MAY 4 - MAY 6, 2005 |
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| Ergodic Theory and Statistical Mechanics Seminar | |
| Topic: | Stability of the absolutely continuous spectrum of random Schroedinger operators on tree graphs |
| Presenter: | Simone Warzel, Princeton University |
| Date: | Thursday, May 5, 2005, Time: 2:00 p.m., Location: Fine Hall 322 |
| Abstract: | We consider radial tree extensions of periodic or quasi-periodic one-dimensional Schroedinger operators and establish the stability of their absolutely continous spectrum under weak but extensive perturbations by a random potential. |
| 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: | Measure rigidity and p-adic Littlewood type problems |
| Presenter: | Dmitry Kleinbock, Brandeis University |
| Date: | Tuesday, May 10, 2005, Time: 11:30 a.m., Location: Fine Hall PL |
| Abstract: | A drama in four acts, loosely based on my new work with Manfred Einsiedler. Brief synopsis: recent developments in measure rigidity of higher rank actions on homogeneous spaces due to Lindenstrauss and Einsiedler-Katok-Lindenstrauss give rise to new results and conjectures in so-called multiplicative Diophantine approximation over the product of real and p-adic fields. |
| Algebraic Geometry Seminar | |
| Topic: | Hilbert 14-th Problem and Cox rings |
| Presenter: | Ana-Maria Castravet, University of Texas |
| Date: | Tuesday, May 10, 2005, Time: 4:30 p.m., Location: Fine Hall 322 |
| Abstract: | I will describe generators of the total coordinate ring of the blow-up of $P^n$ in any number of points that lie on a rational normal curve. As a corollary, I will show that the algebra of invariants of an action of the two-dimensional additive group introduced by Nagata is finitely generated by certain explicit determinants. The finite generation of certain algebras of invariants of actions of additive groups related to T-shaped Dynkin diagrams introduced by Mukai also follows. This is joint work with E. Tevelev. |
| 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. |