MAY 11 - MAY 14, 2005 |
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| Graduate Student Seminar | |
| Topic: | On the total curvature of knots |
| Presenter: | Josh Green, Princeton University |
| Date: | Wednesday, May 11, 2005, Time: 12:30 p.m., Location: Fine Hall 1201 |
| Abstract: | The title for this talk is stolen from a paper that John Milnor wrote when he was a freshman at Princeton. In it he answers a famous question of Borsuk by showing that a non-trivial knot in 3-space has total curvature greater than 4*pi. I will give a recent and very charming proof of this fact due to Ari Turner, which he also discovered while an undergraduate here. Since the talk is just about undergraduate research, it will be accessible to everyone. |
| Special Analysis Seminar *** Please note special date | |
| Topic: | Complex analytic zeroes of smooth functions |
| Presenter: | Nefton Pali, Princeton University |
| Date: | Wednesday, May 11, 2005, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: | We will explain a differential criteria which allows to find complex analytic zeros of smooth functions. An application of our criteria concerns a method which allows to find complex analytic sets which are obtained by smooth deformations of other ones. We will give a idea of the proof in some particular case. The principal difficulty of the proof is the solution of a quasi-linear differential equation with standard $\bar{\partial}$ as its principal term. We are able to find a solution of this differential equation, using a Nash-Moser fast iteration method. |
| Joint Institute for Advanced Study and Princeton University Number Theory Seminar ***CANCELLED*** | |
| 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. |
MAY 23 - MAY 27, 2005 |
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| Special Analysis Seminar *** Please note special date, time, and location | |
| Topic: | Uncertainty inequalities on groups of polynomial growth |
| Presenter: | Fulvio Ricci, Scuola Norm. di Pisa |
| Date: | Wednesday, May 25, 2005, Time: 3:00 p.m., Location: Fine Hall 314 |