APRIL 27 - 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: | Wednesday, April 27, 2005, Time: 4:30 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 ******* POSTPONED UNTIL FALL SEMESTER 2005 *********** | |
| Topic: | TBA |
| Presenter: | Igor Rodnianski, Princeton University |
| Date: | Thursday, April 28, 2005, Time: 4:00 p.m., Location: Fine Hall 214 |
| Topology Seminar | |
| Topic: | Fredholm Theory for Polyfolds |
| 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. |
| Joint Institute for Advanced Study and Princeton University Number Theory Seminar | |
| Topic: | Analytic continuation of overconvergent modular forms |
| Presenter: | Payman Kassaei, McGill University |
| Date: | Friday, April 29, 2005, Time: 2:00 p.m., Location: Fine Hall 801 |
| Abstract: | It is well-known that to study the space of modular forms of a fixed weight and level over $Q_P$, it is useful to embed this finite-dimensional space in a $p$-adic Banach space of overconvergent modular forms, and use methods of $p$-adic analysis and geometry. An important theorem of Coleman (Inv. Math, 96) states that overconvergent modular forms of small slope are classical, and hence provides us with a way to identify elements of the above finite-dimensional space within p-adic Banach spaces of overconvergent modular forms. I will present a new method for proving (a generalization of) Coleman's theorem which applies to give similar results in the context of quaternionic and unitary Shimura curves. The new method is based on analytic continuation of modular forms and uses a result of Buzzard (JAMS 03). I will first briefly review $p$-adic overconvergent modular forms, and then present the steps involved in the method. |
| 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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| Group Actions and Automorphic Forms Seminar | |
| Topic: | Ergodic theory for the horocycle flow on periodic hyperbolic surfaces (joint with F. Ledrappier) |
| Presenter: | Omri Sarig, Penn State University |
| Date: | Tuesday, May 3, 2005, Time: 11:30 a.m., Location: Fine Hall PL |
| Abstract: | The horocycle flow of a non-geometrically finite hyperbolic surface may have many different (infinite) ergodic invariant Radon measures. (This should be contrasted with co-compact or co-finite volume case where there is just one non-trivial measure - up to scaling). We classify these measures for the class of periodic surfaces: regular covers of surfaces of finite volume. It turns out that in this case there are as many measures as there are positive eigenfunctions for the Laplacian of the surface. In some situations, only one of these measures is "relevant" from an ergodic theoretic point of view. |
| 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 ***** CANCELLED ******** | |
| Topic: | TBA |
| Presenter: | Markus Keel, University of Minnesota |
| Date: | Thursday, May 5, 2005, Time: 4:00 p.m., Location: Fine Hall 214 |
| Geometry, Representation Theory, and Moduli Seminar **** Please note special date and location | |
| Topic: | TBA |
| Presenter: | Maryam Mirzakhani, Princeton University |
| Date: | Thursday, May 5, 2005, Time: 4:30 p.m., Location: Fine 322 |
MAY 9 - MAY 14, 2005 |
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| Group Actions and Automorphic Forms Seminar | |
| Topic: | TBA |
| Presenter: | Dmitry Kleinbock, Brandeis University |
| Date: | Tuesday, May 10, 2005, Time: 11:30 a.m., Location: Fine Hall PL |
| 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: | A Simple Nonparametric Estimator of a Monotone Regression Function |
| Presenter | Holger Dette, Ruhr-Universität Bochum, Germany |
| Date: | Monday, May 16, 2005, Time: 4:30 p.m., Location: Room E-219, Engineering Quad |
| Abstract: | In this paper a new method for monotone estimation of a regression function is proposed. The estimator is obtained by the combination of a density and a regression estimate and is appealing to users of conventional smoothing methods as kernel estimators, local polynomials, series estimators or smoothing splines. The main idea of the new approach is to construct a density estimate from the estimated values of the regression function to use these data for the calculation of an estimate of the inverse of the regression function. The final estimate is then obtained by a numerical inversion. Compared to the conventionally used techniques for monotone estimation the new method is computationally more efficient, because it does not require constrained optimization techniques for the calculation of the estimate. We prove asymptotic normality of the new estimate and compare the asymptotic properties with the unconstrained estimate. In particular it is shown that for kernel estimates or local polynomials the monotone estimate is first order asymptotically equivalent to the unconstrained estimate. We also illustrate the performance of the new procedure by means of a simulation study. References: [1] Holger Dette, Natalie Neumeyer, Kay F. Pilz (2004). A simple nonparametric estimator of a monotone regression function, under Revision. Technical Report Ruhr-Universitat Bochum. [2] Holger Dette, Natalie Neumeyer, Kay F. Pilz (2005). A note on nonparametric estimation of the effective dose in quantal bioassay, J. Americ. Statist. Assoc., to appear. Technical Report Ruhr-Universit¨at Bochum. |