Topic: Exponential mixing of the 2D stochastic Navier Stokes dynamics November 29

Presenter: Antti Kupiainen, Helsinki University and IAS

Topic: Periodic Orbits, Holomorphic Curves and Algebraic Invariants November 29

Presenter: H. Hofer, Courant Institute and Princeton University

Abstract: Gromov-Witten invariants are invariants of symplectic manifolds obtained by counting pseudoholomorphic curves. Cutting symplectic manifolds along hypersurfaces should give relative Gromov-Witten invariants with values in some algebraic object associated to the hypersurface. Symplectically a hypersurface is a Hamiltonian energy surface and its invariants have to be related to the underlying dynamics. The talk describes some aspects of the current research activities.

Topic: Programming Parallel Computers for Real-Time Stream Processing November 30

Presenter: Dr. Jeremy Kepner, MIT Lincoln Laboratory

Abstract: Real-time stream processing consumes the majority of the world's computing power. Traditionally, this computing has taken the form custom computing chips (i.e. ASICs). The rapid advances of programmable microprocessors now make it possible to address a wide variety of stream processing applications (e.g. scientific, video, wireless, medical, encoding, radar and sonar) with commercial massively parallel processors. Stream processing presents unique software challenges both in parallel computation, communication and complexity. To address these challenges we have developed a variety of new software technologies for improving abstraction of stream processing problems, increasing computation and communication performance, and enabling fault tolerant parallel applications. This talk discusses these technologies with particular emphasis on quantitative comparisons with standard parallel stream programming practices.

After the talk Dr. Kepner will be conducting an information session on career opportunities at MIT Lincoln Laboratory. This will be held in Fine Hall Room 224 at 2:00pm.

Topic: Induction theorems in algebra and topology November 30

Presenter: Jesper Grodal, Institute for Advanced Study

Abstract: The plan is to give 4 talks. The first talk will be an overview talk where I'll explain the basics of homology decompositions. A homology decomposition is an expression of the classifying space BG of a group G as a homotopy colimit of classifying spaces of proper subgroups. I will explain how they relate to induction theorems in group theory and can be used to calculate group cohomology. I will also explain how they can be used to classify group action on spaces, and maybe examine the case of a sphere in more detail. In the next talks I will elaborate on these issues, also depending on the interests of the participants.

Topic: FGA algebras November 30

Presenter: V. Shokurov, Johns Hopkins University

Topic: The splitting of of primes in division fields of elliptic curves November 30

Presenter: Arpad Toth, Princeton University

Topic: Structures of Quantum Field Theory December 1

Presenter: Slava Rychkov, Princeton University

Abstract: In 2 lectures (12/1/00 and 12/8/00) I will try to give an exposition of basic objects and ideas of Quantum Field Theory. The list of topics will include: Feynman path integrals, Wightman axiomatics, Feynman diagram techniques for perturbation theory, renormalization group, and conformal field theories. If time permits, we will discuss asymptotic freedom and mass gap in gauge field theories, which is the subject of one of the $1,000,000 Clay Institute Problems. No prior knowledge of QFT will be assumed.

Topic: A Moser-Trudinger inequality for Toda systems December 1

Presenter: Wang Guo-Fang, Max Planck Institute

Topic: d-bar-regularity for weakly pseudoconvex domains in compact Hermitian December 4

symmetric spaces with respect to invariant metrics

Presenter: Yum-Tong Siu, Harvard University

Topic: Revisting an Old Problem: Random Close Packing of Spheres December 4

Presenter: Salvatore Torquato, Chemistry and PMI, Princeton University

Abstract: Bernal (1965) has remarked that "heaps (random close-packed arrangements of particles) were the first things that were ever measured in the form of basketfuls of grain for the purpose of trading or of collection of taxes." Random packings of identical spheres have been studied by biologists, materials scientists, engineers, chemists and physicists to understand the structure of living cells, liquids, granular media, glasses and amorphous solids, to mention but a few examples. Despite its long history, there are many fundamental issues concerning random packings of spheres that remain elusive, including a precise definition of random close packing (RCP). If such a definition of the RCP state could be presented, then one might go about quantifying the problem with the rigor that has been used very recently to prove that the densest possible packing fraction of spheres in three-dimensional space is 0.7405..., corresponding to the close-packed face-centered cubic (FCC) lattice or its stacking variants. It is shown that the current picture of the RCP state cannot be made mathematically precise and support this conclusion via a molecular dynamics study of hard spheres. We suggest that this impasse can be broken by introducing the new concept of a "maximally random jammed" state, which can be made precise.

Topic: The Theta Body and Partitionable Graphs December 5

Presenter: Bruce Shepherd, Lucent Technologies

Topic: The moduli space of cubic surfaces is complex hyperbolic December 5

Presenter: Jim Carlson, University of Utah

Topic: Diophantine geometry over groups and the elementary theory of a free group December 5

Presenter: Zlil Sela, Hebrew University of Jerusalem

Topic: Nonperturbative analysis of a Model Quantum System under Time December 6

Periodic Forcing: Generic and Exceptional Cases

Presenter: Ovidiu Costin, Rutgers University

Abstract: We analyze the time evolution of a one-dimensional quantum system with an attractive delta function potential whose strength is subjected to a time periodic (zero mean) parametric variation $\eta(t)$. The amplitude of $\eta$ is unrestricted. We show that for generic $\eta(t)$, which includes the sum of any finite number of harmonics, the system, started in a localized state, gets fully ionized (the particle leaves the bound state) as time grows indefinitely, irrespective of the magnitude or frequency (resonant or not) of $\eta(t)$. There are however exceptions to full ionization which while very non-generic include rather simple explicit functions. For these $\eta(t)$ the system evolves to a nontrivial localized stationary state which is related to eigenfunctions of the Floquet operator.

Topic: Billiards in Rational Polygons and Moduli Spaces of Holomorphic Differentials December 6

Presenter: Alex Eskin, University of Chicago

Abstract: A polygon is called rational if all angles are rational multiples of pi. It turns out that the problem of counting periodic billiard trajectories on such a polygon can be reduced to a certain dynamical problem of the moduli space of pairs (M,w) where M is a Riemann surface, and w is a holomorphic 1-form on M. Even though it is not locally homogeneous, this moduli space is analogous in many ways to the moduli space of Euclidean lattices SL(n,R)/SL(n,Z). I will discuss these constructions and some associated problems in combinatorial enumeration.

Topic: Gluing procedures for minimal and constant mean curvature surfaces: December 7

methods and applications

Presenter: Frank Pacard, University of Paris, 12

Topic: TBA December 7

Presenter: Bill Minicozzi, Johns Hopkins University

Topic: Structures of Quantum Field Theory December 8

Presenter: Slava Rychkov

Abstract: In 2 lectures (12/1/00 and 12/8/00) I will try to give an exposition of basic objects and ideas of Quantum Field Theory. The list of topics will include: Feynman path integrals, Wightman axiomatics, Feynman diagram techniques for perturbation theory, renormalization group, and conformal field theories. If time permits, we will discuss asymptotic freedom and mass gap in gauge field theories, which is the subject of one of the $1,000,000 Clay Institute Problems. No prior knowledge of QFT will be assumed.

Topic: Ricci Curvature, Minimal Volumes, and Seiberg-Witten Theory December 8

Presenter: Claude Le Brun, SUNY Stony Brook

Topic: Mixed norm estimates for a model restricted X-ray transform December 11

Presenter: Burak Ergodan, Caltech

Topic: Brownian Dynamics Methods for the Solution of Complex Polymeric December 11

Flows Based on Kinetic Theory Models: Early (CONNFFESSIT) and

More Recent (Configuration Field) Approaches

Presenter: Antony N. Beris, University of Delaware

Abstract: In the past, closed-form continuous models have been used for the solution of complex (i.e. multidimensional and/or time dependent) flow problems involving polymer solutions or melts. However, those models involve closure approximations that result in unpredictable errors in the complex flows that they are employed. Nevertheless, the presence of one or more internal variables makes the dimensionality of the microscopic problem prohibitively large to allow for a direct solution of the microscopic equations (such as those arising from kinetic theory) in even the simplest multidimensional flow problems. Fortunately, in the last decade new methodologies has emerged that allow for such solutions to be obtained at significantly less computational cost through the coupling of a stochastic solution for the polymer chain configuration to a more traditional macroscopic finite-element or spectral flow approximation of the momentum and continuity equations. In this presentation, after reviewing the first of these approaches (called CONNFFESSIT) which has first been developed by Laso and Oettinger, we will discuss the more recently developed (by Hulsen and co-workers) configuration fields approach that result in even more reduced computational requirements.

Topic: Coherent and Dissipative Electronic Transport in Aperiodic Media December 12

Presenter: Jean V. Bellissard, Universite Paul Sabatier, Toulouse, France and Institut Universitaire de France