seminar

Current Seminars
updated 2/2/2005


FEBRUARY 2 - FEBRUARY 4, 2005

*Discrete Mathematics* Seminar
Topic:	On the extremal hypergraph problem of Brown, Erdős and Sós
Presenter:	Asaf Shapira, Tel Aviv University
Date:	Wednesday, February 2, 2005, Time: 2:15 p.m., Location: Fine Hall 224
Abstract:	Click here

Topology Seminar
Topic:	Exotic smooth structures on rational surfaces
Presenter:	Andras Stipsicz, IAS and Renyi Institute of Mathematics
Date:	Thursday, February 3, 2005, Time: 4:30 p.m., Location: Fine Hall 314
Abstract:	Most known smoothable simply-connected 4--manifolds admit infinitely many different smooth structures (distinguished, for example, by their Seiberg--Witten invariants). There are some 4--manifolds, though, for which the existence of such 'exotic' structures is still open, the most notable examples being the 4--dimensional sphere S^4 and the complex projective plane CP^2. In a recent project with Z. Szabo and J. Park we found constructions of exotic smooth structures on the five- and six-fold blow--up of CP^2. In the lecture we describe the construction of these 4--manifolds and indicate the necessary input from Seiberg--Witten theory for proving their exoticness.

SPECIAL Number Theory Seminar *** See special date, time, and location
Topic:	Main Conjectures and Modular Forms
Presenter:	Christopher Skinner, University of Michigan
Date:	Friday, February 4, 2005, Time: 2:00 p.m., Location: Fine Hall 214
Abstract:	The study of L-functions (such as the Riemann zeta-function) has long been a central focus of numbey theory, especially analytic number theory. But over the last half-century it has become increasingly clear that values of these function at special points (special values) reflect arithmetic information. The most celebrated examples of this are the Class Number Formula for zeta functions for number fields and the Birch-Swinnerton-Dyer Conjecture (BSD) for elliptic curves. The latter predicts that the order of vanishing at s=1 of the L-function L(E,s) of an elliptic curve E over a number field K is equal to the rank r(E) of the group of K-rational points on E. A refined version of this conjecture also expresses the leading coefficient of the Taylor series of L(E,s) around s=1 in terms of arithmetic data coming from E. This talk will be about work related to proving parts of the refined BSD, at least when L(E,1) is non-zero. These results for L(E,1) are obtained through Iwasawa theory. More precisely, I will report on work relating the p-adic L-function of an elliptic curve (or even a holomorphic eigenform for GL(2)) that is ordinary at a prime p to the characteristic ideal of the associated p-adic Selmer group. The Main Conjecture for elliptic curves (or modular forms) asserts that the latter is generated by the former. K. Kato has shown that the characteristic ideal contains the p-adic L-function in many cases. I will discuss joint work with E. Urban that uses the arithmetic of automorphic forms on unitary groups, esp. U(2,2), to show the opposite inclusion.

Geometric Analysis Seminar
Topic:	Existence and uniqueness for p-minimizers in the Heisenberg group
Presenter:	Jih-Hsin Cheng, Academica Sinica, Taipei
Date:	Friday, February 4, 2005, Time: 3:00 p.m., Location: Fine Hall 314
Abstract:	We consider the p-minimal graph equation in the Heisenberg group. This is a degenerate elliptic and hyperbolic PDE in dimension 2 and a subelliptic equation in the nonsingular domain for higher dimensions. Moreover, it is the Euler-Lagrange equation associated to a degenerate energy functional. In this talk, we will prove the existence of a Lipschitz continuous minimizer for such an energy functional with a given boundary value. We will also show the uniqueness of minimizers. Besides, we will give an example to show the impossibility of getting better regularity for a C^1 minimizer having a smooth boundary value in dimension 2.

FEBRUARY 7 - FEBRUARY 11, 2005

* RESCHEDULED * Mathematical Physics Seminar *** Please note special day and location
Topic:	Localization effects of random surface potentials
Presenter:	Gunter Stolz, University of Alabama at Birmingham
Date:	Tuesday, February 8, 2005, Time: 2:00 p.m., Location: Jadwin 343

Princeton University/Institute for Advanced Study Complex Geometry Seminar
Topic:	A Hodge theoretic approach to the decomposition theorem
Presenter:	Luca Migliori, University of Bologna
Date:	Tuesday, February 8, 2005, Time: 2:30 p.m., Location: IAS Simonyi 101
Abstract:	Let $f:X \to Y$ be a projective map, and assume for simplicity $X$ to be smooth. The Decomposition Theorem of Beilinson, Bernstein, Deligne and Gabber states that the (derived) direct image of the constant sheaf ${\bf Q}_X$ is isomorphic to a direct sum of shifted intersection cohomology complexes of local systems. In the talk I will describe a recent proof of the theorem for complex varieties, developed by M.A. de Cataldo and myself (preprint math.AG 0306030 version2), based on classical Hodge Theory. In this approach a major role is played by a series of ``intersection forms along the strata'' which are naturally associated to $f$, and the Decomposition Theorem is shown to be equivalent with their non-degeneracy. We show that these forms are in fact definite, a generalization of Grauert criterion for contractibility of curves on a surface. This result is achieved by studying the nilpotent endomorphism on the rational cohomology of $X$ given by the cup product with the pullback of an ample line bundle on $Y$, and relating its Jordan canonical form to the topology of the map. In the talk I will illustrate how this approach works on some lower dimensional geometric examples, especially contractions, where this sort of ``Decomposition Theorem with signs'' seems to carry interesting geometric information.

PACM Colloquium * Note special day and location *
Topic:	Selection pressures on proteins at the genomic scale: Applications to microbial evolution
Presenter:	Joshua Plotkin, Harvard University
Date:	Tuesday, February 8, 2005, Time: 4:00 p.m., Location: Carl Icahn Lab 101

*Algebraic Geometry Seminar*
Topic:	Non--quasi--projective moduli spaces
Presenter:	János Kollár, Princeton University
Date:	Tuesday, February 8, 2005, Time: 4:30 p.m., Location: Fine Hall 322
Abstract:	We show that every smooth toric variety can be realized as a moduli space for smooth, projective, polarized varieties. Some of these are not quasi--projective. This contradicts a recent paper (Quasi--projectivity of moduli spaces of polarized varieties, Ann. of Math. 159 (2004) 597--639.)

*Operations Research and Financial Engineering Seminar*
Topic:	Models: Theory and Practice
Presenter:	Emanuel Derman, Columbia University
Date:	Tuesday, February 8, 2005, Time: 4:30 p.m., Location: Room E-219, Engineering Quad
Abstract:	Although the language of financial theory closely resembles the language of mathematics and physics, there are actually very few reliable and accurate principles on which to base the practice of quantitative finance. This talk compares modeling styles in physics and finance, and discusses the appropriate way to work with models in financial markets.

*Discrete Mathematics* Seminar
Topic:	Intersection patterns of geometric objects
Presenter:	Rados Radoicic, Rutgers University
Date:	Wednesday, February 9, 2005, Time: 2:15 p.m., Location: Fine Hall 224
Abstract:	Click here

*Department Colloquium*
Topic:	Causal geometry of space-times with bounded curvature flux
Presenter:	Sergiu Klainerman, Princeton University
Date:	Wednesday, February 9, 2005, Time: 4:30 p.m., Location: Fine Hall 314
Abstract:	I will describe my recent result with I. Rodnianski concerning the absence of singularities for solutions to the Einstein field equations with bounded curvature flux. This is a natural $L²$ bound on components of the curvature tensor on null and space-like hypersurfaces. I will compare the result with other removal of singularity results in Riemannian geometry and nonlinear PDE's such as Euler and Navier-Stokes equations.

*Ergodic Theory and Statistical Mechanics Seminar*
Topic:	Mixing properties of a stochastic flow describing inertial particles
Presenter:	Leonid Piterbarg , University of Southern California
Date:	Thursday, February 10, 2005, Time: 2:00 p.m., Location: Fine Hall 322
Abstract:	Click here

*Joint Analysis Seminar*
Topic:	Paraproducts on polydiscs
Presenter:	Camil Muscalu, Cornell University
Date:	Thursday, February 10, 2005, Time: 4:00 p.m., Location: Fine Hall 214
Abstract:	We will describe a result which extends the classical Coifman-Meyer theorem to the multi-parameter setting of polydiscs. This is based on work recently completed jointly with Jill Pipher, Terry Tao and Christoph Thiele.

Topology Seminar
Topic:	Transcendental submanifolds of RP^n
Presenter:	Selman Akbulut, Michigan State University and the Institute for Advanced Study
Date:	Thursday, February 10, 2005, Time: 4:30 p.m., Location: Fine Hall 314
Abstract:	Algebraic numbers are dense in R. The problem of whether smooth submanifolds of of R^n can be approximated by algebraic subsets could be viewed as a higher dimensional version of this property. In this talk we will discuss positive results and then construct submanifolds of RP^n which can not be isotopic to real parts of nonsingular complex subvarieties of CP^n (joint work with H.King)

*Geometric Analysis Seminar*
Topic:	Fefferman-Graham's ambient metric construction beyond the obstruction
Presenter:	Kengo Hirachi, University of Tokyo and Princeton University
Date:	Friday, February 11, 2005, Time: 3:00 p.m., Location: Fine Hall 314
Abstract:	In 1985, Fefferman and Graham introduced a method of constructing conformal invariants of n-dimensional manifolds by using a Ricci-flat, Lorentzian manifold of dimension n+2, which is now called the ambient space. This construction works perfectly well when n is odd, but it is obstructed at a finite jet when n is even. In this talk, I will describe a way to get over this obstruction by considering a Ricci-flat metric with singularity. In particular, I will formulate a jet isomorphism theorem in even-dimensional conformal geometry. (This is an interim report on a joint work with Robin Graham.)

FEBRUARY 14 - FEBRUARY 18, 2005

*PACM Colloquium*
Topic:	On Fair and Balanced Presentations of Election Data
Presenter:	Robert Vanderbei, Operations Research and Financial Engineering, Princeton University
Date:	Monday, February 14, 2005, Time: 4:00 p.m., Location: Fine Hall 214
Abstract:	The media has made much of the red-blue divide in America. As is well known, the sparsely populated states are mostly republican whereas the densely populated urban areas are mostly democratic. This creates interesting challenges in data representation which will be discussed.

Group Actions and Automorphic Forms Seminar * NEW *
Topic:	TBA
Presenter:	Emmanuel Breuillard, IHES
Date:	Tuesday, February 15, 2005, Time: 11:30 a.m., Location: Fine Hall PL

*Operations Research and Financial Engineering Seminar*
Topic:	TBA
Presenter:	Steve Kou, Columbia University
Date:	Tuesday, February 15, 2005, Time: 4:30 p.m., Location: Room E-219, Engineering Quad

*Discrete Mathematics* Seminar
Topic:	TBA
Presenter:	Peter Keevash, Caltech
Date:	Wednesday, February 16, 2005, Time: 2:15 p.m., Location: Fine Hall 224

*Department Colloquium*
Topic:	Anderson localization: the state of the problem and applications
Presenter:	Michael Goldstein, University of Toronto
Date:	Wednesday, February 16, 2005, Time: 4:30 p.m., Location: Fine Hall 314
Abstract:	Eigen-functions and spectrum of Schrödinger equation with potentials exhibiting random behavior were studied extensively in the last forty years starting from the famous works of Anderson and Harper. Properties of this type of equations are fundamental in understanding phase transitions in quantum mechanical disordered systems of solid state physics. Besides their relevance to physics these equations suggest a rich mathematical program. The central part of this program consists of the study of the structure of the so-called set of resonances and intersections of the different shifts of this set under the translations in the space of potentials. The most important questions regarding the properties of the eigen-functions, in particular their exponential decay, known as Anderson localization, are closely related to this set. The answers to these questions are expected to depend on the dimension of the problem and also on the stochastic properties of the translations in the space of potentials (regular stationary processes, hyperbolic dynamical systems and just i.i.d. random values like in the Anderson model or quasi-periodic dynamics like in Harper’s model). These questions were studied first in perturbative regimes with use of ideas of KAM theory. In the last five years new methods of the analysis of resonances for quasi-periodic and skew-shifted dynamics were developed in the works of Bourgain, Goldstein and Schlag. In this talk we will describe the status of the main problems in this field, some recent results and prospective applications.

*Ergodic Theory and Statistical Mechanics Seminar*
Topic:	Anderson localization and distribution of zeroes of trigonometric polynomials
Presenter:	Michael Goldstein, University of Toronto
Date:	Thursday, February 17, 2005, Time: 2:00 p.m., Location: Fine Hall 322
Abstract:	Click here

Topology Seminar
Topic:	Crossing changes, Dehn surgery and knot invariants
Presenter:	Efstratia Kalfagianni, Michigan State University and the Institute for Advanced Study
Date:	Thursday, February 17, 2005, Time: 4:30 p.m., Location: Fine Hall 314
Abstract:	We will discuss the applicability of Dehn surgery techniques in the study of certain simultaneous unknotting operations that appear in the theory of finite type knot invariants.

FEBRUARY 21 - FEBRUARY 25, 2005

*PACM Colloquium*
Topic:	Discrete Denoising
Presenter:	Sergio Verdu, Applied Mathematics and Electrical Engineering, Princeton University
Date:	Monday, February 21, 2005, Time: 4:00 p.m., Location: Fine Hall 214
Abstract:	Finite-alphabet signals corrupted by discrete noisy channels arise naturally in a wide range of applications spanning fields such as statistics, engineering, and computer science. Examples include DNA sequence analysis and processing, text correction, Hidden Markov model state estimation, and image denoising. While the field of filtering or denoising of continuous-alphabet signals has a long history, the field of discrete denoising has seen far less progress. In many discrete denoising applications, a good model for the randomness of the noisy channel is known, whereas the statistical description of the noiseless signal is either unknown or too complex. It is therefore of considerable interest to pose the problem of discrete universal denoising where no knowledge exists about the statistics of the noiseless signal while the channel statistics are assumed known. I will present the DUDE algorithm for discrete universal denoising which has linear complexity and attains universal optimality in a stochastic sense as well as a stronger semi-stochastic sense. I will also show several DUDE-based algorithms for channel decoding of systematically encoded redundant data. Joint work with E. Ordentlich, G. Seroussi, M. Weinberger and T. Weissman.

Princeton University/Institute for Advanced Study Complex Geometry Seminar
Topic:	Volume minimization and comparison for isotropic surfaces
Presenter:	Ed Goldstein, Institute for Advanced Study
Date:	Tuesday, February 22, 2005, Time: 2:30 p.m., Location: Fine Hall 110
Abstract:	We'll start by exhibiting volume-minimizing properties for certain isotropic submanifolds in complex projective spaces via integral geometry. This will lead us to a problem of finding the infimum of areas for isotropic surfaces with a given boundary in a Kahler manifold.

*Algebraic Geometry Seminar*
Topic:	The Geometry of Grassmannians and Flag Manifolds
Presenter:	I. Coskun, MIT
Date:	Tuesday, February 22, 2005, Time: 4:30 p.m., Location: Fine Hall 322
Abstract:	The Grassmannian $G(k,n)$ parametrizes $k$-dimensional subspaces of an $n$-dimensional vector space. It is a central object in geometry, representation theory and the theory of symmetric functions. Consequently, it is important to understand its cohomology ring very explicitly. The classes of Schubert varieties generate the cohomology ring of the Grassmannian. In this talk I will describe a new geometric Littlewood-Richardson rule for computing products of Schubert cycles in terms of combinatorial objects called Mondrian tableaux. The algorithm gives a fast way of answering corresponding problems in related fields. I will then explain generalizations to Flag manifolds.

*Operations Research and Financial Engineering Seminar*
Topic:	TBA
Presenter:	Raymond Carroll, Texas A&M University
Date:	Tuesday, February 22, 2005, Time: 4:30 p.m., Location: Room E-219, Engineering Quad

*Discrete Mathematics* Seminar
Topic:	Tournaments, voting paradoxes and non-transitive dice
Presenter:	Noga Alon, Tel Aviv University and IAS
Date:	Wednesday, February 23, 2005, Time: 2:15 p.m., Location: Fine Hall 224
Abstract:	Click here

*Department Colloquium*
Topic:	TBA
Presenter:	Markus Rost, Institute for Advanced Study and the University of Bielefeld
Date:	Wednesday, February 23, 2005, Time: 4:30 p.m., Location: Fine Hall 314

Geometric Analysis Seminar *** Please note special day, time, and location
Topic:	Existence of Infinitely many equilibrium configurations of the liquid crystal system for non-constant boundary data
Presenter:	Min-Chun Hong, University of Queensland
Date:	Thursday, February 24, 2005, Time: 2:00 p.m., Location: Fine Hall 322

*Joint Analysis Seminar*
Topic:	Localization in the higher dimensional Anderson-Bernoulli model
Presenter:	Jean Bourgain, IAS
Date:	Thursday, February 24, 2005, Time: 4:00 p.m., Location: Fine Hall 214

FEBRUARY 28 - MARCH 4, 2005

*PACM Colloquium*
Topic:	Invariant-Based Face Recognition
Presenter:	Nigel Boston, University of Wisconsin
Date:	Monday, February 28, 2005, Time: 4:00 p.m., Location: Fine Hall 214
Abstract:	After a brief review of recent striking applications of algebra to engineering and computer science, the currently significant problem of face recognition is addressed. We introduce a new approach to obtaining invariants of Lie groups adapted to this problem and describe its success in implementations.

Group Actions and Automorphic Forms Seminar * NEW *
Topic:	TBA
Presenter:	Tsachik Gelander, Yale University
Date:	Tuesday, March 1, 2005, Time: 11:30 a.m., Location: Fine Hall PL

*Algebraic Geometry Seminar*
Topic:	D-modules and singularities
Presenter:	Nero Budur, Johns Hopkins University
Date:	Tuesday, March 1, 2005, Time: 4:30 p.m., Location: Fine Hall 322
Abstract:	We will present new relations and generalize old ones between different points of view on singularities: D-modules, resolutions of singularities, Hodge structures on Milnor fibers, Bernstein-Sato polynomials (joint work with Mircea Mustata, Morihiko Saito).

*Operations Research and Financial Engineering Seminar*
Topic:	Bounding the Greeks
Presenter:	Mete Soner, Koc University, Turkey
Date:	Tuesday, March 1, 2005, Time: 4:30 p.m., Location: Room E-219, Engineering Quad
Abstract:	The classical Black-Scholes price of an option depends on many factors such as the current price of the underlying, volatility, time to maturity. The sensitivity parameters, called the Greeks, are simply the partial derivatives of the price with respect to these factors. From a practical point of view, it is desirable to bound the sensitivity parameters. Mathematically, the problem is to obtain minimal prices with sensitivity parameters satisfying given a priori bounds. This is achieved by increasing the price in a controlled manner and one approach is to consider the minimal super-replication cost. In this talk, I will outline the super-replication problem with several constraints and their solutions. In the classical Black-Scholes model, these solutions are described through a simple stopping time problem. This is joint work with Nizar Touzi of Paris and Patrick Cheridito of Princeton.

*Department Colloquium*
Topic:	TBA
Presenter:	Tadeusz Iwaniec, Syracuse University
Date:	Wednesday, March 2, 2005, Time: 4:30 p.m., Location: Fine Hall 314

*Joint Analysis Seminar*
Topic:	TBA
Presenter:	Alexandru Ionescu, University of Wisconsin - Madison
Date:	Thursday, March 3, 2005, Time: 4:00 p.m., Location: Fine Hall 214

Topology Seminar
Topic:	TBA
Presenter:	Matthew Hedden, Columbia University
Date:	Thursday, March 3, 2005, Time: 4:30 p.m., Location: Fine Hall 314

*Geometric Analysis Seminar*
Topic:	Calibrated Manifolds and Gauge theory
Presenter:	Selman Akbulut, Michigan State University and the Institute for Advanced Study
Date:	Friday, March 4, 2005, Time: 3:00 p.m., Location: Fine Hall 314
Abstract:	Calibrated geometries (introduced by Harvey and Lawson) give Interesting class of 3 and 4 dimensional submanifolds of 7 and 8 manifolds with exceptional holonomies G_2 and Spin(7). They are called associative and Cayley submanifolds. We will relate the deformation theory of these submanifolds to their gauge theories (recent joint work with Sema Salur), e.g. Seiberg-Witten equations appear as deformation equations of certain calibrated submanifolds. We will discuss how to associate invariants to G_2 manifolds from Seiberg-Witten for families.

MARCH 7 - MARCH 11, 2005

*PACM Colloquium*
Topic:	TBA
Presenter:	Weinan E, Applied Mathematics and Mathematics, Princeton University
Date:	Monday, March 7, 2005, Time: 4:00 p.m., Location: Fine Hall 214

*Operations Research and Financial Engineering Seminar*
Topic:	The Optimal Stopping of a Markov Chain, the Generalized Gittins Index, and Recursive Solution of Poisson and Bellman Equations
Presenter:	Isaac Sonin, University of North Carolina at Charlotte
Date:	Tuesday, March 8, 2005, Time: 4:30 p.m., Location: Room E-219, Engineering Quad

*Discrete Mathematics* Seminar
Topic:	TBA
Presenter:	Oleg Pikhurko, Carnegie Mellon University
Date:	Wednesday, March 9, 2005, Time: 2:15 p.m., Location: Fine Hall 224

MARCH 14 - MARCH 18, 2005

Group Actions and Automorphic Forms Seminar * NEW *
Topic:	TBA
Presenter:	Thomas Ward, University of East Anglia (UK)
Date:	Tuesday, March 15, 2005, Time: 11:30 a.m., Location: Fine Hall PL

MARCH 21 - MARCH 25, 2005

*PACM Colloquium*
Topic:	Finite frames and quantum detection
Presenter:	John Benedetto, University of Maryland
Date:	Monday, March 21, 2005, Time: 4:00 p.m., Location: Fine Hall 214
Abstract:	We discuss quantum measurement in terms of positive operator-valued measures (POMs). For any tight frame with frame constant 1 for a separable Hilbert space there is an associated POM. Our setup is d-dimensional Hilbert space H and frames for H consisting of N elements. H represents a physical system, and it is known that the state x of the system is in E, a set of N given possible states. The problem is to perform a measurement in order to determine x. This is equivalent to constructing a POM on the subsets of E with a natural probabilistic property. Because of the relationship with frames, the problem reduces to constructing a tight frame with frame constant 1 which minimizes a probability of detection functional defined in terms of E. A compactness argument shows the existence of a solution. We solve the problem using techniques from Lagrangian mechanics and properties of SO(N) with the goal of constructing solutions numerically from the resulting equations. Geometrically uniform and Grassmannian frames are natural background material. This is a collaboration with Andrew Kebo.

*Algebraic Geometry Seminar*
Topic:	TBA
Presenter:	Esnault/Viehweg, Essen
Date:	Tuesday, March 22, 2005, Time: 4:30 p.m., Location: Fine Hall 322

*Operations Research and Financial Engineering Seminar*
Topic:	TBA
Presenter:	Bin Yu, University of California, Berkeley
Date:	Tuesday, March 22, 2005, Time: 4:30 p.m., Location: Room E-219, Engineering Quad

*Discrete Mathematics* Seminar
Topic:	TBA
Presenter:	Tibor Szabo, ETH
Date:	Wednesday, March 23, 2005, Time: 2:15 p.m., Location: Fine Hall 224

MARCH 28 - APRIL 1, 2005

*PACM Colloquium*
Topic:	TBA
Presenter:	Nick Duffield, AT&T
Date:	Monday, March 28, 2005, Time: 4:00 p.m., Location: Fine Hall 214

*Algebraic Geometry Seminar*
Topic:	TBA
Presenter:	Esnault/Viehweg, Essen
Date:	Tuesday, March 29, 2005, Time: 4:30 p.m., Location: Fine Hall 322

*Discrete Mathematics* Seminar
Topic:	TBA
Presenter:	David Gamarnik, IBM Research
Date:	Wednesday, March 30, 2005, Time: 2:15 p.m., Location: Fine Hall 224

APRIL 4 - APRIL 8, 2005

*PACM Colloquium*
Topic:	33 Years of Bin Packing
Presenter:	David Johnson, AT&T
Date:	Monday, April 4, 2005, Time: 4:00 p.m., Location: Fine Hall 214
Abstract:	In the bin packing problem, one is given a list of 1-dimensional items and asked to pack them into a minimum number of unit-capacity bins. This was one of the first NP-hard problems to be studied from the "approximation algorithm" point of view, and over the years it has served as a laboratory for the study of new questions about approximation algorithms and the development of new techniques for their analysis. In this talk I present a brief survey of this history, covering worst-case, average-case, and experimental results. The latter have led to many interesting conjectures and theorems, as well as the new "sum-of-squares" algorithm for the problem.

Group Actions and Automorphic Forms Seminar * NEW *
Topic:	TBA
Presenter:	Dave Witte Morris,University of Lethbridge
Date:	Tuesday, April 5, 2005, Time: 11:30 a.m., Location: Fine Hall PL

APRIL 11 - APRIL 15, 2005

*PACM Colloquium*
Topic:	TBA
Presenter:	Pino Martin, Mechanical & Aerospace Engineering, Princeton University
Date:	Monday, April 11, 2005, Time: 4:00 p.m., Location: Fine Hall 214

*Operations Research and Financial Engineering Seminar*
Topic:	TBA
Presenter:	Albert N. Shiryaev, Steklov Mathematics Institute, Russia
Date:	Tuesday, April 12, 2005, Time: 4:30 p.m., Location: Room E-219, Engineering Quad

*Department Colloquium*
Topic:	The Inverse Problem in Invariant Theory
Presenter:	Michael Larsen, Indiana University
Date:	Wednesday, April 13, 2005, Time: 4:30 p.m., Location: Fine Hall 314
Abstract:	The direct problem in invariant theory is to describe the category of representations of a given group. Its inverse is to extract information about a group from information about its representations. The prototypical result in this direction is Tannaka duality. The ultimate goal is to recognize compact Lie groups which appear in nature, where in practice one typically does not know the category of representations up to isomorphism.

Topology Seminar
Topic:	The Reduced Algebraic K-theory of Square-Zero Extensions by Free Modules
Presenter:	Ayelet Lindenstrauss, Indiana University
Date:	Thursday, April 14, 2005, Time: 4:30 p.m., Location: Fine Hall 314
Abstract:	This talk is about joint work with Randy McCarthy (UIUC). We give a method for finding the completion at a prime p of the reduced (over A) K-theory of the square-zero extension of A by a free A-module of finite rank, $\tilde K(A \semiprod (A^{\oplus k}))^\wedge _p$. The calculation is carried out when $A$ satisfies a technical condition which (by work of Hesselholt and Madsen) is satisfied by perfect fields of characteristic $p$, and in that case generalizes the dual numbers ($k=1$) case which Hesselholt and Madsen calculate by different methods. Our calculation uses an invariant we call $W(A;M)$, which can be thought of as a Witt ring of $A$ with coefficients in $M$, or alternatively as cyclic homology of $A$ with coefficients in $M$. By Goodwillie calculus methods, $\tilde K (A \semiprod M) \simeq W(A;M\otimes S¹)$, so what we actually study is $W(A; A^{\oplus k}\otimes S¹)$. The completion at $p$ is needed for a topological analog of breaking the Witt ring down into a product of $p$-Witt vectors.

APRIL 18 - APRIL 22, 2005

*PACM Colloquium*
Topic:	TBA
Presenter:	David Cai, New York University
Date:	Monday, April 18, 2005, Time: 4:00 p.m., Location: Fine Hall 214

Group Actions and Automorphic Forms Seminar * NEW *
Topic:	TBA
Presenter:	Alexander Gorodnik, Caltech
Date:	Tuesday, April 19, 2005, Time: 11:30 a.m., Location: Fine Hall PL

*Operations Research and Financial Engineering Seminar*
Topic:	TBA
Presenter:	Christian Menn, Cornell University
Date:	Tuesday, April 19, 2005, Time: 4:30 p.m., Location: Room E-219, Engineering Quad

*Department Colloquium*
Topic:	TBA
Presenter:	Gregory Margulis, Yale University
Date:	Wednesday, April 20, 2005, Time: 4:30 p.m., Location: Fine Hall 314

Topology Seminar
Topic:	TBA
Presenter:	Peter Kronheimer, Harvard University
Date:	Thursday, April 21, 2005, Time: 4:30 p.m., Location: Fine Hall 314

APRIL 25 - APRIL 29, 2005

*Operations Research and Financial Engineering Seminar*
Topic:	Stochastic Gradient Estimation
Presenter:	Michael Fu, University of Maryland
Date:	Tuesday, April 26, 2005, Time: 4:30 p.m., Location: Room E-219, Engineering Quad
Abstract:	We survey the methods of stochastic gradient estimation, including perturbation analysis, the likelihood ratio method, and weak derivatives. We illustrate the techniques using models in queueing, inventory, and finance. In the latter case, the methods can be used for estimating the so-called Greeks, which are crucial for hedging, and also for pricing American-style options (derivatives with early exercise opportunities). Computational examples using the estimators in stochastic approximation algorithms are described.