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FEBRUARY 23  FEBRUARY 25, 2005 

Discrete Mathematics Seminar  
Topic:  Tournaments, voting paradoxes and nontransitive 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:  Examples in Algebraic Cobordism 
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 
Abstract:  Characteristic numbers of differentiable or complex manifolds play an important role in the classical theory of cobordism. In recent years there appeared a surprising relation between this topic and Galois cohomology. It turned out that characteristic numbers give rise to certain birational invariants which are of particular interest over nonalgebraically closed fields. In the lecture we will consider various examples which illustrate this new appearance of characteristic numbers in questions from algebra and algebraic geometry. 
Ergodic Theory and Statistical Mechanics Seminar  
Topic:  Mean Field Spin Glasses PART I: Parisi Ansatz and bounds for the free energy of the SK model 
Presenter:  Luca De Sanctis, Princeton University 
Date:  Thursday, February 24, 2005, Time: 2:00 p.m., Location: Fine Hall 322 
Abstract:  We introduce the SK model of mean field spin glass and formulate the Parisi ansatz for the free energy per site. We show how a simple interpolation technique allows to show that the Parisi ansatz provides a bound for the free energy. We also hint at how to prove the opposite bound and why it is more difficult. 
Geometric Analysis Seminar *** Please note special day, time, and location  
Topic:  Existence of Infinitely many equilibrium configurations of the liquid crystal system for nonconstant boundary data 
Presenter:  MinChun Hong, University of Queensland 
Date:  Thursday, February 24, 2005, Time: 2:00 p.m., Location: Fine Hall 214 
Joint Analysis Seminar  
Topic:  Localization in the higher dimensional AndersonBernoulli model 
Presenter:  Jean Bourgain, IAS 
Date:  Thursday, February 24, 2005, Time: 4:00 p.m., Location: Fine Hall 214 
Topology Seminar  
Topic:  A spectral sequence approach to Normal Forms 
Presenter:  Martin Bendersky, CUNY 
Date:  Thursday, February 24, 2005, Time: 4:30 p.m., Location: Fine Hall 314 
Abstract:  This is joint work with Rick Churchill. An incomplete list of applications of normal forms are to vector fields, Hamiltonians at equilibria, differential equations and singularity theory. In general one tries to modify a given element in a Lie algebra into a particularly useful form. The algorithm that performs the conversion (the normal form algorithm) can be a formidable computation. We generalize the notion of normal form to that of an initially linear group representation. In this general setting we are able to interpret the normal form algorithm as a calculation of a particularly simple spectral sequence. As a consequence we can show that various vector spaces that appear in the process of carrying out the normal form algorithm are invariants of the orbit of the group representation. There will be plenty of examples. 
Princeton University Math Graduate Student Seminar *** Please note special date and time  
Topic:  Dealing with Complexity: The Statistical Physics approach 
Presenter:  LouisPierre Arguin, Princeton University 
Date:  Friday, February 25, 2005, Time: 12:00 p.m., Location: Fine Hall 1201 
Abstract:  Statistical physics is roughly the study of structures with many degrees of freedom. The first part of the talk will be an introduction to mathematical statistical physics and its basic tools. These tools have mathematical interests of their own, though they have been developped at first by physicists. In the second part, we will look at the socalled spin glass systems where randomness is added in the structure. These structures exhibits a rich behavior which seems to be fundamental in nature, yet lack a complete mathematical understanding. Spin Glass Theory finds application in Optimization and Neural Networks. This talk is meant to be an elementary introduction to the subject and will use only basic probability and analysis. 
Geometric Analysis Seminar  
Topic:  On the uniqueness of the spheres of constant mean curvature at the asymptotically flat end 
Presenter:  Jie Qing, University of California at Santa Cruz 
Date:  Friday, February 25, 2005, Time: 3:00 p.m., Location: Fine Hall 314 
Abstract:  The uniqueness of spheres of constant mean curvature is a very important issue in understanding the structure of asymptotically flat manifolds. The unique foliation of spheres of constant mean curvature at an asymptotically flat end with positive mass is considered as an intrinsic structure of the end and may also be used to define mathematically a center of the mass. In this talk we will prove the uniqueness of spheres of constant mean curvature at asymptotically flat ends with positive mass. 
FEBRUARY 28  MARCH 4, 2005 

Number Theory Seminar *** Please note special time  
Topic:  Galois groups of pclass towers 
Presenter:  Nigel Boston, University of Wisconsin 
Date:  Monday, February 28, 2005, Time: 12:00 p.m., Location: Fine Hall 224 
PACM Colloquium  
Topic:  InvariantBased 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  
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:  Dmodules 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: Dmodules, resolutions of singularities, Hodge structures on Milnor fibers, BernsteinSato 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 E219, Engineering Quad 
Abstract:  The classical BlackScholes 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 superreplication cost. In this talk, I will outline the superreplication problem with several constraints and their solutions. In the classical BlackScholes 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. 
Discrete Mathematics Seminar  
Topic:  A tight threshold for metric Ramsey phenomena 
Presenter:  Adriana Karagiozova, Princeton University 
Date:  Wednesday, March 2, 2005, Time: 2:15 p.m., Location: Fine Hall 224 
Abstract:  Click here 
Princeton University/Institute for Advanced Study Complex Geometry Seminar *** Note special date and location  
Topic:  An obstruction to constant scalar curvature Kahler metrics 
Presenter:  Julius Ross, Columbia University 
Date:  Wednesday, March 2, 2005, Time: 2:30 p.m., Location: West Building Lecture Hall, IAS 
Abstract:  (Joint work with Richard Thomas) I will discuss Kstability and its relation to constant scalar curvature metrics. This leads to a notion of slope stability for manifolds in terms of its subschemes, which gives an obstruction to finding constant scalar curvature Kahler metrics in a given rational Kahler class. 
Department Colloquium  
Topic:  Jacobian determinants and null Lagrangians 
Presenter:  Tadeusz Iwaniec, Syracuse University 
Date:  Wednesday, March 2, 2005, Time: 4:30 p.m., Location: Fine Hall 314 
Abstract:  Click here 
Ergodic Theory and Statistical Mechanics Seminar  
Topic:  Mean Field Spin Glasses PART II: Random Multi Overlap Structures for Diluted Models and Optimization Problems 
Presenter:  Luca De Sanctis, Princeton University 
Date:  Thursday, March 3, 2005, Time: 2:00 p.m., Location: Fine Hall 322 
Abstract:  We introduce the VianaBray Model of Diluted Mean Field Spin Glass and show how to extend to this model some results, regarding the free energy, obtained for nondiluted systems and discussed in PART I. We also introduce the random pXORSAT and KSAT optimization problems and show that the methods we use extend to such problems as well. 
Joint Analysis Seminar  
Topic:  Uniqueness properties of solutions of Schr\"{o}dinger equations 
Presenter:  Alexandru Ionescu, University of Wisconsin  Madison 
Date:  Thursday, March 3, 2005, Time: 4:00 p.m., Location: Fine Hall 214 
Abstract:  I will talk about some recent joint work with Carlos Kenig on a certain type of uniqueness property for solutions of nonlinear Schr\"{o}dinger equations on $R^d\times R$. 
Topology Seminar  
Topic:  On knot Floer homology and satellite knots 
Presenter:  Matthew Hedden, Columbia University 
Date:  Thursday, March 3, 2005, Time: 4:30 p.m., Location: Fine Hall 314 
Abstract:  I will discuss the knot Floer homology invariants introduced by OzsvathSzabo and Rasmussen and what is known about these invariants for satellite knots. Part of this talk will address recent results calculating the Floer homology of Whitehead doubles of (2,2n+1) torus knots. These results are part of joint work with Philip Ording of Columbia University which aims to calculate the Floer homology of (1,1) satellite knots. 
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. SeibergWitten equations appear as deformation equations of certain calibrated submanifolds. We will discuss how to associate invariants to G_2 manifolds from SeibergWitten for families. 
MARCH 7  MARCH 11, 2005 

PACM Colloquium  
Topic:  Progresses and Challenges in Multiscale Modeling 
Presenter:  Weinan E, Applied Mathematics and Mathematics, Princeton University 
Date:  Monday, March 7, 2005, Time: 4:00 p.m., Location: Fine Hall 214 
Abstract:  In the last several years, there has been tremendous growth of interest on multiscale modeling from many scientific and engineering disciplines. What are the issues involved? How much progress has been made? What are the challenges that we face in order to realize the full potential of multiscale modeling? This talk presents a personal view on these and related questions. We will begin with a quick discussion of the general issues in multiscale modeling. We then review some of the most successful multiscale methods, including the CarParrinello method and the quasicontinuum method for crystalline solids. In the second half of talk, we will focus on the problems from complex fluids and microfluidics. We end the talk with a canonical example in multiscale modeling, the contact line problem. 
Group Actions and Automorphic Forms Seminar  
Topic:  On smooth classification of Z^k and R^k Cartan actions 
Presenter:  Boris Kalinin, University of South Alabama 
Date:  Tuesday, March 8, 2005, Time: 11:30 a.m., Location: Fine Hall PL 
Abstract:  We consider actions of Z^k by hyperbolic diffeomorphisms of a compact manifold and R^k actions normally hyperbolic to the orbit foliation. Algebraic examples of such actions have been extensively studied recently. In contrast to Anosov diffeomorphisms and flows, the higher rank actions exhibit such remarkable properties as rigidity of invariant measures and rigidity of measure preserving isomorphisms. These algebraic actions are often locally rigid, i.e. smoothly conjugate to any small perturbation. We will discuss the problem of smooth classification of nonalgebraic actions, i.e. the existence of a smooth conjugacy to an algebraic model, and related rigidity questions. Our main result is a classification for certain classes of Cartan actions. 
SPECIAL Analysis Seminar *** Please note special date, time, and location  
Topic:  The essential spectrum of advective equations 
Presenter:  Roman Shvydkoy, University of Illinois at Chicago 
Date:  Tuesday, March 8, 2005, Time: 2:00 p.m., Location: Fine Hall 214 
Abstract:  Early numerical simulations of certain 2D fluids revealed an important role of essential spectrum in formation of shortwave instabilities. For any linearized advective equation, such as the Euler equation, a general description of its essential spectrum can be given via the SackerSell dynamical spectrum of an associated finitedimensional system of ODEs. In this talk we discuss the relevant mathematical apparatus, and report on recent progress in finding the exact spectral pictures. 
Algebraic Geometry Seminar  
Topic:  Cohomology and Representations of Finite Group Schemes 
Presenter:  Eric Friedlander, Northwestern University 
Date:  Tuesday, March 8, 2005, Time: 4:30 p.m., Location: Fine Hall 322 
Abstract:  This is a report of joint work with Julia Pevtsova in which we provide a purely representationtheoretic construction of the scheme $Proj H^{ev}(G,k)$, where $G$ is a finite group scheme over a field $k$ of characteristic $p > 0$. Some applications are discussed. Before embarking upon a discussion of an arbitrary finite group scheme, we begin with $G$ the finite group $Z/p$ and then contemplate the much more difficult case of $Z/p \oplus Z/p$. 
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 E219, Engineering Quad 
Abstract:  We discuss a modified version of the Elimination algorithm proposed earlier by the author to solve recursively a problem of optimal stopping of a Markov chain in discrete time and finite or countable state space. This algorithm and the idea behind it are applied to calculation of the classical and the generalized Gittins index and to solve the discrete versions of the Poisson and Bellman equations. 
Discrete Mathematics Seminar  
Topic:  The exact Turán function of the generalized triangle 
Presenter:  Oleg Pikhurko, Carnegie Mellon University 
Date:  Wednesday, March 9, 2005, Time: 2:15 p.m., Location: Fine Hall 224 
Abstract:  Click here 
Department Colloquium  
Topic:  TBA 
Presenter:  Kannan Soundararajan, University of Michigan 
Date:  Wednesday, March 9, 2005, Time: 4:30 p.m., Location: Fine Hall 314 
Ergodic Theory and Statistical Mechanics Seminar  
Topic:  Joinings of Cartan actions 
Presenter:  Manfred Einsiedler, Princeton University 
Date:  Thursday, March 10, 2005, Time: 2:00 p.m., Location: Fine Hall 322 
Abstract:  In joint work with E. Lindenstrauss we obtained a complete classifications of joinings of higher rank Cartan actions on locally homogeneous spaces. Unlike the case of torus actions, here there is no 'up to zero entropy part' in the classification  every ergodic joining is algebraic. Previous results in that direction required additional assumptions. We will discuss the proof and a reformulation as an equidistribution  result. 
MARCH 14  MARCH 18, 2005 

Group Actions and Automorphic Forms Seminar  
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 operatorvalued measures (POMs). For any tight frame with frame constant 1 for a separable Hilbert space there is an associated POM. Our setup is ddimensional 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:  Embracing statistical challenges in the information technology age 
Presenter:  Bin Yu, University of California, Berkeley 
Date:  Tuesday, March 22, 2005, Time: 4:30 p.m., Location: Room E219, Engineering Quad 
Abstract:  Information technology advances are making data collection possible in most if not all fields of science and engineering and beyond. Statistics as a scientific discipline is challenged and enriched by the new opportunities resulted from these highdimensional data sets. In this talk, I will use serveral research projects to demonstrate how these IT challenges are met by finding new applications of traditional statistical thinking and methods and by incorporating compression and computation considerations into statistical estimation. In particluar, I will cover cloud detection over the polar region, microarray image compression for statistical analysis, and L2 boosting as a computationally efficient method for sparse nonparametric regression model fitting. 
Discrete Mathematics Seminar  
Topic:  TBA 
Presenter:  Tibor Szabo, ETH 
Date:  Wednesday, March 23, 2005, Time: 2:15 p.m., Location: Fine Hall 224 
Department Colloquium  
Topic:  TBA 
Presenter:  Dmitry Dolgopyat, University of Maryland 
Date:  Wednesday, March 23, 2005, Time: 4:30 p.m., Location: Fine Hall 314 
Joint Analysis Seminar  
Topic:  TBA 
Presenter:  Susan Friedlander, IAS and University of Illinois at Chicago 
Date:  Thursday, March 24, 2005, Time: 4:00 p.m., Location: Fine Hall 214 
Topology Seminar  
Topic:  TBA 
Presenter:  Walter Neumann, Institute for Advanced Study and Columbia University 
Date:  Thursday, March 24, 2005, Time: 4:30 p.m., Location: Fine Hall 314 
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 
Group Actions and Automorphic Forms Seminar  
Topic:  TBA 
Presenter:  Werner Müller, Bonn and the Institute for Advanced Study 
Date:  Tuesday, March 29, 2005, Time: 11:30 a.m., Location: Fine Hall PL 
Princeton University/Institute for Advanced Study Complex Geometry Seminar  
Topic:  Einstein metrics on Seifert fibered manifolds 
Presenter:  János Kollár, Princeton University 
Date:  Tuesday, March 29, 2005, Time: 2:30 p.m., Location: Fine Hall 110 
Algebraic Geometry Seminar  
Topic:  TBA 
Presenter:  Esnault/Viehweg, Essen 
Date:  Tuesday, March 29, 2005, Time: 4:30 p.m., Location: Fine Hall 322 
Operations Research and Financial Engineering Seminar  
Topic:  TBA 
Presenter:  Kavita Ramanan, Carnegie Mellon University 
Date:  Tuesday, March 29, 2005, Time: 4:30 p.m., Location: Room E219, Engineering Quad 
Discrete Mathematics Seminar  
Topic:  TBA 
Presenter:  David Gamarnik, IBM Research 
Date:  Wednesday, March 30, 2005, Time: 2:15 p.m., Location: Fine Hall 224 
Department Colloquium  
Topic:  TBA 
Presenter:  Gregory Margulis, Yale University 
Date:  Wednesday, March 30, 2005, Time: 4:30 p.m., Location: Fine Hall 314 
Topology Seminar  
Topic:  TBA 
Presenter:  Jacob Rasmussen, Princeton University 
Date:  Thursday, March 31, 2005, Time: 4:30 p.m., Location: Fine Hall 314 
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 1dimensional items and asked to pack them into a minimum number of unitcapacity bins. This was one of the first NPhard 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 worstcase, averagecase, and experimental results. The latter have led to many interesting conjectures and theorems, as well as the new "sumofsquares" algorithm for the problem. 
Group Actions and Automorphic Forms Seminar  
Topic:  TBA 
Presenter:  Dave Witte Morris,University of Lethbridge 
Date:  Tuesday, April 5, 2005, Time: 11:30 a.m., Location: Fine Hall PL 
Operations Research and Financial Engineering Seminar  
Topic:  Useful Bounds on the Expected Maximum of Correlated Normal Variables 
Presenter:  Andrew Ross, Lehigh University 
Date:  Tuesday, April 5, 2005, Time: 4:30 p.m., Location: Room E219, Engineering Quad 
Abstract:  We compute useful upper and lower bounds on the expected maximum of up to a few hundred correlated Normal variables with arbitrary means and variances. Two types of bounding processes are used: perfectly dependent Normal variables, and independent Normal variables, both with arbitrary mean values. The expected maximum for the perfectly dependent variables can be evaluated in closed form; for the independent variables, a single numerical integration is required. Higher moments are also available. We use mathematical programming to find parameters for the processes, so they will give bounds on the expected maximum, rather than approximations of unknown accuracy. Our original application is to the maximum number of people online simultaneously during the day in an infiniteserver queue with a timevarying arrival rate. The upper and lower bounds are tighter than previous bounds, and in many of our examples are within 5 percent of each other. 
Discrete Mathematics Seminar  
Topic:  TBA 
Presenter:  Igor Pak, MIT 
Date:  Wednesday, April 6, 2005, Time: 2:15 p.m., Location: Fine Hall 224 
Topology Seminar  
Topic:  TBA 
Presenter:  Jeff Brock, Brown University 
Date:  Thursday, April 7, 2005, Time: 4:30 p.m., Location: Fine Hall 314 
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 E219, 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. 
Joint Analysis Seminar  
Topic:  TBA 
Presenter:  Vladimir Sverak, University of Minnesota 
Date:  Thursday, April 14, 2005, Time: 4:00 p.m., Location: Fine Hall 214 
Topology Seminar  
Topic:  The Reduced Algebraic Ktheory of SquareZero 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) Ktheory of the squarezero extension of A by a free Amodule 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, $\tilde K (A \semiprod M) \simeq W(A;M\otimes S^{1})$, so what we actually study is $W(A; A^{\oplus k}\otimes S^{1})$. 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  
Topic:  TBA 
Presenter:  Alexander Gorodnik, Caltech 
Date:  Tuesday, April 19, 2005, Time: 11:30 a.m., Location: Fine Hall PL 
Algebraic Geometry Seminar  
Topic:  TBA 
Presenter:  Gordon Heier, Harvard University 
Date:  Tuesday, April 19, 2005, Time: 4:30 p.m., Location: Fine Hall 322 
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 E219, Engineering Quad 
Discrete Mathematics Seminar  
Topic:  Cliquewidth for graph classes defined by forbidden fourvertex subgraphs 
Presenter:  Andreas Brandstaed, University of Rostock 
Date:  Wednesday, April 20, 2005, Time: 2:15 p.m., Location: Fine Hall 224 
Abstract:  Click here 
Department Colloquium  
Topic:  Probabilistic reasoning and Ramsey Theory 
Presenter:  Benjamin Sudakov, Princeton University 
Date:  Wednesday, April 20, 2005, Time: 4:30 p.m., Location: Fine Hall 314 
Abstract:  "Ramsey Theory" refers to a large body of deep results in mathematics concerning the partition of large collections. Its underlying philosophy is captured succinctly by the statement that "In a large system complete disorder is impossible". Since the publication of the seminal paper of Ramsey in 1930, this subject has grown with increasing vitality, and is currently among the most active areas in Combinatorics. An important factor in the development of Ramsey Theory was the successful application of the socalled "Probabilistic Method". This method was initiated more than fifty years ago by Paul Erdos, and became one of the most powerful and widely used tools in Discrete Mathematics. In this talk I will describe some classical results of Ramsey Theory together with recent progress on some old questions of Erdos which was made using probabilistic arguments. I will also discuss the problem of converting existence arguments into deterministic constructions, in particular, the recent explicit constructions of Bipartite Ramsey graphs. 
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 

PACM Colloquium  
Topic:  Discrete Denoising 
Presenter:  Sergio Verdu, Applied Mathematics and Electrical Engineering, Princeton University 
Date:  Monday, April 25, 2005, Time: 4:00 p.m., Location: Fine Hall 214 
Abstract:  Finitealphabet 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 continuousalphabet 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 semistochastic sense. I will also show several DUDEbased algorithms for channel decoding of systematically encoded redundant data. Joint work with E. Ordentlich, G. Seroussi, M. Weinberger and T. Weissman. 
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 E219, 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 socalled Greeks, which are crucial for hedging, and also for pricing Americanstyle options (derivatives with early exercise opportunities). Computational examples using the estimators in stochastic approximation algorithms are described. 
Topology Seminar  
Topic:  TBA 
Presenter:  Helmut Hofer, NYU 
Date:  Thursday, April 28, 2005, Time: 4:30 p.m., Location: Fine Hall 314 
MAY 9  MAY 14, 2005 

Operations Research and Financial Engineering Seminar  
Topic:  TBA 
Presenter:  Peter Bickel, University of California, Berkeley 
Date:  Tuesday, May 10, 2005, Time: 4:30 p.m., Location: Room E219, Engineering Quad 
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