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| Geometric Analysis Seminar *** Please note special date and location | ||
| Topic: | Regularity of biharmonic maps into Riemannian manifolds | |
| Presenter: | Changyou Wang, University of Kentucky | |
| Date: | Wednesday, April 2, 2003, Time: 3:00 p.m., Location: Fine Hall 322 | |
| Abstract: | In this talk, I will consider both intrinsic and extrinsic biharmonic maps into general Riemannian manifolds. I will sketch the ideas to prove smoothness of biharmonic maps from domains of dimension four and partial regularity for stationary biharmonic maps from domains of dimensions five or above. The same theorems were previously proved by Chang-Wang-Yang when the target manifold is the standard sphere. | |
| Department Colloquium | ||
| Topic: | Stochastic Loewner Evolutions | |
| Presenter: | Stanislav Smirnov, Royal Institute of Technology, Stockholm | |
| Date: | Wednesday, April 2, 2003, Time: 4:30 p.m., Location: Fine Hall 314 | |
| Abstract: | We will talk about Loewner Evolutions driven by stochastic processes, starting with Scramm-Loewner Evolution. We will discuss fractal properties of their trajectories and their relation to scaling limits of lattice models. | |
| Ergodic Theory and Statistical Analysis Seminar | ||
| Topic: | Ergodic properties of boundary actions | |
| Presenter: | Tatiana Nagnibeda, Royal Institute of Technology, Stockholm | |
| Date: | Thursday, April 3, 2003, Time: 2:00 p.m., Location: Fine Hall 214 | |
| Abstract: | We shall discuss ergodic properties of the action of a subgroup H of a free group F on the Poisson boundary of the simple random walk on F. The action is ergodic if and only if the quotient F/H admit no non-constant bounded harmonic function. Methods from combinatorial group theory allow us to identify the conservative and the dissipative part of the action. We also present necessary and sufficient conditions of conservativity of the action in terms of geometry of the quotient. This is a joint work with R. Grigorhcuk and V. Kaimanovich. | |
| Joint Institute for Advanced Study /Princeton University/ Rutgers University Number Theory Seminar | ||
| Topic: | Zeros of families of elliptic curve L-functions | |
| Presenter: | Matthew Young, Rutgers University | |
| Date: | Thursday, April 3, 2003, Time: 4:15 p.m., Location: Hill Center 425 (Rutgers University) | |
| Joint Institute for Advanced Study /Princeton University/ Rutgers University Non-Linear Analysis Seminar | ||
| Joseph D'Atri Memorial Lecture | ||
| Topic: | On the Ricci Flow | |
| Presenter: | Richard Hamilton, Columbia University | |
| Date: | Thursday, April 3, 2003, Time: 4:30 p.m., Location: Hill Center 705 (Rutgers University) | |
| Graduate Student Seminar | ||
| Topic: | On Bowen's Construction of Gibbs measures | |
| Presenter: | Alexander I. Bufetov, Princeton University | |
| Date: | Friday, April 4, 2003, Time: 12:00 p.m., Location: Fine Hall 1201 | |
| Abstract: | A Gibbs measure for a stationary process is a natural generalization of a Markov measure. Roughly speaking, it is a measure for which distant past of the process has little influence over its future. For such measures, one can obtain limit theorems for the process and give explicit rates of convergence of time averages to the space average. In the talk, I shall review Bowen's classical construction of Gibbs measures. The talk would assume no background. | |
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| PACM Colloquium | ||
| Topic: |
Interval analysis and set-membership techniques in estimation |
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| Presenter: | Isabelle Braems, MAE, Princeton University | |
| Date: | Monday, April 7, 2003, Time: 4:00 p.m., Location: Fine Hall 214 | |
| Abstract: | Interval analysis has been developed more than four decades ago to control numerical round-off errors in computers, in a rigorous way. It has then reached many other fields (assisted proof demonstrations, numerical simulation, estimation…) and applications (biology, chemical engineering, economics, computer vision, robotics…) where guaranteed computations are essential. In this talk we shall focus on parameter and state estimation problem. We will emphasize how interval analysis permits to estimate in a guaranteed way a reliable enclosure of all the global minima in optimization problems, or of all the acceptable solutions in the bounded-error context. This talk will first briefly present (or recall) the bases of interval analysis. Several applications -including non-identifiable kinetic parameteridentification, reliable characterization of a thermal set-up, and robot localization- will illustrate the performance of this approach. | |
| Cohomology of Groups | ||
| Topic: | Cohomology and representations of finite group schemes Part I | |
| Presenter: | Julia Pevtsova, Institute for Advanced Study | |
| Date: | Tuesday, April 8, 2003, Time: 3:00 p.m., Location: Fine Hall 801 | |
| Abstract: | The study of the prime ideal spectrum of the mod p cohomology of a finite group was initiated by D.Quillen, whose description of the spectrum in terms of elementary abelian subgroups of the finite group is known as "Quillen's stratification theorem". In the subsequent work by Carlson and Avrunin-Scott, the spectrum of cohomology as well as all its conical closed subsets were given a representation-theoretic description. In these talks, we will mention the classical results for finite groups, then describe how the theory works (pointing out some major differences) for connected finite group schemes (e.g., restricted Lie algebras, Frobenius kernels of algebraic groups) and finish with a general set-up connecting the spectrum of cohomology and representation theory for any finite group scheme, which is a joint work with Eric Friedlander. This will be split into three lectures approximately as follows: -1) Quillen's stratification theorem and Carlson's rank varieties, 2) Cohomology of Frobenius kernels and one-parameter subgroups, 3) Cohomology of finite group schemes and maps from the group algebra of a cyclic group. | |
| Algebraic Geometry Seminar | ||
| Topic: | Threefold divisorial contractions contracting an irreducible divisor onto a curve | |
| Presenter: | Nikos Tziolas, Max Planck Institute | |
| Date: | Tuesday, April 8, 2003, Time: 4:30 p.m., Location: Fine Hall 322 | |
| Abstract: | Divisorial contractions is one of the elementary maps that appear in the minimal model program, and their understanding is essential for the study of the birational geometry of threefolds. Given a curve C in a Gorenstein terminal threefold X, I will give conditions depending on the singularities of X and the equations of C, for the existence of a terminal divisorial contraction Y---->X that contracts an irreducible divisor E onto C. I will classify all such contractions and describe their singularities. | |
| Mathematical Physics Seminar | ||
| Topic: | Quantum chaos: universal versus system-specific fluctuations | |
| Presenter: | Oriol Bohigas, Laboratoire de Physique Theorique et Modeles Statistiques (LPTMS), Orsay, France | |
| Date: | Tuesday, April 8, 2003, Time: 4:30 p.m., Location: Jadwin A06 | |
| Abstract: | Are there quantum signatures, for instance in the spectral properties, of the underlying regular or chaotic nature of the corresponding classical motion? Are there universality classes? Within this framework several properties will be discussed. Results will be illustrated with two very different systems: atomic nuclei and the Riemann zeta function. | |
| Topology Seminar *** Please note special date | ||
| Topic: | The Milnor degree and quantum orders of 3-manifolds | |
| Presenter: | Paul Melvin, Bryn Mawr College and the Institute for Advanced Study | |
| Date: | Tuesday, April 8, 2003, Time: 4:30 p.m., Location: Fine Hall 314 | |
| Abstract: | The general purpose of this talk is to indicate how to use quantum invariants to address questions in classical low-dimensional topology. In particular, we will show that the quantum orders of 3-manifolds (a measure of divisibility properties of quantum invariants with values in cyclotomic rings of integers) restrict the class of links in the 3-sphere that can arise in constructing a given 3-manifold by surgery. This is joint work with Tim Cochran. | |
| Department Colloquium | ||
| Topic: | Universality for mathematical and physical systems | |
| Presenter: | Percy Deift, New York University | |
| Date: | Wednesday, April 9, 2003, Time: 4:30 p.m., Location: Fine Hall 314 | |
| Abstract: | All physical systems in equilibrium
obey the laws of thermodynamics. In other words, whatever the precise nature
of the interaction between the atoms and molecules at the microscopic level,
at the macroscopic level, physical systems exhibit universal behavior in the
sense that they are all governed by the same laws and formulae of
thermodynamics. The speaker will recount some recent history of universality ideas in physics starting with Wigner's model for the scattering of neutrons off large nuclei and show how these ideas have led mathematicians to investigate universal behavior for a variety of mathematical systems. This is true not only for systems which have a physical origin, but also for systems which arise in a purely mathematical context such as the Riemann hypothesis, and a version of the card game solitaire called patience sorting. |
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| Cohomology of Groups | ||
| Topic: | Cohomology and representations of finite group schemes Part II | |
| Presenter: | Julia Pevtsova, Institute for Advanced Study | |
| Date: | Thursday, April 10, 2003, Time: 3:00 p.m., Location: Fine Hall 801 | |
| Abstract: | See abstract from April 8, 2003 | |
| Joint Institute for Advanced Study /Princeton University/ Rutgers University Number Theory Seminar | ||
| Topic: | Automorphic Distributions and Summation Formulas | |
| Presenter: | Stephen Miller, Rutgers University | |
| Date: | Thursday, April 10, 2003, Time: 4:15 p.m., Location: Hill Center 705 (Rutgers University) | |
| Abstract: | The talk will center on the analysis of the distributional boundary values of automorphic forms, and some applications of this theory to GL(3,Z)\GL(3,R). Foremost among these is a formula ala Poisson/Voronoi for sums weighted by the Fourier coefficients/Hecke eigenvalues of automorphic forms. This can be used to demonstrate cancellation in such sums, and was an ingredient of the recent sharp estimate of Sarnak-Watson for L_4 norms of Laplace eigenfunctions. I plan to discuss the problem of finding cancellation in sums of the form a_{n,1} exp(2 pi i n alpha), where alpha is irrational. (joint work with Wilfried Schmid). | |
| Geometric Analysis Seminar | ||
| Topic: | A Bernstein problem for special Lagrangian equations | |
| Presenter: | Yu Yuan, University of Washington | |
| Date: | Friday, April 11, 2003, Time: 3:00 p.m., Location: Fine Hall 314 | |
| Abstract: | In this talk, we derive a Bernstein type result for the special Lagrangian equation, namely, any global convex solution must be quadratic. In terms of minimal surfaces, the result says that any global minimal Lagrangian graph with convex potential must be a hyper-plane. | |
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| PACM Colloquium | ||
| Topic: | Elastic strain in epitaxial thin films | |
| Presenter: | Russel Caflisch, University of California at Los Angeles | |
| Date: | Monday, April 14, 2003, Time: 4:00 p.m., Location: Fine Hall 214 | |
| Abstract: | In an epitaxial thin films the lattice properties of the film are determined by those of the underlying substrate. A mismatch between the lattice spacing of the substrate and film will introduce a strain into the film, which can significantly influence the material structure and properties. This talk will describe analysis and computation for strain in an epitaxial film with harmonic interatomic potentials and intrinsic surface stress. The resulting force field at a step and the interactions between steps will be described. Generalizations to epitaxial wires and particles will be presented. | |
| Department Colloquium | ||
| Topic: | TBA | |
| Presenter: | Grisha Perelman, St. Petersburg | |
| Date: | Wednesday, April 16, 2003, Time: 4:30 p.m., Location: Fine Hall 314 | |
| Ergodic Theory and Statistical Analysis Seminar | ||
| Topic: | A spectral gap property for measures;applications to the Anderson model | |
| Presenter: | Carol Shubin, California State University Northridge | |
| Date: | Thursday, April 17, 2003, Time: 2:00 p.m., Location: Fine Hall 214 | |
| Abstract: | We discuss products of random matrices as they arise from studying the discrete Anderson model on the strip. We obtain a quantitative bound of the largest Lyapunov exponent. This was joint work with T. Wolff and R. Vakilian. We discuss extensions of this work by T. Wolff, first to $PSL(2,\R)$ and then more generally to noncompact semi-simple Lie groups. | |
| Topology Seminar | ||
| Topic: | TBA | |
| Presenter: | Alejandro Adem, University of Wisconsen | |
| Date: | Thursday, April 17, 2003, Time: 4:30 p.m., Location: Fine Hall 314 | |
| Geometric Analysis Seminar | ||
| Topic: | A general Liouville type theorem for some conformally invariant fully nonlinear equations | |
| Presenter: | Aobing Li, Rutgers University | |
| Date: | Friday, April 18, 2003, Time: 3:00 p.m., Location: Fine Hall 314 | |
| Abstract: | In this talk, I will talk about some general Liouville type theorem for some conformally invariant fully nonlinear equations on the Euclidean space, i.e., we classified all the classical positive solutions of these equations. I will also present a Liouville type theorem for the same equation but on the upper half plane with the boundary condition. These are the joint works with Yanyan Li. | |
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| Analysis Seminar | ||
| Topic: | From Hilbert's variational principle to Einstein's equations as a well posed initial value problem | |
| Presenter: | James York, Cornell University | |
| Date: | Monday, April 21, 2003, Time: 4:00 p.m., Location: Fine Hall 314 | |
| PACM Colloquium | ||
| Topic: | Questions and models associated with the deliberate release of biological agents and their consequences | |
| Presenter: | Carlos Castillo-Chavez, Cornell University | |
| Date: | Monday, April 21, 2003, Time: 4:00 p.m., Location: Fine Hall 214 | |
| Abstract: | The talk will include two intertwined
parts. One will deal with the 'transmission dynamics of behaviors" and
the second with the spread of epidemics on various topologies. The concept of
(a fixed) core group was introduced in epidemiology by Hethcote and Yorke
(1984) in the context of gonorrhea dynamics. Hadeler and Castillo-Chavez
(1995) and Huang and Castillo-Chavez (2002) have shown that core group
dynamics (in non-structured and structured populations) have important
implications on disease transmission and control. We use these results as the
starting point for the development of simple models for the dynamics of drug
use (ecstasy), collaborative learning and ideologically driven behaviors
(fanaticism).
The results point out to the tremendous impact that "invading" small subpopulations of individuals with strong behaviors can have on the establishment of drug cultures, fanatic ideologies or good learning environments. The models developed naturally support sub-critical bifurcations with troublesome implications for disease dynamics and control (Castillo-Chavez and Baojun Song, 2003). Intertwined with the first topic, I will discuss the spread of diseases on different topologies. I will address some issues that are relevant including recent efforts to define worst-case scenarios or to model epidemics on mass-transportation systems (Gerardo Chowell et al. 2003 and Castillo-Chavez and Baojun, 2003). |
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| Algebraic Geometry Seminar | ||
| Topic: | Spaces of rational curves on Fano hypersurfaces | |
| Presenter: | Jason Starr, MIT | |
| Date: | Tuesday, April 22, 2003, Time: 4:30 p.m., Location: Fine Hall 322 | |
| Abstract: | I will discuss two methods for giving lower bounds on the Kodaira dimensions of spaces of rational curves on Fano hypersurfaces. The motivation comes from the open problem of finding a Fano variety X which is not unirational. The approach, suggested by Kollár, is to find an X which contains no rational surface passing through a very general point of X. The first step is to show that the varieties parametrizing rational curves on X are themselves not uniruled, e.g. the varieties parametrizing rational curves on X have non-negative Kodaira dimension. Part of this research is joint work with A. J. de Jong. | |
| Department Colloquium | ||
| Topic: | Stationary Determinantal Processes (Fermionic Lattice Gases) | |
| Presenter: | Russell Lyons, Indiana University | |
| Date: | Wednesday, April 23, 2003, Time: 4:30 p.m., Location: Fine Hall 314 | |
| Abstract | Eigenvalues of random matrices arise in various areas of physics and mathematics. The most-studied such probability measures have a determinantal form. Several people have studied other specific determinantal processes, as well as a general theory. We shall discuss the general theory of stationary random fields on integer lattices that are defined via minors of multi-dimensional Toeplitz matrices. Explicit examples include combinatorial models, finitely dependent processes, and renewal processes in one dimension. Among the interesting properties of these processes, we focus mainly on whether they have a phase transition analogous to that which occurs in statistical mechanics. We describe necessary and sufficient conditions for the existence of such a phase transition and give several examples to illustrate the theorem. This is joint work with Jeff Steif. | |
| Ergodic Theory and Statistical Analysis Seminar | ||
| Topic: | Diffusive and Coalescing Flows | |
| Presenter: | Yves Le-jan, Université Paris-Sud | |
| Date: | Thursday, April 24, 2003, Time: 2:00 p.m., Location: Fine Hall 214 | |
| Abstract | Coalescence and stickyness are introduced in a simple exemple. Then the compressible Kraichnan model for turbulent advection motivates new developments in the theory of flows driven by sochastic differential equations. It appears that some of these flows cannot be generated by a gaussian noise. | |
| Joint Institute for Advanced Study /Princeton University/ Rutgers University Non-Linear Analysis Seminar | ||
| Topic: | On the time evolution and steady states for inelastic Boltzmann equations | |
| Presenter: | Irene Gamba, University of Texas at Austin | |
| Date: | Thursday, April 24, 2003, Time: 4:00 p.m., Location: Fine Hall 214 | |
| Abstract: | Kinetic models for inelastic
collisions provide an approach to understanding regimes of rapid
granular flows, both for cooling and diffusive states. Stochastic simulations
and experimental measurements indicate these models admite steady states
described by non-classical probabilities with overpopulated tails with respect
to Gaussian behavior. We rigourusly prove that that is the case for some
Boltzmann type equations.
In the first part of the lecture we look at a short survey of related work from the last two years on homogeneous inelastic Boltzmann models. In the second part we shall consider the homogeneous inelastic Boltzmann equation for hard spheres with a diffusive term representing driven granular flows by a random background acceleration. We show of existence and uniqueness of strong solutions with all moment bounded, to the initial value problem. In addition we show the existence of stationary solutions which are pointwise bounded below by $C \exp-(r|v|^b)$, with $r$ depending on the energy bounds and b depending on the rate of collisions to cross section and the forcing term and $b=3/2$. Finally, we present rigourous results on tail decay for solutions of inelastic Boltzmann equation for hard spheres with forcing terms corresponding to diffusive, friction and shear flow, separately. This work is partly in collaboration with C. Villani, A. Bobylev and V. Panferov. |
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| Joint Institute for Advanced Study /Princeton University/ Rutgers University Number Theory Seminar | ||
| Topic: | Are motivic L-functions rational? | |
| Presenter: | Michael Larsen, Indiana | |
| Date: | Thursday, April 24, 2003, Time: 4:15 p.m., Location: Fine Hall 322 | |
| Geometric Analysis Seminar | ||
| Topic: | TBA | |
| Presenter: | Xiaodong Wang, MIT | |
| Date: | Friday, April 25, 2003, Time: 3:00 p.m., Location: Fine Hall 314 | |
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| PACM Colloquium | ||
| Topic: | On the time evolution and steady states for inelastic Boltzmann equations | |
| Presenter: | Irene Gamba, University of Texas at Austin | |
| Date: | Monday, April 28, 2003, Time: 4:00 p.m., Location: Fine Hall 214 | |
| Algebraic Geometry Seminar | ||
| Topic: | Near by fundamental group of Mumford Tate curves | |
| Presenter: | Tomohide Terasoma, Institute for Advanced Study | |
| Date: | Tuesday, April 29, 2003, Time: 4:30 p.m., Location: Fine Hall 322 | |
| Abstract: | We will study a problem of R.Hain. The main result says that the period of the arithmetic mapping class group can be written using multiple zeta values. A similar Galois theoretic result was obtained by Ihara-Nakamura. | |
| Department Colloquium | ||
| Topic: | TBA | |
| Presenter: | S.R.Srinivasa Varadhan, New York University | |
| Date: | Wednesday, April 30, 2003, Time: 4:30 p.m., Location: Fine Hall 314 | |
| Joint Institute for Advanced Study /Princeton University/ Rutgers University Number Theory Seminar | ||
| Topic: | Counting number fields of bounded discrminant | |
| Presenter: | Jordan Ellenberg, Princeton University | |
| Date: | Thursday, May 1, 2003, Time: 4:15 p.m., Location: Fine Hall 322 | |
| Topology Seminar *** Please note - rescheduled from April 3, 2003 | ||
| Topic: | One parameter families of Calabi-Yau threefolds | |
| Presenter: | John Morgan, Columbia University | |
| Date: | Thursday, May 1, 2003, Time: 4:30 p.m., Location: Fine Hall 314 | |
| Abstract: | There are lots of examples of one-parameter families of Calabi-Yau threefolds occurring as hypersurfaces or complete intersections in toric varieties. We study the resulting variations of Hodge structure from these families and compare the results to all possible variations and to various conjectures arising out of mirror symmetry conjectures. | |
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| Department Colloquium | ||
| Topic: | The lost proof of Loewner's theorem | |
| Presenter: | Barry Simon, Caltech | |
| Date: | Wednesday, May 7, 2003, Time: 4:30 p.m., Location: Fine Hall 314 | |
| Abstract | A real-valued function, F, on an interval (a,b) is called matrix monotone if F(A) < F(B) whenever A and B are finite matrices of the same order with eigenvalues in (a,b) and A < B. In 1934, Loewner proved the remarkable theorem that F is matrix monotone if and only if F is real analytic with continuations to the upper and lower half planes so that Im F > 0 in the upper half plane. This deep theorem has evoked enormous interest over the years and a number of alternate proofs. There is a lovely 1954 proof that seems to have been "lost" in that the proof is not mentioned in various books and review article presentations of the subject, and I have found no references to the proof since 1960. The proof uses continued fractions. I'll provide background on the subject and then discuss the lost proof and a variant of that proof which I've found, which avoids the need for estimates, and proves a stronger theorem. | |
| Mathematical Physics Seminar *** Please note special date and time | ||
| Topic: | TBA | |
| Presenter: | Barry Simon, Caltech | |
| Date: | Thursday, May 8, 2003, Time: 2:00 p.m., Location: Jadwin A06 | |
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| Algebraic Geometry Seminar | ||
| Topic: | TBA | |
| Presenter: | B. Guralnick | |
| Date: | Tuesday, May 13, 2003, Time: 4:30 p.m., Location: Fine Hall 322 | |