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| Discrete Mathematics Seminar | ||
| Topic: | On hypergraphs of girth five | |
| Presenter: | Felix Lazebnik, University of Delaware | |
| Date: | Wednesday, April 23, 2003, Time: 2:15 p.m., Location: Fine Hall 224 | |
| Abstract: | View here | |
| 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. | |
| Special Geometry Seminar | ||
| Topic: | Minimal covolume lattices in hyperbolic 3-space | |
| Presenter: | G. Martin, Auckland New Zealand | |
| Date: | Thursday, April 24, 2003, Time: 2:00 p.m., Location: Fine Hall 314 | |
| Abstract: | In 1945 Siegel posed the problem of identifying the minimal covolume lattices of rank one symmetric spaces. He solved the problem for the hyperbolic plane and suggested a connection between this problem and the 84g-84 theorem of Hurwitz (1892) established by Macbeath (1961). Despite considerable effort no other minimal lattice has been identified, though important work of Kazdan-Margulis established the existence of positive lower bounds in each dimension. In this talk we give the solution to Siegel's problem for hyperbolic 3-space and discuss connections with 3 manifolds having very large symmetry groups. | |
| 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. |
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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 | |
| Topology Seminar | ||
| Topic: | Knot Floer Homology | |
| Presenter: | Zoltan Szabo, Princeton University | |
| Date: | Thursday, April 24, 2003, Time: 4:30 p.m., Location: Fine Hall 314 | |
| Geometric Analysis Seminar | ||
| Topic: |
Positive mass theorem for asymptotically hyperbolic manifolds and the rigidity of the ADS spacetime |
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| 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. | |
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| 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. | |
| Special Topology Seminar *** Please note special time, date, and location | ||
| Topic: | Report on Andrew Casson's Arkansas Lectures | |
| Presenter: | Baris Coskunuzer, Princeton University & Ken Baker, University of Texas at Austin | |
| Date: | Tuesday, April 29, 2003, Time: 4:00 p.m., Location: Fine Hall 110 | |
| Abstract: | We will present Casson's reformulations of the Andrews - Curtis and Poincaré Conjectures. | |
| 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. | |
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| Joint Institute for Advanced Study /Princeton University/ Rutgers University Number Theory Seminar | ||
| *** Please note special day and time *** | ||
| Topic: | Non tempered A packets of G_2 | |
| Presenter: | Nadya Gurevich, Princeton University | |
| Date: | Monday, May 5, 2003, Time: 3:00 p.m., Location: Fine Hall 322 | |
| 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. | |
| Joint Institute for Advanced Study /Princeton University/ Rutgers University Number Theory Seminar | ||
| *** Please note special day and time *** | ||
| Topic: | Horocycles and equidistribution | |
| Presenter: | Andreas Strombergsson, Princeton University | |
| Date: | Monday, May 5, 2003, Time: 4:15 p.m., Location: Fine Hall 322 | |
| Abstract: | I will discuss some questions regarding equidistribution and rates of convergence of ergodic averages in the setting of the horocycle flow on the unit tangent bundle of a non-compact hyperbolic surface of finite area. One of the problems which I will discuss is related to the pair correlation density of the sequence $n^2 a$ modulo one. (Joint work with Jens Marklof.) | |
| Special Joint Institute for Advanced Study/Princeton University/Rutgers University Number Theory Seminar | ||
| ** Please note special day, time, and location *** | ||
| 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:
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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. | |
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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 | |