APRIL 7- APRIL 9, 2004 |
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| Discrete Mathematics Seminar | |
| Topic: | Sphere packing in R^n through Graph Theory |
| Presenter: | Michael Krivelevich, Tel Aviv University |
| Date: | Wednesday, April 7, 2004, Time: 3:00 p.m., Location: Fine Hall 224 |
| Abstract: | In this talk I will demonstrate how graph theoretic tools can be utilized to show that for all sufficiently large n there exist sphere packings in R^n of density at least cn/2^n, matching up to a constant factor best known lower bounds for this classical problem of Minkowski. A joint work with Simon Litsyn (Tel Aviv University) and Alexander Vardy (University of California at San Diego). |
| Department Colloquium | |
| Topic: | From foliations of three manifolds to representations of their fundamental groups |
| Presenter: | Tom Mrowka, MIT and the Institute for Advanced Study |
| Date: | Wednesday, April 7, 2004, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: | Recent progress in understanding symplectic four-manifolds (due to Eliashberg building on a long line of work in particular that of Gabai , Thurston-Eliashberg and Giroux) combined with results in Gauge theory (in particular results of Feehan and Leness relating the Donaldson and Seiberg-Witten invariants) has led to the resolution of some long-standing questions about three manifolds. For example one can now show (independently of Perelman's work) that non trivial surgery on a non-trivial knot can never yield a counter example to the Poincar'e conjecture (the property P question). In general one can show taut foliations of three manifolds imply the existence non-trivial representations of their fundamental groups in to SU(2). |
| Joint Analysis Seminar | |
| Topic: | Integrability, geometry, and singularities of the solutions of a dispersive wave equation |
| Presenter: | Adrian Constantin, Brown University and the University of Lund |
| Date: | Thursday, April 8, 2004, Time: 3:30 p.m., Location: Fine Hall 214 |
| Abstract: | A recently derived nonlinear partial differential equation models the unidirectional propagation of waves on shallow water and in elastic rods. The uniquely rich structure of the equation is the object of our presentation. The equation is a completely integrable infinite-dimensional Hamiltonian system. It can also be viewed in terms of the geodesic flow on the diffeomorphism group of the circle. Moreover, it possesses waves of permanent form (traveling solitary waves) and waves that "break," meaning that the solution remains bounded but its slope becomes unbounded in finite time. However, its solitary waves are stable and they interact like solitons. There is an associated isospectral problem that governs the soliton behavior. |
| Ergodic Theory and Statistical Mechanics Seminar - *** Please note special time and location | |
| Topic: | Bounded geodesics and slowly recurrent billiard trajectories |
| Presenter: | Dmitry Kleinbock, Brandeis University |
| Date: | Thursday, April 8, 2004, Time: 4:30 p.m., Location: Fine Hall 601 |
| Abstract: | This is a joint work with Barak Weiss. In the moduli space of quadratic differentials on a Riemann surface we construct points with bounded Teichmuller geodesic trajectories. An application to billiards in rational polygons provides a construction of rational billiard analogue of badly approximable numbers. |
| Topology Seminar | |
| Topic: | Knots with unknotting number 1 |
| Presenter: | Cameron Gordon, University of Texas, Austin |
| Date: | Thursday, April 8, 2004, Time: 4:30 p.m., Location: Fine Hall 314 |
APRIL 12- APRIL 16, 2004 |
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| Joint Princeton University/Institute for Advanced Study Number Theory Seminar | |
| Topic: | Central values of twisted L-functions |
| Presenter: | Zhengyu Mao, Rutgers University - Newark |
| Date: | Monday, April 12, 2004, Time: 4:00 p.m., Location: Fine Hall 322 |
| Abstract: | Kohnen-Zagier formula is one of many versions of a formula relating the central values of twisted L-functions of a weight 2k cusp form and the Fourier coefficients of a half integral weight form. We describe a formula that holds in the general setting of automorphic forms, and derive from it the generalization of Kohnen-Zagier. We also discuss the computation of L-values using this formula. |
| PACM Colloquium | |
| Topic: | Inequalities of Quantum Information Theory |
| Presenter: | Nicholas J. Pippenger, Computer Science, Princeton University |
| Date: | Monday, April 12, 2004, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstact: | The recent upsurge of interest in quantum communication and quantum computation has led to a renewed interest in quantum information theory. Specifically, many results concerning quantum communication and quantum computation involve the quantum entropy, a measure of quantum information, introduced by von Neumann in 1927, that generalizes the classical entropy introduced by Shannon in 1948. (The classical entropy is the special case of quantum entropy in which all density matrices are diagonal.) Even for classical information, a complete characterization of the inequalities satisfied by the entropy is available only when the number of variables is at most three, or when the allocation of entropy is symmetric (though some tantalizing results due to Z. Zhang and R. W. Yeung hint at the complexity of the general case. In this talk we shall discuss the extent to which this theory can be extended to the quantum case. |
| Algebraic Geometry Seminar | |
| Topic: | Vanishing of Chow (or cohomology) classes on the moduli space of curves |
| Presenter: | Ravi Vakil, Stanford University |
| Date: | Tuesday, April 13, 2004, Time: 4:30 p.m., Location: Fine Hall 322 |
| Abstact: | I will discuss a theorem (with T. Graber) that all codimension i tautological classes on the moduli space of curves are trivial away from boundary strata corresponding to curves with at least i-g+1 rational components. (I will define the moduli space and its tautological ring.) In some sense, this is the geometric content behind many vanishing conjectures and theorems on moduli spaces of curves (due to Getzler, Ionel, Faber, Looijenga, Pandharipande, Diaz, and others). I will show how the theorem implies these various results via straightforward graph combinatorics, and how in most cases it extends them. This suggests the potential importance of a strange stratification of the moduli space of curves by number of rational components. If there is time, I will discuss some of the ideas behind the proof, which is an easy consequence of "relative virtual localization" (localization on J. Li's space of relative stable maps). This latter theorem has many other consequences. |
| Mathematical Physics Seminar | |
| Topic: | Approach and return to equilibrium in quantum statistical mechanics |
| Presenter: | Vojkan Jaksic, McGill University |
| Date: | Tuesday, April 13, 2004, Time: 4:30 p.m., Location: Jadwin A06 |
| Discrete Mathematics Seminar | |
| Topic: | Learning in Groups |
| Presenter: | Robert Calderbank , Princeton University |
| Date: | Wednesday, April 14, 2004, Time: 3:00 p.m., Location: Fine Hall 224 |
| Ergodic Theory and Statistical Mechanics Seminar | |
| Topic: | Modulational stability of cellular flows |
| Presenter: | Alexei Novikov, Penn State University. |
| Date: | Thursday, April 15, 2004, Time: 2:00 p.m., Location: Fine Hall 322 |
| Abstract: | We investigate stability of the initial modulational perturbations of stationary solutions to the two-dimensional Navier-Stokes equations with a time-independent periodic rapidly oscillating forcing. The stationary solutions are cellular flows and they are determined by the stream function $\phi = \sin x_1/\epsilon \sin x_2/\epsilon + \delta\cos x_1/\epsilon \cos x_2/\epsilon$, $0 \leq \delta \leq 1$. The perturbations satisfy the modulation equation. For small Reynolds number we determine the stability for the fully nonlinear modulation equation. For any Reynolds number we determine the stability of the linearized modulation equation. |
| Ergodic Theory and Statistical Mechanics Seminar - *** Please note special time and location | |
| Topic: | Linear and sub-linear behavior of random walks in random environments on a strip |
| Presenter: | Ilya Goldsheid, Queen Mary, University of London |
| Date: | Thursday, April 15, 2004, Time: 4:30 p.m., Location: Fine Hall 601 |
| Abstract: | The remarkable fact that a transitive random walks in random environment does not necessarily grow linearly but may also exhibit sub linear behavior has been known since 1975 (Solomon; Kesten-Kozlov-Spitser). These results were proved for the case of the simplest random walk in dimension one. The attempts to establish similar results for other cases had a limited success. I shall discuss necessary and sufficient conditions leading to a relatively full description of this sort of behavior for a wide range of one- and quasi one-dimensional models. |
| Special Algebra Seminar | |
| Topic: | Mordell-Weil Lattices and Modular Forms |
| Presenter: | Tetsuji Shioda , Rikkyo University. |
| Date: | Thursday, April 15, 2004, Time: 4:30 p.m., Location: Fine Hall 322 |
| Bill Browder Birthday Topology Seminar Doubleheader - Note special times | |
| Topic: | Representations and K-Theory of the Braid Group |
| Presenter: | Alejandro Adem, University of Wisconsin |
| Date: | Thursday, April 15, 2004, Time: 3:00 p.m., Location: Fine Hall 314 |
| Topic: | Enlargeability and Index Theory |
| Presenter: | Bernhard Hanke, Universitat Muenchen |
| Date: | Thursday, April 15, 2004, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstact: | Let M be a smooth, compact enlargeable spin manifold. Independently of the Baum-Connes conjecture, we prove nonvanishing of a universal index obstruction associated witn M. This implies the result by Gromov and Lawson that M does not admit a metric of positive scalar curvature. As an application of our methods we show that the map --> B\pi_1(M) classifying the universal cover of M sends the fundamental homology class of M to a non trivial class in H_*(B\pi_1(M); Q. This answers a question of D. Burghelea (1983). |
APRIL 19 - APRIL 23, 2004 |
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| Joint Princeton University/Institute for Advanced Study Number Theory Seminar | |
| Topic: | TBA |
| Presenter: | Harald Helfgott, Yale University |
| Date: | Monday, April 19, 2004, Time: 4:00 p.m., Location: Fine Hall 322 |
| Algebraic Geometry Seminar | |
| Topic: | TBA |
| Presenter: | Mikhail Kapranov, Yale University |
| Date: | Tuesday, April 20, 2004, Time: 4:30 p.m., Location: Fine Hall 322 |
| Discrete Mathematics Seminar | |
| Topic: | Lower Bounds for Degeneracy Testing |
| Presenter: | Bernard Chazelle, Princeton University |
| Date: | Wednesday, April 21, 2004, Time: 3:00 p.m., Location: Fine Hall 224 |
| Abstract: | I will discuss how to prove lower bounds in a decision tree model for the problem of testing whether out of n numbers k of them sum up to 0. This is joint work with Nir Ailon. |
APRIL 26 - APRIL 30, 2004 |
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| Joint Princeton University/Institute for Advanced Study Number Theory Seminar | |
| Topic: | TBA |
| Presenter: | Ben Brubaker, Stanford University |
| Date: | Monday, April 26, 2004, Time: 4:00 p.m., Location: Fine Hall 322 |
| PACM Colloquium | |
| Topic: | PlanetLab: Introducing Disruptive Technology into the Internet |
| Presenter: | Larry Peterson, Computer Science, Princeton University |
| Date: | Monday, April 26, 2004, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: | A new class of geographically distributed network services is emerging, and the most effective way to design, evaluate, and deploy these services is by using an overlay-based testbed. Unlike conventional network testbeds, however, we advocate an approach that supports both researchers that want to develop new services, and clients that want to use them. This dual use, in turn, suggests four design principles that are not widely supported in existing testbeds: services should be able to run continuously and access a slice of the overlay's resources, control over resources should be distributed, overlay management services should be unbundled and run in their own slices, and APIs should be designed to promote application development. This talk describes this high-level vision, and reports the status and plan for the realization of the vision in PlanetLab. |
| Algebraic Geometry Seminar | |
| Topic: | TBA |
| Presenter: | Jaroslaw Wisniewski, Purdue University and Warsaw |
| Date: | Tuesday, April 27, 2004, Time: 4:30 p.m., Location: Fine Hall 322 |
| Department Colloquium | |
| Topic: | A deformation of Hodge theory |
| Presenter: | Jean-Michel Bismut, Universite Paris-Sud |
| Date: | Wednesday, April 28, 2004, Time: 4:30 p.m., Location: Fine Hall 314 |
MAY 3 - MAY 7, 2004 |
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| Algebraic Geometry Seminar | |
| Topic: | The Enriques conjecture; or, How canonical is the canonical bundle? |
| Presenter: | Joe Harris, Harvard University |
| Date: | Tuesday, May 4, 2004, Time: 4:30 p.m., Location: Fine Hall 322 |
| Abstract: | The question we're dealing with is this: Is there any way of associating to each smooth curve C of genus g ---or at least to each C in an open subset of moduli---a line bundle on C, other than by taking powers of the canonical bundle? (The answer, by the way, is no: the canonical bundle is truly canonical.) This question was posed almost a century ago; a bogus proof was given by Franchetta in the '40s (as a result of which the statement is usually called Franchetta's conjecture, and a correct proof was given in the '80s by Harer and Mestrano, based on a topological argument of Harer's. In fact, the statement is immediately implied by a stronger conjecture made by Enriques decades earlier. Enriques claimed (or suggested; it's not always clear) an analogous statement for the Severi variety, namely that the only ways of choosing a line bundle on a general plane curve C of degree d and genus g are combinations of the canonical bundle K_C and the hyperplane bundle O_C(1). In this talk I'll discuss a little of the history of the Enriques conjecture, and variants of it; but the main purpose of the talk will be to give a proof of the conjecture that Deepee Khosla and I found recently. |
| Geometry, Representation, and Moduli Seminar | |
| Topic: | TBA |
| Presenter: | Alexander Braverman, Brown University |
| Date: | Wednesday, May 5, 2004, Time: 3:00 p.m., Location: Fine Hall 214 |
| Geometric Analysis Seminar | |
| Topic: | Deforming mappings by Mean Curvature Flow |
| Presenter: | Mao-Pei Tsui, Columbia University |
| Date: | Friday, May 7, 2004, Time: 3:00 p.m., Location: Fine Hall 314 |
MAY 10 - MAY 14, 2004 |
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| Joint Princeton University/Institute for Advanced Study Number Theory Seminar | |
| Topic: | TBA |
| Presenter: | David J. Burns, King's College, London |
| Date: | Monday, May 10, 2004, Time: 4:00 p.m., Location: Fine Hall 322 |
MAY 17 - MAY 21, 2004 |
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| Geometry, Representation, and Moduli Seminar | |
| Topic: | TBA |
| Presenter: | R. Thomas, Imperial College |
| Date: | Wednesday, May 19, 2004, Time: 3:00 p.m., Location: Fine Hall 214 |