APRIL 20 - APRIL 22, 2005 |
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| Graduate Student Seminar | |
| Topic: | Linear invariants of points in the complex plane |
| Presenter: | Andrew Snowden, Princeton University |
| Date: | Wednesday, April 20, 2005, Time: 12:30 p.m., Location: Fine Hall 1201 |
| Abstract: | The general linear group GL(2, C) acts on the complex plane (together with infinity) via linear fractional transformations. One of the classical problems of invariant theory is to describe the algebraic expressions in n points which remain invariant under the group action. In 1894 Kempe gave a beautiful and elementary answer to one aspect of this problem, which I will present. I will also mention the relationship of this problem to that of finding linear invariants of polynomials (such as the discriminant) and some recent work I have been involved with on this problem. |
| 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: | Higher-rank Donaldson invariants for four-manifolds |
| Presenter: | Peter Kronheimer, Harvard University |
| Date: | Thursday, April 21, 2005, Time: 4:30 p.m., Location: Fine Hall 314 |
| Joint Institute for Advanced Study and Princeton University Number Theory Seminar | |
| Topic: | The weight part of Serre's conjecture over totally real fields |
| Presenter: | Fred Diamond, Brandeis University |
| Date: | Friday, April 22, 2005, Time: 2:00 p.m., Location: Fine Hall 801 |
| Abstract: | Serre conjectured that all continuous, irreducible, odd $\rho:G_{\mathbf{Q}} \to \mathrm{GL}_2(\overline{\mathbf{F}}_p)$ arise from modular forms. If $\rho$ is modular, then proven refinements provide recipes for the possible weights and levels of the forms giving rise to it in terms of the local behavior of $\rho$. A natural generalization to the context of a totally real field $F$ predicts that all continuous, irreducible, totally odd $\rho:G_F \to {\mathrm{GL}}_2(\overline{\mathbf{F}}_p)$ arise from Hilbert modular forms. The recipe for the possible levels is similar to the case of $F= \mathbf{Q}$, but the (conjectural) recipe for the weights reveals features not so apparent for $F= \mathbf{Q}$. In particular, if $\rho$ is locally reducible at a prime $\mathcal P$ over $p$, then the possible weights depend strongly on the corresponding extension of local characters. If $\rho$ is locally semisimple at $\mathcal P$, then the recipe can be described in terms of the reduction of a corresponding irreducible characteristic zero representation of $\mathrm{GL}_2(\mathcal{O}_F/\mathcal{P})$. |
| 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 |
| Geometric Analysis Seminar *** Please note special time and location | |
| Topic: | Spectral invariants on surfaces and Markov Chains |
| Presenter: | Jean Steiner, Courant Institute |
| Date: | Friday, April 22, 2005, Time: 4:30 p.m., Location: Fine Hall 214 |
| Abstract: | In this talk we will consider Green's functions on surfaces and on discrete Markov chains. In both settings, the regularized trace of the Laplacian emerges as an interesting spectral invariant, and we will consider relevant analogies and probabilistic interpretations. |
| 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 |
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| Operations Research and Financial Engineering Seminar *** Special series of lectures *** | |
| Topic: | Jump diffusion models with applications in credit risk and option pricing |
| Presenter: | Steve Kou, Columbia University |
| Date: | Monday, April 25, 2005, Time: 3:00 p.m., Location: Room E-225, Engineering Quad |
| Abstract: | The topics to be covered include: (1) Modeling credit spread, implied volatility, optimal capital structure with endogenous default and jump risk (2) First passage times for jump diffusion processes (3) Analytical approximations for finite-maturity American options. (4) Analytical solutions for barrier and lookback options. |
| 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: | On the local behaviour of ordinary Galois representations |
| Presenter: | Eknath Ghate, Tata Institute |
| Date: | Monday, April 25, 2005, Time: 4:30 p.m., Location: Fine Hall 322 |
| Abstract: | Let $f$ be a primitive cusp form of weight at least 2, and let $\rho_f$ be the $p$-adic Galois representation attached to $f$. If $f$ is $p$-ordinary, then it is known that the restriction of $\rho_f$ to a decomposition group at $p$ is `upper triangular'. If in addition $f$ has CM, then this representation is even `diagonal'. In this paper we provide evidence for the converse. More precisely, we show that the local Galois representation is not diagonal, for all except possibly finitely many of the arithmetic members of a non-CM family of $p$-ordinary forms. We assume $p$ is odd, and work under some technical conditions on the residual representation. We also settle the analogous questionfor $p$-ordinary $\Lambda$-adic forms, under similar conditions. This is joint work with Vinayak Vatsal. |
| Algebraic Geometry Seminar | |
| Topic: | Holomorphic Forms and Birational Geometry |
| Presenter: | Tie Luo, UTA and NSF |
| Date: | Tuesday, April 26, 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. |
| Operations Research and Financial Engineering Seminar *** Special series of lectures *** | |
| Topic: | Jump diffusion models with applications in credit risk and option pricing |
| Presenter: | Steve Kou, Columbia University |
| Date: | Wednesday, April 27, 2005, Time: 3:00 p.m., Location: Room E-225, Engineering Quad |
| Abstract: | The topics to be covered include: (1) Modeling credit spread, implied volatility, optimal capital structure with endogenous default and jump risk (2) First passage times for jump diffusion processes (3) Analytical approximations for finite-maturity American options. (4) Analytical solutions for barrier and lookback options. |
| Ergodic Theory and Statistical Mechanics Seminar | |
| Topic: | A GUE central limit theorem and universality of last passage percolation passage times in thin rectangles |
| Presenter: | Toufic Suidan, Courant Institute |
| Date: | Thursday, April 28, 2005, Time: 2:00 p.m., Location: Fine Hall 322 |
| Abstract: | I will discuss a central limit theorem whose limit is the Gaussian unitary ensemble Tracy-Widom distribution. This CLT is intimately related to first and last passage percolation problems. In addition, I will discuss the O'Connell-Yor procedure and it's relation to the Tracy-Widom top n eigenvalue joint distribution. This is joint work with Jinho Baik. |
| 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 |
| Operations Research and Financial Engineering Seminar *** Special series of lectures *** | |
| Topic: | Jump diffusion models with applications in credit risk and option pricing |
| Presenter: | Steve Kou, Columbia University |
| Date: | Friday, April 29, 2005, Time: 11:00 a.m., Location: Room E-225, Engineering Quad |
| Abstract: | The topics to be covered include: (1) Modeling credit spread, implied volatility, optimal capital structure with endogenous default and jump risk (2) First passage times for jump diffusion processes (3) Analytical approximations for finite-maturity American options. (4) Analytical solutions for barrier and lookback options. |
| 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. |
| Geometric Analysis Seminar *** Note special time | |
| Topic: | Combinatorial Yamabe flow |
| Presenter: | David Glickenstein, MIT |
| Date: | Friday, April 29, 2005, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: | We shall study a piecewise-linear geometry which lies somewhere between the geometry of graphs and the geometry of Riemannian manifolds. In our context, the geometry comes from a simplicial complex whose vertices are given weights which determine the lengths of edges (so the vertices and edges form a weighted graph), and hence the area and volume of higher dimensional simplices. Combinatorial Yamabe flow is a way to deform the geometry into something less complicated via an ordinary differential equation, an analogue of the Ricci or Yamabe flow in Riemannian geometry designed for a piecewise-linear object instead of a smooth manifold. Such equations may be helpful in applying the successful methods of geometric evolution equations to new realms of problems in physics, topology, algebraic geometry, numerical analysis, graph theory, and other fields. The methods will involve basic Euclidean geometry as well as the application of simple ideas from partial differential equations to functions on graphs. This talk will be self-contained and should be easily accessible to graduate students and those in other fields. |
MAY 2 - MAY 6, 2005 |
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| Geometric Analysis Seminar *** Please note special date | |
| Topic: | Higher order conformal covariant operators on the sphere |
| Presenter: | Fengbo Hang, Michigan State University |
| Date: | Thursday, May 5, 2005, Time: 3:00 p.m., Location: Fine Hall 314 |
| Abstract: | The standard metric on the sphere minimizes the scaling invariant scalar curvature integral. This may be rewritten in terms of variational problems for conformal Laplacian operator and is equivalent to the classical sharp Sobolev inequality. We will discuss similar problems for the Q-curvature and 2mth order conformal covariant operator on the sphere, which was introduced by Graham-Jenne-Mason-Sparling and Branson. The case 2m>n (the dimension) is of particular interest since negative exponent appears. |
| 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 |
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| Operations Research and Financial Engineering Seminar | |
| Topic: | On the borders of Statistics and Computer Science |
| Presenter: | Peter Bickel, University of California, Berkeley |
| Date: | Tuesday, May 10, 2005, Time: 4:30 p.m., Location: Room E-219, Engineering Quad |
| Abstract: | Machine learning in computer science and prediction and classification in statistics are essentially equivalent fields. I will try to illustrate the relation between theory and practice in this huge area by a few examples and results. In particular I will try to address an apparent puzzle: Worst case analyses, using empirical process theory, seem to suggest that even for moderate data dimension and reasonable sample sizes good prediction (supervised learning) should be very difficult. On the other hand, practice seems to indicate that even when the number of dimensions is very much higher than the number of observations, we can often do very well. We also discuss a new method of dimension estimation and some features of cross validation. |
| 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 |
| Topology Seminar | |
| Topic: | Circle actions on 5--manifolds |
| Presenter: | Janos Kollar, Princeton University |
| Date: | Thursday, May 12, 2005, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: | The aim is to give a classification of simply connected compact 5--manifolds which admit a fixed point free circle action. There are several restrictions and some constructions, but also some unknown cases between the two. |
| 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: 3:00 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 |
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| 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 |