| WEEK OF DECEMBER 10 - DECEMBER 13, 2002 | |
| Algebraic Geometry Seminar | |
| Topic: | Jets, arcs and minimal log discrepancies |
| Presenter: | Mircea Mustata, Clay and Harvard University |
| Date: | Tuesday, December 10, 2002, Time: 4:30 p.m., Location: Fine Hall 322 |
| Statististical Mechanics Seminar | |
| Topic: | Kolmogorov and Anosov Flows: from Classical to Quantum |
| Presenter: | Gerard Emch, University of Florida, Gainesville |
| Date | Wednesday, December 11, 2002, Time: 2:00 p.m., Location: Jadwin 343 |
| Abstract: | The place of classical Kolmogorov and Anosov flows in the hierarchy of classical ergodic theory will be reviewed with the help of elementary models (from Boltzmann and Hadamard up). I will then explain how these notions generalize naturally to the quantum realm with the help of a few tools from functional analysis, in particular von Neumann algebras, a toolbox that will be open slowly enough to make the generalisations appear natural indeed. |
| Department Colloquium | |
| Topic: | Gauge Symmetry Breaking |
| Presenter: | Ed Witten, Institute for Advanced Study |
| Date: | Wednesday, December 11, 2002, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: | I will describe the gauge symmetry breaking that is observed in superconductors and has an analog in four-manifold theory, and the gauge symmetry breaking in elementary particle physics that physicists are still aiming to understand more fully. |
| Discrete Mathematics Seminar | |
| Topic: | A generalisation of a conjecture of Erdos and Rothschild |
| Presenter: | Peter Keevash, Princeton University |
| Date: | Thursday, December 12, 2002, Time: 2:15 p.m., Location: Fine Hall 224 |
| Abstract: | Please click here to view abstract |
| Joint Princeton University/IAS Number Theory Seminar | |
| Topic: | Automorphic representations of a symplectic group |
| Presenter: | Yuval Flicker, Ohio State University |
| Date: | Thursday, December 12, 2002, Time: 4:30 p.m., Location: Fine Hall 322 |
| Abstract: | I would like to describe the admissible and automorphic representations of PGSp(2) in terms of liftings related to PGL(4), PGL(2)xPGL(2), SO(4), stated using character relations. This permits a definition of packets, proof of multiplicity one, listing all counter-examples to Ramanujan's conjecture, and potential applications toShimura varieties. |
| Topology Seminar *** Please note change in time | |
| Topic: | Negative curvature and exotic smooth surfaces |
| Presenter: | Tom Farrell, State University of New York at Binghamton |
| Date: | Thursday, December 12, 2002: Time: 4:30p.m., Location: Fine Hall 314 |
| Graduate Student Seminar | |
| Topic: | Using Torsion to Bound the Rank of An Elliptic Curve |
| Presenter: | Chris Hall, Princeton University |
| Date: | Friday, December 13, 2002, Time: 12:30 p.m., Location: Fine Hall 1201 |
| Abstract: | Given an elliptic curve $E$ over a global field $K$ the basic form of the Birch--Swinnerton-Dyer (BSD) conjecture asserts that the analytic rank and algebraic rank of the curve are equal. When $K=F_q(C)$ is a function field a theorem of Tate implies that the analytic rank bounds the algebraic rank from above. Using an elementary argument I will show how one can use $l$-torsion to deduce the mod-$l$ reduction of the associated L-function $L(T,E/K)$. We will apply this to infinite families of curves to show that the analytic rank and hence algebraic rank are at most one. Using an unpublished result of D. Ulmer one may deduce that BSD holds for these families. Most of the talk will focus on one concrete case, and I will define things as they are needed. Those familiar with elliptic curves and L-functions will certainly be more comfortable, but I will try to explain things so that others will get something out of the talk as well. |