|
|
||
| Special Seminar | ||
| Topic: | Hamilton's work on the Ricci flow | |
| Presenter: | Simon Brendle, Princeton University | |
| Date: | Tuesday, April 15, 2003, Time: 3:00 p.m., Location: Fine Hall 601 | |
| Algebraic Geometry Seminar | ||
| Topic: | Geometric Proofs of Horn and Saturation conjectures | |
| Presenter: | Prakash Belkale, Chapel Hill | |
| Date: | Tuesday, April 15, 2003, Time: 4:30 p.m., Location: Fine Hall 322 | |
| Abstract: | We are going to describe a geometric approach to the Horn and Saturation conjectures (due to Klyachko-Knutson-Tao). The Horn conjecture is about intersection theory in Grassmann varieties. The Saturation Conjecture is a a statement on the multiplicities in the tensor product of two irreducible representation of Gl(n). If time permits we will describe the Quantum generalisations of these conjectures and implications to transversality fo Schubert calculus in char p. | |
| Mathematical Physics Seminar | ||
| Topic: | An extension of the Harish-Chandra (Itzykson-Zuber) formula to non-unitary symmetries | |
| Presenter: | Edouard Brezin, Lab. Physique Theorique, Ecole Normale Superieure | |
| Date: | Tuesday, April 15, 2003, Time: 4:30 p.m., Location: Jadwin A06 | |
| Abstract: | The Itzykson-Zuber formula plays a central role in matrix models. It is used for chains of matrices, random scatterers (H=H_0+V, V random), etc. For the unitary group, the formula is WKB exact. For non-unitary groups (GOE, GSE, ...) there is a semi-classical expansion which, surprisingly, terminates after a finite number of terms in some cases of interest. | |
| Discrete Mathematics Seminar | ||
| Topic: | Coloring Powers of Hamilton Cycles from Random Lists | |
| Presenter: | Michael Krivelevich, Tel Aviv University | |
| Date: | Wednesday, April 16, 2003, Time: 2:15 p.m., Location: Fine Hall 224 | |
| Abstract: | View abstract | |
| Department Colloquium *** Please note special time and location | ||
| Topic: | The entropy formula for the Ricci flow and its geometric applications | |
| Presenter: | Grisha Perelman, St. Petersburg | |
| Date: | Wednesday, April 16, 2003, Time: 3:00 p.m., Location: Taplin Hall | |
| 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. | |
| Cohomology of Groups | ||
| Topic: | On nilpotent ideals in the cohomology ring of a group | |
| Presenter: | Jonathan Pakianathan, University of Rochester | |
| Date: | Thursday, April 17, 2003, Time: 3:00 p.m., Location: Fine Hall 801 | |
| Joint Institute for Advanced Study /Princeton University/ Rutgers University Number Theory Seminar | ||
| Topic: | An arithmetic theta function | |
| Presenter: | Stephen Kudla, University of Maryland | |
| Date: | Thursday, April 17, 2003, Time: 4:15 p.m., Location: Fine Hall 322 | |
| Abstract: | The arithmetic theta function is a modular form of weight 3/2 valued in the arithmetic Chow group of the arithmetic surface attached to a Shimura curve of Q. This function can be used to define a theta lift from modular forms of weight 3/2 to the elements of the arithmetic Chow group. A conjectural analogue of a result of Waldspurger gives a characterization of the nonvanishing of this arithmetic theta lift in terms of (i) local obstructions and (ii) the nonvanishishing of the central derivative of the L-function. This result is proved in some cases. | |
| Topology Seminar | ||
| Topic: | Fixity and Group Actions | |
| Presenter: | Alejandro Adem, University of Wisconsen | |
| Date: | Thursday, April 17, 2003, Time: 4:30 p.m., Location: Fine Hall 314 | |
| Abstract: | In this talk I will discuss recent work on constructing free group actions on products of spheres. This makes use of the notion of fixity of representations, homotopy theory and propagation of group actions. In particular we show that for p>3, every rank two p-group acts freely and smoothly on a product of two spheres. | |
| 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. | |
|
|
||
| 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). |
|
| Cohomology of Groups | ||
| Topic: | Cohomolgy and representations of finite group schemes, Part III | |
| Presenter: | Julia Pevtsova, IAS | |
| Date: | Tuesday, April 22, 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: - Quillen's stratification theorem and Carlson's rank varieties. - Cohomology of Frobenius kernels and one-parameter subgroups. - Cohomology of finite group schemes and maps from the group algebra of a cyclic group. |
|
| 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. | |
| Cohomology of Groups | ||
| Topic: | Constructing group actions on manifolds | |
| Presenter: | Frank Quinn, Virginia Tech and Princeton University | |
| Date: | Thursday, April 24, 2003, Time: 3:00 p.m., Location: Fine Hall 801 | |
| Abstract: | A great deal of work on this topic was done in the 70s and 80s, but it got lost in a dense fog of obstructions and invariants. The objective here is to consider the type of actions being described (smooth, topological,..) as a variable, and look for a type that minimizes the data needed. We describe a speculative program that goes from construction of free actions on homotopy types all the way through to manifolds. This suggests what the data-minimizing action type should be, and what the minimum data might involve. | |
| 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. |
|
| 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: |
Positive mass theorem for asymptotically hyperbolic manifolds and the rigidity of the ADS spacetime |
|
| Presenter: | Xiaodong Wang, MIT | |
| Date: | Friday, April 25, 2003, Time: 3:00 p.m., Location: Fine Hall 314 | |
| Abstract: | I will discuss the mass of asymptotically hyperbolic manifolds and its positivity. As an application I will show the uiqueness of the ADS spacetime among all static anti-de Sitter vacuum spacetimes with the same conformal infinity. | |
|
|
||
| PACM Colloquium | ||
| Topic: | Quantum charged transport models in bounded domains | |
| Presenter: | Irene Gamba, University of Texas at Austin | |
| Date: | Monday, April 28, 2003, Time: 4:00 p.m., Location: Fine Hall 214 | |
| Abstract: | We shall discuss quantum hydrodynamic models (QHM)-Poisson systems in bounded domains with inflow boundary conditions in the context of charged transport to induced by an electric field for a rather general termalization closure. These problems appear in the modeling of nano-scale electronic devices as well as Bose Einstein condensates and other approximations to charged non-linear Shroedinger transport by WKB expansions. We show non-existence of weak solutions to stationary states for a large set of boundary conditions, and, in particular, a blow up in finite time for transient solutions. However the stationary problem is solvable when a nonlinear friction term is added. Finally, we discuss comparisons corresponding Wigner-Poisson systems, both for either collision or collisionless regimes and we present numerical approximations to solutions of the Wigner equation and discuss the relation to QHD models. These results are part of recent collaborations with Ansgar Jungel, Ping Zhang and Jing Shi. | |
| 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: | Random walks in a random environment | |
| Presenter: | S.R.Srinivasa Varadhan, New York University | |
| Date: | Wednesday, April 30, 2003, Time: 4:30 p.m., Location: Fine Hall 314 | |
| Abstract: | We will discuss results on the large deviation behavior of Random Walks in a Random Environment. These concern the quenched walk that have an almost sure large deviation behavior and the averaged walk that exhibits a large deviation behavior that could be partly due to large deviations in the environment itself. The quenched case has connections to homogenization of random Hamilton Jacobi equations with small viscosity. | |
| 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. | |
|
|
||
| Analysis Seminar | ||
| Topic: | Combinatorics of distance sets and applications | |
| Presenter: | Alex Iosevich, University of Missouri at Columbia | |
| Date: | Monday, May 5, 2003, Time: 4:00 p.m., Location: Fine Hall 314 | |
| Abstract: | Let $E$ be a subset of ${\Bbb R}^d$ and let $\Delta(E)=\{|x-y|: x,y \in E\}$, the distance set. It is well-known that information about $E$ can be used to deduce estimates on $\Delta(E)$, and vice-versa, in both the discrete and continious settings. We will discuss some recent results of this type and applications to problems in harmonic analysis and geometric combinatorics. | |
| Special Joint Institute for Advanced Study/Princeton University/Rutgers University Number Theory Seminar | ||
| Topic: | Maximal p-extensions of Q with restricted ramification | |
| Presenter: | Helmut Koch, Humboldt University, Berlin | |
| Date: | Tuesday, May 6, 2003, Time: 2:00 p.m., Location: Fine Hall 110 | |
| Abstract: | Let p be a prime, K an algebraic number field and S a finite set of places of K. Then K_S denotes the maximal p-extension unramified outside S. The Galois group G_S of K_S/K is a pro-p-group with finitely many generators and relations. Subject of the talk is the finer structure of G_S mostly in the case of K=\mathbb{Q}. After an historical introdution, we explain recent results of Boston, Leedham-Green, Eick and the speaker. | |
| 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: | A Canonical Factorization for Meromorphic Herglotz Functions on the Disk and a Proof of the Jacobi Matrix P2 Sum Rule on One Foot | |
| Presenter: | Barry Simon, Caltech | |
| Date: | Thursday, May 8, 2003, Time: 2:00 p.m., Location: Jadwin A06 | |
| Abstract: | Last year Killip and Simon provided a complete description of the spectral measure associated to Jacobi matrices with L2 potentials. I will present a simple proof of their result that relies on two elements: an analysis of the general form of meromorphic Herglotz functions on the disk and the upper semicontinuity of the entropy. I'll begin by describing the general issue of the spectral and inverse spectral problems for Jacobi matrices, the significance of the P2 sum rule, then the canonical factorization and then the proof of the P2 sum rule. | |
| Joint Institute for Advanced Study /Princeton University/ Rutgers University Number Theory Seminar | ||
| Topic: | Small gaps between primes | |
| Presenter: | Dan Goldston, San Jose State University | |
| Date: | Thursday, May 8, 2003, Time: 4:15 p.m., Location: Fine Hall 322 | |
| Abstract: | This talk will discuss the main new idea behind the proof that there are infinitely many primes much closer together than the average spacing between primes, and how this idea was discovered. A sketch of the proof will be given. This is joint work with C. Yalcin Yildirim. | |
| Joint Institute for Advanced Study /Princeton University/ Rutgers University Number Theory Seminar | ||
| *** Please note special day and time *** | ||
| Topic: | Recent Developments Related to Prime Gaps | |
| Presenter: | Dan Goldston, San Jose State University | |
| Date: | Friday, May 9, 2003, Time: 2:00 p.m., Location: Fine Hall 322 | |
| Abstract: | This talk will discuss improvements in the method for detecting small gaps between primes made by a number of people in the last two months, and problems that still need to be examined. | |
|
|
||
| Algebraic Geometry Seminar | ||
| Topic: | TBA | |
| Presenter: | B. Guralnick | |
| Date: | Tuesday, May 13, 2003, Time: 4:30 p.m., Location: Fine Hall 322 | |