FEBRUARY 9 - FEBRUARY 11, 2005 |
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| 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 |
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| 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: | The asymptotic shape of metric balls in groups of polynomial growth, and pointwise ergodic theorems |
| Presenter: | Emmanuel Breuillard, IHES |
| Date: | Tuesday, February 15, 2005, Time: 11:30 a.m., Location: Fine Hall PL |
| Abstract: | Let $G$ be a locally compact group of polynomial growth, i.e.vol(U^n)=O(n^K) for some K>0 and some compact generating set U. We show that there is a number c(U)>0 and an integer d that can be computed explicitely such that the n^(-d)vol(U^n) converges to c(U) as n tends to infinity. We give a geometric interpretation of the asymptotic volume c(U) as the volume of the unit ball for some Carnot-Caratheodory metric on a stratified simply connected nilpotent Lie group naturally associated to G. As a consequence we get in particular that the balls {U^n}_n form a Folner sequence, thus answering Greenleaf's "localization" problem in this case. The results hold for a large class of other metrics on G, such as left invariant Riemannian metrics if G is Lie, and enable to prove pointwise ergodic theorems for such averages, thus answering a question of A. Nevo. |
| Operations Research and Financial Engineering Seminar | |
| Topic: | Financial Engineering in Wonderland: an Adventure with Riemann, Lisa, and Dickens |
| Presenter: | Steve Kou, Columbia University |
| Date: | Tuesday, February 15, 2005, Time: 4:30 p.m., Location: Room E-219, Engineering Quad |
| Abstract: | This talk will give an overview of the following four research topics: (1) Using compound Poisson processes to model asset prices (e.g. stocks, bonds, etc.) and credit risk. (2) Using birth-death and diffusion processes to model growth stocks (e.g. biotechnology and internet stocks). (3) Using renewal theory to price discrete path-dependent options, such as discrete barrier and lookback options. (4) Using financial engineering in revenue management. The unusual connections in the title will be revealed during the course of the talk. |
| Discrete Mathematics Seminar | |
| Topic: | Pairwise intersections and forbidden configurations |
| Presenter: | Peter Keevash, Caltech |
| Date: | Wednesday, February 16, 2005, Time: 2:15 p.m., Location: Fine Hall 224 |
| Abstract: | Click here |
| 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. |
| Geometric Analysis Seminar | |
| Topic: | Regularized determinants of Laplace type operators and analytic surgery |
| Presenter: | Werner Muelle, Institute for Advanced Study |
| Date: | Friday, February 18, 2005, Time: 3:00 p.m., Location: Fine Hall 314 |
| Abstract: | Analytic surgery is a special type of a singular deformation of a Riemannian metric on a closed manifold modeling surgery in the sense of cutting the manifold along a hypersurface. The corresponding singular limit is a complete manifold with cylindrical ends. In the talk I will discuss the behavior of regularized determinants of Laplace type operators under such metric degenerations. Applications are, for example, surgery formulas for determinants and related spectral invariants. |
FEBRUARY 21 - FEBRUARY 25, 2005 |
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| PACM Colloquium | |
| Topic: | Signal Processing and Wireless Networks |
| Presenter: | Vincent Poor, Electrical Engineering and Applied Mathematics, Princeton University |
| Date: | Monday, February 21, 2005, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: | A major issue in today's wireless world is the dramatic increase in demand for new capacity and higher performance of wireless networks. The development of these capabilities is limited severely by the scarcity of two of the principal resources in wireless networks, namely energy and bandwidth. Consequently, the community has turned to a third principal resource, the addition of intelligence throughout the network, in order to exploit increases in processing power afforded by Moore's Law type improvements in microelectronics. This talk will focus on two aspects of this phenomenon: the effects of advanced node-level signal processing on the higher-layer performance of wireless communication networks, including energy efficiency, spectral efficiency, throughput and delay; and the use of advanced signal processing principles, including collaborative beam-forming, sensor scheduling, and distributed learning, in the design, deployment and operation of wireless sensor networks. |
| Group Actions and Automorphic Forms Seminar *** NEW *** | |
| Topic: | Existence and Weyl's law for cusp forms |
| Presenter: | Akshay Venkatesh, CIMS/Clay |
| Date: | Tuesday, February 22, 2005, Time: 11:30 a.m., Location: Fine Hall PL |
| Abstract: | I will explain joint work with Elon Lindenstrauss, establishing Weyl's law for cusp forms on congruence quotients of higher rank symmetric spaces. The key ingredient is a new type of "simple trace formula", which allows us to evade the usual difficulties with Eisenstein series. I will first explain the underlying ideas in the context of the modular surface SL(2,Z)\H, and then discuss how they extend to higher rank quotients. |
| 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 |
| Ergodic Theory and Statistical Mechanics Seminar | |
| Topic: | Parisi Ansatz and bounds for the free energy of the SK mean field model of spin glasses |
| Presenter: | Luca de Santis, 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 non-constant boundary data |
| Presenter: | Min-Chun 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 Anderson-Bernoulli 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. |
FEBRUARY 28 - MARCH 4, 2005 |
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| 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. |
| 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 K-stability 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 |
| 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 |
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| 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 Car-Parrinello method and the quasicontinuum method for crystalline solids. In the second half of talk, we will focus on the problems from complex fluids and micro-fluidics. We end the talk with a canonical example in multiscale modeling, the contact line problem. |
| Group Actions and Automorphic Forms Seminar *** NEW *** | |
| Topic: | TBA |
| Presenter: | Boris Kalinin, University of South Alabama |
| Date: | Tuesday, March 8, 2005, Time: 11:30 a.m., Location: Fine Hall PL |
| 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 |
| Department Colloquium | |
| Topic: | TBA |
| Presenter: | Kannan Soundararajan, University of Michigan |
| Date: | Wednesday, March 9, 2005, Time: 4:30 p.m., Location: Fine Hall 314 |
MARCH 14 - MARCH 18, 2005 |
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| 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 |
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| 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 |
| Department Colloquium | |
| Topic: | TBA |
| Presenter: | Dmitry Dolgopyat, University of Maryland |
| Date: | Wednesday, March 23, 2005, Time: 4:30 p.m., Location: Fine Hall 314 |
MARCH 28 - APRIL 1, 2005 |
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| 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 *** NEW *** | |
| 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 |
| 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 E-219, 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 |
APRIL 4 - APRIL 8, 2005 |
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| 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 |
| Operations Research and Financial Engineering Seminar | |
| Topic: | Useful Bounds on the Expected Maximum of Correlated Normal Variables |
| Presenter: | Andrew Ross, Leghigh University |
| Date: | Tuesday, April 5, 2005, Time: 4:30 p.m., Location: Room E-219, 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 on-line simultaneously during the day in an infinite-server queue with a time-varying 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 |
| Department Colloquium | |
| Topic: | TBA |
| Presenter: | Benjamin Sudakov, Princeton University |
| Date: | Wednesday, April 6, 2005, Time: 4:30 p.m., Location: Fine Hall 314 |
APRIL 11 - APRIL 15, 2005 |
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| 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 |
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| 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 |
| Discrete Mathematics Seminar | |
| Topic: | Clique-width for graph classes defined by forbidden four-vertex subgraphs |
| Presenter: | Andreas Brandstaed, University of Rostock |
| Date: | Wednesday, April 20, 2005, Time: 2:15 p.m., Location: Fine Hall 224 |
| Abstract: | Click here |
| 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 |
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| 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: | 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. |
| 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. |
| Topology Seminar | |
| Topic: | TBA |
| Presenter: | Helmut Hofer, NYU |
| Date: | Thursday, April 28, 2005, Time: 4:30 p.m., Location: Fine Hall 314 |