
Differential Geometry and Geometric Analysis Seminar
Topic: Energy functionals, Kahler-Einstein metrics, and the Moser-Trudinger-Onofri inequality
Presenter: Yanir Rubinstein, MIT
Date:  Friday, April 6, 2007, Time: 3:00 p.m., Location: Fine 314
Abstract: The problem of finding necessary and sufficient conditions for the existence of a Kahler-Einstein metric on a Fano manifold has attracted much attention. Fundamental work done in the '80s related this question to certain energy functionals defined on the infinite-dimensional space of Kahler metrics. In the mid '90s Tian provided a first characterization of Kahler-Einstein manifolds in terms of two such functionals. In this talk we present a generalization of this analytic characterization to a family of energy functionals defined by Chen and Tian. We also show how our arguments provide a new proof of the classical Moser-Trudinger-Onofri inequality on the sphere and how they can be used to formulate an extension of it for higher-dimensional manifolds, extending the work of Ding and Tian.
   
Analysis Seminar
Topic: TBA
Presenter: Jared Wunsch, Northwestern University
Date:  Monday, April 9, 2007, Time: 4:00 p.m., Location: Fine 110
   
PACM Colloquium
Topic: Dispersive shock waves in homogeneous and periodic systems
Presenter: Jason W. Fleischer, Electrical Engineering, Princeton University
Date:  Monday, April 9, 2007, Time: 4:00 p.m., Location: Fine 214
Abstract: Dispersive shock waves (DSW) are a fundamental type of nonlinear wave and appear in many hydrodynamic settings, including fluids, superfluids, plasma, and optics. Their basic existence conditions are a dispersive medium with positive pressure (e.g. repulsive interactions or defocusing nonlinearity) and a high density/intensity region atop a low-level background. In the ensuing dynamics, different components of the initial hump couple to the background and walk off from each other. Unlike ordinary shock waves, which have a well-defined front due to viscosity, DSWs are characterized by an oscillating front. Here, an overview of DSWs is given in both homogeneous and periodic media. In homogeneous media, particular attention is paid to shock wave interactions and the dynamics of mode coupling, in both one and two dimensions. In periodic media, the focus is on modified dynamics due to the underlying Floquet-Bloch mode structure and the momentum-dependent dispersion profile. The results show enhanced energy transport among modes and bands and represent the opposite nonlinear regime from lattice (gap) solitons. In all cases, theory is compared to recent experiments in nonlinear optical systems, Bose-Einstein condensates, and plasma.
   
Priuceton University and Institute for Advanced Study Number Theory Seminar
Topic: Iwasawa theory and non-abelian class field theory
Presenter: K.Fujiwara, Nagoya
Date:  Tuesday, April 10, 2007, Time: 3:00 p.m., Location: Fine 314
Abstract: Since the proof of Iwasawa's main conjecture in the classical case (theorem of Mazur and Wiles), automorphic forms on GL(2) have played an essential role to understand Iwasawa theory for GL(1). In this lecture, Leopoldt 's conjecture for totally real fields will be discussed from this perspective.
   
Algebraic Geometry Seminar
Topic: TBA
Presenter: Jacob Lurie, Harvard and AIM
Date:  Tuesday, April 10, 2007, Time: 4:30 p.m., Location: Fine 322
   
Operations Research and Financial Engineering Seminar
Topic: Reliable methods for rare event estimation
Presenter: Paul Dupuis, Brown University
Date:  Tuesday, April 10, 2007, Time: 4:30 p.m., Location: E-219, E-Quad
Abstract: Monte Carlo estimation of small probabilities and expected values determined by rare events can be tricky. The two most commonly applied methods are those based on change-of-measure arguments and known as importance sampling, and those which use branching processes and are referred to as multi-level splitting. There are a number of heuristic guides to the design of schemes, and certainly successful applications have been reported. However, it is also known that these guides can suggest schemes that perform badly. In this talk we first review both approaches and the sources of poor performance. When the probability of interest can be approximated via large deviations, there is a naturally related nonlinear partial differential equation (known as a Hamilton-Jacobi-Bellman equation). Schemes for both types of approximation can be associated with what are called importance functions. We will show that these schemes are stable in an appropriate sense if and only if the importance function is a subsolution to this equation, and also characterize the performance of the scheme in terms of the value of the function at a certain point.
   
Discrete Mathematics Seminar
Topic: TBA
Presenter: David Gamarnik, MIT
Date:  Wednesday, April 11, 2007, Time: 2:15 p.m., Location: Fine 224
   
Geometry, Representation Theory, and Moduli Seminar
Topic: TBA
Presenter: Samuel Grushevsky, Princeton University
Date:  Wednesday, April 11, 2007, Time: 3:00 p.m., Location: Fine 214
   
Department Colloquium
Topic: Spectral gap and effective equidistribution
Presenter: Manfred Einsiedler, Ohio State University
Date:  Wednesday, April 11, 2007, Time: 4:30 p.m., Location: Fine 314
Abstract: The dynamics on homogeneous spaces has many interesting connections to number theory. One of the main problems here is to understand the distribution of closed orbits for subgroups H of the ambient Lie group G. In an ongoing joint work with G.Margulis and A.Venkatesh we prove an error rate in the equidistribution for semisimple subgroups H acting on congruence quotients of G. This makes use of spectral gap in the form of property (tau). However, the proof of our theorem can also be used to prove all cases of property (tau) except for groups of type A_1. We will discuss the relationship between spectral gap, effective decay of matrix coefficients, lattice counting, and effective equidistribution, as well as the main ideas of our argument.
   
Ergodic Theory and Statistical Mechanics Seminar
Topic: Quantum random walks on integer lattices
Presenter: Robin Pemantle, Univ. of Penn.
Date:  Thursday, April 12, 2007, Time: 2:00 p.m., Location: Fine 401
Abstract: Motivated by quantum information theory, a number of nearest neighbor quantum particle models have been introduced, mostly in the last five years, under the name quantum random walk (QRW). Many of these results may be unified and extended by working directly with a space-time generating function. Obtaining the generating function is in fact quite simple. Transferring this back to limiting behavior of QRW is a matter of harnessing some recent technology concerning asymptotics of multivariate generating functions. This is joint work with M. Wilson, Y. Baryshnikov and others.
   
Princeton University and Institute for Advanced Study Number Theory Seminar
Topic: A construction of Kahane Polynomials
Presenter: E.Bombieri, IAS
Date:  Thursday, April 12, 2007, Time: 4:30 p.m., Location: IAS SH-101
Abstract: In 1957 Erdos asked what is the smallest maximum modulus of a trigonometric polynomial of degree n all whose coefficients have modulus 1. He thought that there should be a c>0 such that this max modulus is larger than (1+c)sqrt(n).In 1966 Littlewood conjectured the opposite and 1980 Kahane proved this in a strong form. He gave a probablistic construction of such polynomials with essentially constant modulus sqrt(n).In this talk we will give a new explicit construction of such polynomials with an improved remainder for the fluctuation about sqrt(n).This is joint work with Jean Bourgain.
   
Symplectic Geometry Seminar
Topic: Moduli spaces of folded holomorphic maps
Presenter: Jens von Bergmann, University of Notre Dame
Date:  Friday, April 13, 2007, Time: 2:00 p.m., Location: Fine 214
Abstract: The theory of folded holomorphic maps is a program to extend the tools of $J$--holomorphic curves to all oriented 4--manifolds by utilizing folded symplectic structures. A folded symplectic structure on a manifold is a closed 2-form that is non-degenerate away from a real codimension 1 hypersurface ("fold"), on which its kernel gives a 1-dimensional foliation. Every oriented 4--manifold admits such a structure. Folded holomorphic maps are pairs of $J$--holomorphic maps from two halfs of a Riemann surfaces. The halfs are separated by a codimension 1 submanifold, which has image on the fold and is satisfying an appropriate boundary condition. This boundary condition constitutes the heart of the theory and can be visualized by "tunneling" in the fold, allowing maps to exit at a location that is different from where they enter the fold. We prove that under the simplifying assumption that the fold is "circle-invariant" this leads to a Fredholm problem. Such folds occur frequently. Under suitable genericity assumptions, moduli spaces of folded holomorphic maps have the expected dimension. In the case of pseudoconvex folds we show that they possess a natural compactification with boundary stratum of codimension at least 2. We will explain the theory and the mentioned results and give examples of moduli spaces of folded holomorphic maps, including moduli spaces of maps into the the 4-sphere.
   
Differential Geometry and Geometric Analysis Seminar
Topic: TBA
Presenter: Xiuxiong Chen, University of Winsconsin
Date:  Friday, April 13, 2007, Time: 3:00 p.m., Location: Fine 314
   
Analysis Seminar
Topic: Soliton collision for the nonintegrable gKdV equations
Presenter: Yvan Martel, Versailles
Date:  Monday, April 16, 2007, Time: 4:00 p.m., Location: Fine 110
Abstract: See http://www.math.princeton.edu/~seminar/2006-07-sem/MartelAbstract4-16-2007.pdf
   
PACM Colloquium
Topic: TBA
Presenter: Daniel Rockmore, Mathematics, Dartmouth College
Date:  Monday, April 16, 2007, Time: 4:00 p.m., Location: Fine 214
   
Algebraic Geometry Seminar
Topic: TBA
Presenter: Junecue Suh, Princeton University
Date:  Tuesday, April 17, 2007, Time: 4:30 p.m., Location: Fine 322
   
Geometry, Representation Theory, and Moduli Seminar
Topic: TBA
Presenter: J. Wise, Brown University
Date:  Wednesday, April 18, 2007, Time: 3:00 p.m., Location: Fine 214
   
Department Colloquium
Topic: Billiards and dynamics over moduli space
Presenter: Curtis T McMullen, Harvard University
Date:  Wednesday, April 18, 2007, Time: 4:30 p.m., Location: Fine 314
   
Symplectic Geometry Seminar
Topic: TBA
Presenter: Jean-Michel Bismut, U Paris-Sud and NYU
Date:  Friday, April 20, 2007, Time: 2:00 p.m., Location: Fine 214
   
PACM Colloquium
Topic: Heterogeneous Lipid Bilayers: Evolving Microstructures in Biology
Presenter: Mikko Haataja, MAE, Princeton University
Date:  Monday, April 23, 2007, Time: 4:00 p.m., Location: Fine 214
Abstract:

The design and processing of materials with novel physical and mechanical properties requires a fundamental understanding of the connections between processing, microstructure, and properties. For example, mechanical properties in pure metals and alloys can be varied by manipulating the polycrystalline grain size or the size of the compositional domains through heat treatment, while elastic strain provides a way to tune the optical properties of self-assembled quantum dots during growth. In an analogous manner, the biological function of cell membranes is strongly affected by the details of the local "microstructure".

Typically, microstructural evolution takes place across multiple length and time scales, ranging from atomistic to mesoscopic ones. In this talk I will describe our recent efforts in developing physically-based, coarse-grained continuum models, which bridge the atomistic and mesoscopic scales, to elucidate lateral organization and non-equilibrium dynamics of heterogeneous lipid bilayers. In particular, I will focus on spatially organized, dynamic heterogeneities in the local lipid composition ("lipid rafts") which have been implicated in many important cellular processes including signal transduction, membrane trafficking, cytoskeleton organization, and pathogen entry.

   
Algebraic Geometry Seminar
Topic: TBA
Presenter: David Harbater, University of Pennsylvania
Date:  Tuesday, April 24, 2007, Time: 4:30 p.m., Location: Fine 322
   
Operations Research and Financial Engineering Seminar
Topic: TBA
Presenter: Andreas Hamel, Princeton University
Date:  Tuesday, April 24, 2007, Time: 4:30 p.m., Location: E-219, E-Quad
   
Discrete Mathematics Seminar
Topic: TBA
Presenter: Assaf Naor, NYU
Date:  Wednesday, April 25, 2007, Time: 2:15 p.m., Location: Fine 224
   
Department Colloquium
Topic: TBA
Presenter: Jacob Rasmussen, Princeton University
Date:  Wednesday, April 25, 2007, Time: 4:30 p.m., Location: Fine 314
   
Symplectic Geometry Seminar
Topic: Vanishing of the fundamental class of displaceable Lagrangian submanifolds
Presenter: Peter Albers, NYU
Date:  Friday, April 27, 2007, Time: 2:00 p.m., Location: Fine 214
Abstract: In this talk I will sketch a proof of the following theorem. The fundamental class of a displaceable monotone Lagrangian submanifold vanishes. This proof uses an geometric argument and Hamiltonian Floer homology. Afterwards I will put this into a more conceptual context involving Lagrangian and Hamiltonian Floer homology and their interplay. This yields another (slightly more general proof of the aforementioned theorem and some further corollaries concerned with topological properties of Lagrangian submanifolds.
   
Differential Geometry and Geometric Analysis Seminar
Topic: TBA
Presenter: Meijun Zhu, University of Oklahoma
Date:  Friday, April 27, 2007, Time: 3:00 p.m., Location: Fine 314
   
MAY 2007
   
Algebraic Geometry Seminar
Topic: TBA
Presenter: Charles Cadman, University of Michigan
Date:  Tuesday, May 1, 2007, Time: 4:30 p.m., Location: Fine 322
   
Operations Research and Financial Engineering Seminar
Topic: TBA
Presenter: Rong Chen, University of Illinois at Chicago
Date:  Tuesday, May 1, 2007, Time: 4:30 p.m., Location: E-219, E-Quad
   
Department Colloquium
Topic: TBA
Presenter: Tamar Ziegler, University of Michigan
Date:  Wednesday, May 2, 2007, Time: 4:30 p.m., Location: Fine 314
   
Ergodic Theory and Statistical Mechanics Seminar
Topic: Bulk Universality and Related Properties of Hermitian Matrix Models
Presenter: L.Pastur, Institute for Low Temperatures, Kharkiv, Ukraine
Date:  Thursday, May 3, 2007, Time: 2:00 p.m., Location: Fine 401
Abstract: We give a new proof of universality properties in the bulk of spectrum of the hermitian matrix models, assuming that the potential that determines the model is globally $C^{2}$ and locally $C^{3}$ function. The proof is based on the orthogonal polynomial techniques but does not use asymptotics of orthogonal polynomials. Rather, we obtain the $sin$-kernel as a unique solution of a certain non-linear integro-differential equation that follows from the determinant formulas for the correlation functions. We also present a simplified and strengthened version of the proof of existence and properties of the limiting Normalized Counting Measure of eigenvalues.
   
Operations Research and Financial Engineering Seminar
Topic: TBA
Presenter: Frank Heyde, MLU Halle-Wittenberg
Date:  Tuesday, May 8, 2007, Time: 4:30 p.m., Location: E-219, E-Quad
   
Symplectic Geometry Seminar
Topic: TBA
Presenter: Robert Lipshitz, Columbia University
Date:  Friday, May 11, 2007, Time: 2:00 p.m., Location: Fine 214