MARCH 30 - APRIL 1, 2005 |
|
| Graduate Student Seminar | |
| Topic: | A curious pair of integers |
| Presenter: | Michael Volpato, Princeton University |
| Date: | Wednesday, March 30, 2005, Time: 12:30 p.m., Location: Fine Hall 1201 |
| Abstract: | In the Gentleman's Diary of 1795, mathematician J. Saul observed a pair of rather fascinating integers, namely the pair (345, 184). They are interesting because their sum, sum of squares and sum of cubes are all simultaneously perfect squares. Using the theory of elliptic curves we will show that the set of pairs of integers whose sum, sum of squares, and sum of cubes are all simultaneously perfect squares is infinite, and we give a recursion relation which generates all such pairs. [No knowledge of elliptic curves will be assumed.] |
| Discrete Mathematics Seminar | |
| Topic: | Applications of the local weak convergence method to random graph problems |
| Presenter: | David Gamarnik, IBM Research |
| Date: | Wednesday, March 30, 2005, Time: 2:15 p.m., Location: Fine Hall 224 |
| Abstract: | Click here |
| Department Colloquium | |
| Topic: | Markoff spectrum, expanding properties, and spectral gap |
| Presenter: | Gregory Margulis, Yale University |
| Date: | Wednesday, March 30, 2005, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: | The purpose of the talk is to explain how effective estimates for the Markoff spectrum in dimensions 3 and 4 can be obtained using expanding properties for the actions of semisimple Lie groups on the quotients by arithmetic subgroups. These expanding properties follow from the spectral gap for the Laplace operator. |
| Operations Research and Financial Engineering Seminar *** Special series of lectures *** | |
| Topic: | Optimal stopping and free boundary problems |
| Presenter: | Albert N. Shiryaev, Rutgers University |
| Date: | Wednesday, March 30, 2005, Time: 4:30 p.m., Location: Room E-225, Engineering Quad |
| Abstract: | Professor Shiryaev will discuss selected topics in: (A) the theory of probability: maximal inequalities in stochastic analysis, (B) the mathematical statistics: sequential testing and quickest detection problems for Wiener and Poisson processes, (C) the mathematical finance: American options (standard, Russian, Asian, power) which can be reformulated as problems of optimal stopping of stochastic processes and solved by a reduction to free-boundary problems of real analysis (Stefan problems). |
| Ergodic Theory and Statistical Mechanics Seminar | |
| Topic: | Transport and Aggregation in Two Dimensions |
| Presenter: | Martin Bazant, MIT |
| Date: | Thursday, March 31, 2005, Time: 2:00 p.m., Location: Fine Hall 322 |
| Abstract: | Perhaps the most ubiquitous equation in physics is Laplace's equation, which is conformal invariant in two dimensions. This special property has led to many theoretical advances, especially in nonlinear pattern formation, such as (continuous) viscous fingering and (stochastic) diffusion-limited aggregation (DLA). Here, we note that some other equations are also conformally invariant and discuss new applications of conformal mapping to advection-diffusion, gravity currents, and ion transport. First, we present a variety of exact solutions to the Navier-Stokes equations of fluid mechanics and the Nernst-Planck equations of electrochemistry. Next, we generalize models of viscous fingering and DLA (the Hastings-Levitov formulation) to a broad class of non Laplacian growth phenomena. By analyzing the case of advection-diffusion-limited aggregation (DLA in a fluid flow), we shed light on the failure of the mean-field approximation to describe the average shape of fractal clusters. |
| Joint Analysis Seminar | |
| Topic: | Maps with values into S1 and minimal connections |
| Presenter: | Augusto Ponce, IAS |
| Date: | Thursday, March 31, 2005, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: | Maps in W^{1,1} from the sphere S2 into the circle S1 can have, at most, countably many topological singularities. I will present some techniques which allow us to localize and quantify those "defects". Joint work with H. Brezis and P. Mironescu. |
| Topology Seminar | |
| Topic: | Deformations of the Khovanov Homology |
| Presenter: | Jacob Rasmussen, Princeton University |
| Date: | Thursday, March 31, 2005, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: | The Khovanov homology is a homological generalization of the Jones polynomial. The technique of deforming the definition of this theory was introduced by Lee and studied in the sl(n) case by Gornik. It has proven to be a very powerful one. In this talk I'll describe the space of possible deformations, and give some applications, both to computing the sl(n) theory and to better understanding its structure. |
| Geometric Analysis Seminar | |
| Topic: | Positivity of Quasi-local Mass |
| Presenter: | Chiu-Chu Liu, Harvard University |
| Date: | Friday, April 1, 2005, Time: 3:00 p.m., Location: Fine Hall 314 |
| Abstract: | Quasi-local mass is a quantity associated to a spacelike 2-surface in a four dimensional spacetime. Several definitions of quasi-local mass have been proposed. I will discuss the positivity of one particular quasi-local mass based on joint works with Shing-Tung Yau. |
| Geometric Analysis Seminar *** Please note special time | |
| Topic: | Existence and regularity of stable branched minimal hypersurfaces |
| Presenter: | Neshan Wickramasekera, MIT |
| Date: | Friday, April 1, 2005, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: | I will describe the following local regularity theorem and its consequences: If an immersed stable minimal hypersurface having a small singular set is weakly close to a multiplicity 2 hyperplane in a ball, then in the interior, it is a branched 2-valued $C^{1, \alpha}$graph. I will also present an existence theorem for branched stable minimal hypersurfaces. The latter result is joint work with Leon Simon |
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. |
| Operations Research and Financial Engineering Seminar *** Special series of lectures *** | |
| Topic: | Optimal stopping and free boundary problems |
| Presenter: | Albert N. Shiryaev, Rutgers University |
| Date: | Monday, April 4, 2005, Time: 4:30 p.m., Location: Room E-225, Engineering Quad |
| Abstract: | Professor Shiryaev will discuss selected topics in: (A) the theory of probability: maximal inequalities in stochastic analysis, (B) the mathematical statistics: sequential testing and quickest detection problems for Wiener and Poisson processes, (C) the mathematical finance: American options (standard, Russian, Asian, power) which can be reformulated as problems of optimal stopping of stochastic processes and solved by a reduction to free-boundary problems of real analysis (Stefan problems). |
| Group Actions and Automorphic Forms Seminar | |
| Topic: | Some arithmetic groups that cannot act on the line |
| Presenter: | Dave Witte Morris,University of Lethbridge |
| Date: | Tuesday, April 5, 2005, Time: 11:30 a.m., Location: Fine Hall PL |
| Abstract: | It is known that finite-index subgroups of the arithmetic group SL(3,Z) have no interesting actions on the real line. This naturally led to the conjecture that most other arithmetic groups (of higher real rank) also cannot act on the line. This problem remains open, but joint work with Lucy Lifschitz verifies the conjecture for many examples. This includes all finite-index subgroups of SL(2,Z[a]) or SL(2,Z[1/n]), where a is any real, irrational algebraic integer, and n > 1. The proofs are based on the fact, proved by D.Carter, G.Keller, and E.Paige, that every element of these groups is a product of a bounded number of elementary matrices. |
| Joint Institute for Advanced Study and Princeton University Complex Geometry Seminar | |
| Topic: | Asymptotic geometry of incomplete metrics on the moduli space of Riemann surfaces |
| Presenter: | Zheng Huang, University of Michigan |
| Date: | Tuesday, April 5, 2005, Time: 2:30 p.m., Location: Fine Hall 110 |
| Abstract: | An incomplete metric, the Weil-Petersson metric, has played a significant role in the study of the geometry of Teichmuller space. We will mainly discuss the asymptotics of the curvatures of this metric in this talk. Some aspects of another metric will aslo be discussed. |
| Algebraic Geometry Seminar | |
| Topic: | Conic bundles and noncommutative geometry |
| Presenter: | P. Hacking, Yale University |
| Date: | Tuesday, April 5, 2005, Time: 4:30 p.m., Location: Fine Hall 322 |
| Abstract: | A conic bundle is a 3-fold fibred over a surface with general fibre a smooth rational curve. These varieties are important in the classification of 3-folds as described by Mori's minimal model program. A conic bundle corresponds to an algebra over the surface with general fibre 2x2 matrices. We use a version of the MMP for this noncommutative surface to construct simple birational models of conic bundles. The noncommutative singularities which arise have many nice properties, for example, they are simultaneously Clifford algebras and quotients of matrix algebras. This is joint work with Daniel Chan and Colin Ingalls. |
| 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 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. |
| Topology Seminar *** Please note special date, time, and location | |
| Topic: | On knot Floer homology and satellite knots |
| Presenter: | Matthew Hedden, Columbia University |
| Date: | Tuesday, April 5, 2005, Time: 5:00 p.m., Location: Fine Hall 214 |
| Abstract: | I will discuss the knot Floer homology invariants introduced by Ozsvath-Szabo and Rasmussen and what is known about these invariants for satellite knots. Part of this talk will address recent results calculating the Floer homologies 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. |
| Discrete Mathematics Seminar | |
| Topic: | The Nature of Partition Bijections |
| Presenter: | Igor Pak, MIT |
| Date: | Wednesday, April 6, 2005, Time: 2:15 p.m., Location: Fine Hall 224 |
| Abstract: | Click here |
| Operations Research and Financial Engineering Seminar *** Special series of lectures *** | |
| Topic: | Optimal stopping and free boundary problems |
| Presenter: | Albert N. Shiryaev, Rutgers University |
| Date: | Wednesday, April 6, 2005, Time: 4:30 p.m., Location: Room E-225, Engineering Quad |
| Abstract: | Professor Shiryaev will discuss selected topics in: (A) the theory of probability: maximal inequalities in stochastic analysis, (B) the mathematical statistics: sequential testing and quickest detection problems for Wiener and Poisson processes, (C) the mathematical finance: American options (standard, Russian, Asian, power) which can be reformulated as problems of optimal stopping of stochastic processes and solved by a reduction to free-boundary problems of real analysis (Stefan problems). |
| Ergodic Theory and Statistical Mechanics Seminar | |
| Topic: | On the distributions of maximal downfalls of Brownian motion with drift |
| Presenter: | Albert N. Shiryaev, Moscow State University and Russian Academy of Sciences |
| Date: | Thursday, April 7, 2005, Time: 2:00 p.m., Location: Fine Hall 322 |
| Abstract: | We shall discuss the problem of finding distributions of big drops "from a peak to a bottom" of the Brownian trajectories on (0,T) We shall deriveseveral explicit formulas and give the expressions for Laplace transforms in some cases. |
| Topology Seminar | |
| Topic: | TBA |
| Presenter: | Jeff Brock, Brown University |
| Date: | Thursday, April 7, 2005, Time: 4:30 p.m., Location: Fine Hall 314 |
| Operations Research and Financial Engineering Seminar *** Please note special date, time, location | |
| Topic: | Columbia-Princeton Probability Day |
| Presenter: | List of prospective speakers include: Alain Bensoussan, University of Texas at Dallas Hans Föllmer, Humboldt University, Germany Albert N. Shiryaev, Steklov Mathematical Institute, Russian |
| Date: | Friday, April 8, 2005, Time: TBA, Location: TBA |
| Special Seminar | |
| Topic: | Theory of valuations on manifolds |
| Presenter: | S. Alesker, Tel Aviv University and IAS |
| Date: | Friday, April 8, 2005, Time: 2:00 p.m., Location: Fine Hall 1201 |
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 *** Special series of lectures *** | |
| Topic: | Optimal stopping and free boundary problems |
| Presenter: | Albert N. Shiryaev, Rutgers University |
| Date: | Monday, April 11, 2005, Time: 4:30 p.m., Location: Room E-225, Engineering Quad |
| Abstract: | Professor Shiryaev will discuss selected topics in: (A) the theory of probability: maximal inequalities in stochastic analysis, (B) the mathematical statistics: sequential testing and quickest detection problems for Wiener and Poisson processes, (C) the mathematical finance: American options (standard, Russian, Asian, power) which can be reformulated as problems of optimal stopping of stochastic processes and solved by a reduction to free-boundary problems of real analysis (Stefan problems). |
| 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. |
| Operations Research and Financial Engineering Seminar *** Special series of lectures *** | |
| Topic: | Optimal stopping and free boundary problems |
| Presenter: | Albert N. Shiryaev, Rutgers University |
| Date: | Wednesday, April 13, 2005, Time: 4:30 p.m., Location: Room E-225, Engineering Quad |
| Abstract: | Professor Shiryaev will discuss selected topics in: (A) the theory of probability: maximal inequalities in stochastic analysis, (B) the mathematical statistics: sequential testing and quickest detection problems for Wiener and Poisson processes, (C) the mathematical finance: American options (standard, Russian, Asian, power) which can be reformulated as problems of optimal stopping of stochastic processes and solved by a reduction to free-boundary problems of real analysis (Stefan problems). |
| PACM Colloquium - Distinguised Lecture Series | |
| Topic: | More Unknowns than Equations? Bring it on! |
| Presenter: | David Donoho, Department of Statistics, Stanford University |
| Date: | Wednesday, April 13, 2005, Time: 8:00 p.m., Location: A02 McDonnell Hall |
| Abstract: | Everything you were taught about underdetermined systems of linear equations is wrong... Okay, that's too strong. But you have been taught things in undergraduate linear algebra which, if you are an engineer or scientist, may be holding you back. The main one is that if you have more unknowns than equations, you're lost. Don't believe it. At the moment there are many interesting problems in the information sciences where researchers are currently confounding expectations by turning linear algebra upside down: (a) An imaging system can produce an accurate N-pixel image using only N^{1/4} log^3(N) (specially chosen) samples to reconstruct it, far fewer than the N pixel samples you might have naively thought. (b) A Fourier imaging system can observe just the lowest frequencies of a sparse nonnegative signal and perfectly reconstruct all the unmeasured high frequencies of the signal. (c) a communications system can transmit a very weak signal perfectly in the presence of intermittent but arbitrarily powerful jamming. <\p> Moreover, in each case the methods are convenient and computationally tractable. Mathematically, what's going on is a recent explosion of interest in finding the sparsest solution to certain systems of underdetermined linear equations. This problem is known to be NP-Hard in general, and hence the problem sounds intractable. Surprisingly, in some particular cases, it has been found that one can find the sparsest solution by $l^1$ minimization, which is a convex optimization problem and so tractable. Many researchers are now actively working to explain and exploit this phenomenon. It's responsible for the examples given above. In my talk, I'll discuss that this curious behavior of $l^1$ minimization and connect with some deep mathematics and a broad range of fun applications. |
| 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 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. |
| Joint Institute for Advanced Study and Princeton University Number Theory Seminar *** Please note special date, time, and location | |
| Topic: | The inverse Galois problem for p-adic Lie algebras |
| Presenter: | Michael Larsen, Indiana University |
| Date: | Friday, April 15, 2005, Time: 2:00 p.m., Location: Fine Hall 801 |
| Abstract: | For a number field K and a (compact) p-adic Lie groups G, the inverse Galois problem asks whether G can be realized as the Galois group of an extension of K. Already in the case that G is zero-dimensional, this is too difficult. So I propose to relax the problem and ask which p-adic Lie algebras can be realized. |
| Geometry, Representation Theory, and Moduli Seminar | |
| Topic: | Relative Gromov-Witten Invariants and Symplectic Field Theory |
| Presenter: | E. Katz, Duke University |
| Date: | Friday, April 15, 2005, Time: 4:30 p.m., Location: Fine Hall 314 |
APRIL 18 - APRIL 22, 2005 |
|
| Joint Analysis Seminar *** Please note special date and location | |
| Topic: | Existence of solutions to the nonlinear wave equation with an inverse-square potential |
| Presenter: | Paschalis Karageorgis, Northwestern University |
| Date: | Monday, April 18, 2005, Time: 4:00 p.m., Location: Fine Hall 314 |
| Abstract: | Focusing on the nonlinear wave equation with an inverse-square potential, we address the existence of solutions under assumptions which are optimal in some sense. In particular, the well-known theorem of Fritz John for a zero potential is shown to hold for potentials which are not necessarily small or positive. |
| Joint Institute for Advanced Study and Princeton University Number Theory Seminar | |
| Topic: | Equidistribution for Hecke eigenforms |
| Presenter: | Wenzhi Luo, Ohio State University |
| Date: | Monday, April 18, 2005, Time: 4:30 p.m., Location: Fine Hall 322 |
| Abstract: | In this talk, I'd like to describe my recent work with P.Sarnak concerning the equidistribution properties for Hecke eigenforms on the modular surface. We evaluate asymptotically the variance for the equidistribution by means of the trace formula and analyze its subtle arithmetic structure and connections to Hecke operators and central values of triple product L-functions. |
| 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: | Ergodic theory of semisimple lattices |
| Presenter: | Alexander Gorodnik, Caltech |
| Date: | Tuesday, April 19, 2005, Time: 11:30 a.m., Location: Fine Hall PL |
| Abstract: | Consider a measure-preserving action of a lattice (in semisimple Lie group) on a probability measure space. For such actions, we prove strong maximal inequality, mean and pointwise ergodic theorems. For lattices satisfying property (T), we get ergodic theorems with exponential rate of convergence. In the case of algebraic lattice actions that preserve finite measure, we show that all dense orbits are equidistributed. Our methods can be also applied to some infinite volume homogeneous spaces. This is joint work with Amos Nevo and Barak Weiss. |
| 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: | Smoothly Truncated Stable Distributions, GARCH-Models, and Option Pricing |
| Presenter: | Christian Menn, Cornell University |
| Date: | Tuesday, April 19, 2005, Time: 4:30 p.m., Location: Room E-219, Engineering Quad |
| Abstract: | Click here |
| 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 |
| 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 so-called "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 |
| Geometric Analysis Seminar | |
| Topic: | The structure of singularities of mean curvature flow |
| Presenter: | Bruce Kleiner, University of Michigan |
| Date: | Friday, April 22, 2005, Time: 3:00 p.m., Location: Fine Hall 314 |
| Geometry, Representation Theory, and Moduli Seminar | |
| Topic: | TBA |
| Presenter: | Maryam Mirzakhani, Princeton University |
| Date: | Friday, April 22, 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: | 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. |
| Joint Institute for Advanced Study and Princeton University Number Theory Seminar | |
| Topic: | TBA |
| Presenter: | Fred Diamond, Brandeis University |
| Date: | Monday, April 25, 2005, Time: 4:30 p.m., Location: Fine Hall 322 |
| 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. |
| Joint Analysis Seminar | |
| Topic: | TBA |
| Presenter: | Igor Rodnianski, Princeton University |
| Date: | Thursday, April 28, 2005, Time: 4:00 p.m., Location: Fine Hall 214 |
| Topology Seminar | |
| Topic: | TBA |
| Presenter: | Helmut Hofer, NYU |
| Date: | Thursday, April 28, 2005, Time: 4:30 p.m., Location: Fine Hall 314 |
| Geometric Analysis Seminar | |
| Topic: | Ricci flow on locally homogeneous closed 4-manifolds |
| Presenter: | Peng Lu, University of Oregon |
| Date: | Friday, April 29, 2005, Time: 3:00 p.m., Location: Fine Hall 314 |
| Abstract: | We discuss the Ricci flow on homogeneous 4-manifolds. After list the classification these manifolds, we show that there are families of initial metrics such that we can diagonalize them and the Ricci flow preserves the diagonalization, then we analyze the long time behavior of these families. |
MAY 2 - MAY 6, 2005 |
|
| Joint Analysis Seminar | |
| Topic: | TBA |
| Presenter: | Markus Keel, University of Minnesota |
| Date: | Thursday, May 5, 2005, Time: 4:00 p.m., Location: Fine Hall 214 |
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 E-219, Engineering Quad |
| Joint Institute for Advanced Study and Princeton University Number Theory Seminar *** Please note special date, time, and location | |
| Topic: | From Laplace to Langlands via Restriction from SO(2n+1) to SO(2n) |
| Presenter: | Benedict Gross, Harvard University |
| Date: | Thursday, May 12, 2005, Time: 1:30 p.m., Location: Fine Hall 314 |
| Mathematical Physics Seminar *** Please note special date, time, and location | |
| Topic: | On a Class of Exactly Integrable Radial Solutions of the Continuity and Euler Equations for nD systems with Long Range Interactions |
| Presenter: | Philippe Choquard, Institute of Theoretical Physics, Lausanne |
| Date: | Friday, May 13, 2005, Time: 3:15 p.m., Location: Jadwin Hall 343 |
| Abstract: | Hamiltonian fluids with Newtonian or Coulombian self-interactions in nD are considered. Exact integrability of radial solutions of the corresponding Euler, Poisson and continuity equations is shown to result from the existence of two constants of integration. Representative examples of implicit solutions are given for the pure attractive and repulsive systems for the models with homogenous and compensating background densities, i.e., the One Component Plasma and the model of Cold Dark Matter in an expanding universe. |
MAY 16 - MAY 20, 2005 |
|
| Operations Research and Financial Engineering Seminar *** Please note special day | |
| Topic: | TBA |
| Presenter | Holger Dette, Ruhr-Universität Bochum, Germany |
| Date: | Monday, May 16, 2005, Time: 4:30 p.m., Location: Room E-219, Engineering Quad |