Special Analysis Seminar - Princeton University



Week of November 1 - 5, 1999

Thinking About Mathematics (Postponed Until 11-10-99) Wednesday 8:00 Jadwin A10

Topic: The Surreal Numbers November 3

Presenter: John Conway, Princeton University

Princeton Discrete Math Seminar Thursday 1:30 Fine 214

Topic: Nowhere-zero flows in birected graphs November 4

Presenter: Matthew Devos, Princeton University

Abstract: The study of nowhere-zero flows began with a key observation of Tutte that in planar graphs, nowhere-zero k-flows are dual to k-colorings (in the form of k-tensions). Tutte conjectured that every graph without a cut-edge has a nowhere-zero 5-flow. Seymour proved that it is true with 5 replaced by 6.

For a graph drawn on an orientable surface of higher genus, flows are not dual to colorings, but to "local-tensions"; so every graph on an orientable surface without the obvious obstruction has a 6-local-tension. Bouchet conjectured that the same holds on non-orientable surfaces (although there the duality with flows breaks down). Equivalently, every bidirected graph without the obvious obstruction should have a nowhere-zero 6-flow.

Improving on several previous results, we show that Bouchet's conjecture is true with 6 replaced by 12. For 4-edge-connected bidirected graphs, we resolve Bouchet's conjecture, showing that every such graph (without the obvious obstruction) has a nowhere-zero 4-flow.

Nonlinear Analysis Seminar Thursday 4:00 Hill Center

Topic: On the free surface of a liquid November 4

Presenter: Hans Lindblad, Princeton University

Location: Rutgers, Hill Center room 705, Tea ia available in the 7th floor lounge of Hill Center 3:30 - 4:30 p.m.

Week of November 8 - 12, 1999

Mathematics Beyond the Boundaries of Academia Monday 12:00 PL

Topic: The Cantor Set and Cryptology November 8

Presenter: Lee Neuwirth, Retired IDA

Abstract: The Cantor set, in the guise of the space X^{\infty} of bi-infinite sequences of 0 and 1 (and often called the full 2-shift) is a compact metric space which seems to crop up in many contexts; geodesics on Riemannian manifolds, phase plane portraits of ordinary differential equations, coding and information theory, game theory, dynamical systems, ergodic theory, statistical mechanics, C*-algebras, formal language theory, etc., etc.

This talk concerns yet another area in which the space X^{\infty} is of interest, namely Cryptology. We hope to show why the presence of shift registers in many cryptographic devices leads naturally to the study of endomorphisms of X^{\infty}.

Examples and properties of these "onto" maps will be discussed and if time permits a generalization of the 2-adic solenoid which arises will be shown.

Analysis Seminar Monday 4:00 Fine 314

Topic: Lie groups, maximal functions and pointwise ergodic theory November 8

Presenter: Amos Nevo, Princeton University & Technion Haifa

PACM Colloquium Monday 4:30 Fine 224

Topic: Multigrid methods and applications November 8

Presenter: Jinchao Xu, Penn State University

Abstract: The speaker will first give a brief description on the state of the art on multigrid methods for solving partial differential equations and then present some recent results and applications.

Joint Colloquium - Computer Science & Mathematics Tuesday 12:00 Fine 314

Topic: Implementation and Application of Machine-Checked Proofs November 9

Presenter: Andrew Appel, Princeton University

Algebraic Geometry Seminar Tuesday 2:30 Fine 314

Topic: Flag manifolds, quantum cohomology, K-theory and Toda lattices November 9

Note: Special time & place: 2:30 p.m. in Fine 314

Presenter: A. Givental, UC Berkley

Algebraic Geometry Seminar Tuesday 4:15 Fine 322

Topic: Ample divisors on holomorphic symplectic fourfolds November 9

Presenter: Brendan Hassett, University of Chicago

Abstract: Let S be a polarized K3 surface. The Picard group Pic(S) may be regarded as an integral quadratic form with respect to the intersection pairing. There is a dictionary between the geometry of S and the arithmetic properties of this form. For example, there are criteria for the existence of smooth rational curves in terms of the integers represented by the form. This yields a simple arithmetic description of the ample cone of S. Our goal is to extend this dictionary to certain higher dimensional analogs to K3 surfaces, known as holomorphic symplectic manifolds. These include punctual Hilbert schemes (i.e., desingularized symmetric products) of K3 surfaces. We give a conjectural framework generalizing the picture for K3 surfaces and provide evidence for our conjectures.

Statistical Mechanics Seminar Wednesday 2:00 Jadwin 343

Topic: A review of the chaotic hypothesis November 10

Presenter: Giovanni Gallovotti, University of Rome

Colloquium Wednesday 4:30 Fine 314

Topic: On a theorem of Jordan November 10

Presenter: J-P Serre, College de France

Thinking About Mathematics Wednesday 8:00 Jadwin A10

Topic: The Surreal Numbers November 10

Presenter: John Conway, Princeton University

Ergodic Theory & Statistical Mechanics Seminar Thursday 2:30 Fine 110

Title: Correlation kernels arising in asymptotic representation theory November 11

Speaker: Grigori Olshanskii, IITP (Moscow) and University of Pennsylvania

Abstract: Representation theory of "big" groups (like the infinite symmetric group) provides new interesting examples of random point processes. The aim of the talk is to discuss these examples, their connection to random matrix theory and computation of the correlation functions. This is a recent joint work with Alexei Borodin (U. Penn).

Topology & Symplectic Geometry Seminar Thursday 4:30 Fine 314

Title: TBA November 11

Presenter: Kim Froyshev, Harvard University

Symplectic Geometry Seminar Friday 2:30 Fine 401

Topic: Introduction to Symplectic Field Theory November 12

Presenter: Yakov Eliashberg, Princeton University

Geometry Seminar Friday 3:00 Fine 314

Topic: Property (T) and Kazhdan constants for generic hyperbolic groups November 12

Presenter: Andrej Zuk, ENS Lyon

Week of November 15 - 19, 1999

Analysis Seminar Monday 4:00 Fine 314

Topic: Newton diagrams and the decay of oscillatory integrals November 15

Presenter: Jacob Sturm, Rutgers University

PACM Colloquium Monday 4:30 Fine 224

Topic: Morphological Instabilities of Surfaces and Growing Films November 15

Presenter: David Srolovitz, PMI/MAE, Princeton University

Abstract: While surface tension is capable of stabilizing flat surfaces against shape perturbations in unstressed solids, the presence of a stress can destabilize the surface. I will begin by discussing thermodynamic and kinetic issues associated with the stability of surfaces of stressed solids. I will show that non-hydrostatic stresses will destabilize flat surfaces of isotropic solids at wavenumbers that depend on the stress, surface tension and elastic modulus. I will then show numerical evidence that these instabilities produce cusp like features that can be thought of in terms of cracks. Next, I will consider the stability of the surface of a growing film and demonstrate that multilayer films can be stabilized against this form of morphological instability.

Algebraic Geometry Seminar Tuesday 4:15 Fine 322

Topic: Arithmeticity of discrete subgroups containing lattices in November 16

horospherical subgroups

Presenter: Hee Oh, Princeton University

Abstract: Let G be a connected simple Lie group with finite center. A unipotent subgroup of G is called "horospherical" if it is the unipotent radical of a proper parabolic subgroup. Margulis conjectured that if the (real) rank of G is at least 2, any discrete subgroup of G containing lattices in a pair of opposite horospherical subgroups is an arithmetic subgroup of G. This conjecture has been settled in many cases, in particular, the cases when G is split over real (but not locally isomorphic to SL_3(R)). I will talk about some ideas in the proof as well as discuss open cases of the conjecture.

Statistical Mechanics Seminar Wednesday 2:00 Jadwin 343

Topic: Atoms in neutron star magnetic fields: High B asymptotics at fixed Z November 17

Presenter: Jakob Yngvason, University of Vienna

Colloquium Wednesday 4:30 Fine 314

Topic: Difference equations with quasi-periodic coefficients: November 17

Anderson localization of eigen functions

Positivity of the Lyapunov exponent

Holder continuity of the distribution of eigen values

Connection with averages of shifts of plurisubharmonic functions

Presenter: M. Goldstein, IAS, University of Toronto

Abstract: The purpose of this talk to explain recent progress in the subject achieved in the works by J.Bourgain, M.Goldstein, W.Schlag.

Ergodic Theory & Statistical Mechanics Seminar Thursday 2:30 Fine 110

Topic: TBA November 18

Presenter: Dmitri Burago, Pennsylvania State University

Topology & Symplectic Geometry Seminar Thursday 4:30 Fine 314

Title: TBA November 18

Presenter: Ronnie Lee, Yale University

Week of November 22 - 26, 1999

Analysis Seminar Monday 4:00 Fine 314

Topic: Matrix coefficients of unitary representations of semisimple Lie groups November 22

Presenter: Hee Oh, Princeton University

Abstract: Let G be a semisimple algebraic group over a local field k (not of characteristic 2) and K a good maximal compact subgroup of G. A unitary representation of G is called "class one" if it has a non-trivial K-invariant vector. This talk concerns the matrix coefficients of a class one unitary representation of G with respect to K-invariant vectors. We present a class of pointwise bounds for all matrix coefficients (with respect to K-invariant vectors) of the class one part of its unitary dual (of course, except the trivial representation). These are sharper than those previously obtained by Howe and Colwing. In particular, these pointwise bounds are optimal for G=SL_n(k) (n>2) or Sp_{2n}(k) (n>1). I will try to explain the construction of these bounds for SL_n(k) case.

PACM Colloquium Monday 4:30 Fine 224

Topic: Scherk's First Surface, Twist-Grain-Boundaries and All That November 22

Presenter: Randall Kamien, University of Pennsylvania

Abstract: Large twist-angle grain boundaries in layered structures are often described by Scherk's first surface whereas small twist-angle grain boundaries are usually described in terms of an array of screw dislocations. I will discuss this and other minimal surfaces and will show that there is no essential distinction between minimal surface and topological defect descriptions and that, in particular, their comparative energetics depends crucially on the core structure of their screw-dislocation topological defects.

Joint Colloquium - Computer Science & Mathematics Tuesday 12:00 Computer

Topic: Lie Groups and Quantum Circuits November 23 Science 401

Presenter: Robert Solovay, UC Berkeley

Symplectic Geometry Seminar Tuesday 2:30 Fine 1201

Topic: Introduction to Symplectic Field Theory November 23

Presenter: Yakov Eliashberg, Princeton University

Algebraic Geometry Seminar Tuesday 4:15 Fine 322

Topic: A differential analogue of Kummer theory on semi-abelian varieties November 23

Presenter: D. Bertrand, Universite de Paris 6

Abstract: Kummer theory on a semi-abelian variety studies the fields of definition of the division points of given rational points. These extensions are controlled by the unipotent radical of the image $G$ of the Galois representations attached to certain one-motives $M$. In the 80's, $R_u(G)$ was described in detail by K. Ribet, who showed that it can be abelian only under a strong condition of a geometric nature on $M$. Linear differential equations $M$ yield monodromy representations, or more generally, differential Galois groups $G$, whose unipotent radicals can be computed with precisely the same cohomological tools as Kummer theory. We shall thus describe necessary and sufficient conditions for $R_u(G)$ to be `a big as possible' (a typical illustration is here given by polylogarithms), and show that when $M$ decomposes into three irreducible factors, $R_u(G)$ can be abelian only under a strong duallity condition, similar to Ribet's. The (much simpler) proof of the latter fact is based on a study of signs in Lagrange's bilinear concomitants.

Week of November 29 - December 3, 1999

Symplectic Geometry Seminar (Cancelled) Tuesday 2:30 Fine 1201

Topic: Introduction to Symplectic Field Theory November 30

Presenter: Yakov Eliashberg, Princeton University

Statistical Mechanics Seminar Wednesday 2:00 Jadwin 343

Topic: Constructive criteria for locatization in random operators December 1

Presenter: Michael Aizenman, Princeton University

Ergodic Theory & Statistical Mechanics Seminar Thursday 2:30 Fine 110

Topic: Universality in 2D Ising Model December 2

Presenter: Haru Pinson, Institute for Advanced Studies

Topology & Symplectic Geometry Seminar Thursday 4:30 Fine 314

Title: TBA December 2

Presenter: Feng Luo, Rutgers University

Week of December 6 - 10, 1999

Symplectic Geometry Seminar Thursday 2:30 Fine 401

Topic: Introduction to Symplectic Field Theory December 2

Presenter: Yakov Eliashberg, Princeton University

Algebraic Geometry Seminar Tuesday 4:15 Fine 322

Topic: TBA December 7

Presenter: William Fulton, Unviersity of Michigan

Statistical Mechanics Seminar Wednesday 2:00 Jadwin 343

Topic: Smooth dynamics and new theoretical ideas in December 8

nonequilibrium statistical mechancis

Presenter: David Ruelle, I.H.E.S.

Ergodic Theory & Statistical Mechanics Seminar Thursday 2:30 Fine 110

Topic: Universality in 2D Ising Model December 9

Presenter: Haru Pinson, IAS

Symplectic Geometry Seminar Thursday 2:30 Fine 401

Topic: Introduction to Symplectic Field Theory December 9

Presenter: Yakov Eliashberg, Princeton University

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