Princeton University Mathematics Department
Seminar Bulletin, Spring 1999 - 2000
Current info: http://www.math.princeton.edu/~web/seminar.html
Wednesday, March 29, 2000
Week of March 27 - 31, 2000
Department Colloquium Wednesday 4:30 Fine 314
Topic: Geometric zeta functions on locally symmetric manifolds March 29
Presenter: R. Stanton, Ohio State University
Abstract: Geodesics on a closed Riemann surface of constant negative curvature were assembled into a zeta function by Selberg. Subsequently, global properties of the surfaces were found to be expressible as "special values" of these zeta functions. I shall survey developments towards the constructions on locally symmetric manifolds of such geometric zeta functions. Various uses of harmonic analysis to compute topological invariants appearing in these functions will be highlighted. Examples of global geometric properties that can be extracted from these geometric zeta functions will be given.
Ergodic Theory & Statistical Mechanics Thursday 2:30 Fine 110
Topic: Deviation of ergodic averages for area-preserving flows March 30
on higher genus surfaces
Presenter: Giovanni Forni, Princeton University
Abstract: We give a proof of a substantial part of a conjecture by Kontsevich and Zorich concerning the behaviour of ergodic averages of smooth functions for generic conservative flows on higher genus surfaces (and related systems such as interval exchange transformations).
Topology Seminar Thursday 4:30 Fine 314
Topic: Contact structures on the boundaries of subcritical Stein domains March 30
Presenter: Ilya Ustilovsky, New York University
Graduate Student Seminar Friday 12:30 Fine 214
Topic: A geometric proof of existence of Whitney's stratification March 31
Presenter: Vadim Kaloshin, Princeton University
Abstract: A stratification of a set, e.g. an analytic variety, is, roughly, a partition of it into manifolds so that these manifolds fit together "regularly". A "regular" partition is usually called a Whitney stratification. The stratification theory was originated by Thom and Whitney for the algebraic and analytic sets. It was one of key ingredients for Mather's proof of topological stability theorem. During the talk we present an elementary geometric proof of existence of Whitney stratification based on Rolle's lemma.
Princeton Discrete Math Seminar Friday 2:30 Fine 322
Topic: Constructing representations of a matroid March 31
Presenter: Jim Geelen, University of Waterloo
Abstract: ``For $M$ is a matroid that is not representable over a finite field {\bf F}, we consider the problem of finding a short certificate that $M$ is not representable over {\bf F}$.'' The purpose of this talk is to explain the previous sentence and to present partial results toward the solution of the problem. This is joint work with James Oxley, Dirk Vertigan, and Geoff Whittle.
Geometry Seminar Friday 3:00 Fine 314
Topic: A priori estimates for two classes of fully nonlinear March 31
equations without convexity
Presenter: Yu Yuan, University of Texas
Abstract: (I) We derive an a priori estimate for the fully nonlinear elliptic equations with convex level sets. We do not need any convexity assumption for the proof of two dimensional case, as the classical result indicates. This is a joint work with L. A. Caffarelli. (II) We also derive an a priori estimate in dimension three for the special Lagrangian equations, which fail both the usual convexity condition and the assumption in (I).
Geometry Seminar Friday 4:00 Fine 314
Topic: Uniqueness of tangent connections of Yang-Mills connections March 31
of isolated singularities
Presenter: Yang Boazhong, M.I.T.
Week of April 3 - 7, 2000
Analysis Seminar Monday 4:00 Fine 314
Topic: Discrete analogues of the spherical maximal function April 3
Presenter: Stephen Wainger, University of Wisconson
PACM Colloquium Monday 4:00 Fine 224
Topic: A Variational Approximation Scheme for Three Dimensional April 3
Elastodynamics with Polyconvex Energy
Presenter: Athanasios Tzavaras, Department of Mathematics, University of Wisconsin-Madison
Abstract: The topic of this talk is the construction of a variational approximation scheme for the equations of three dimensional elastodynamics with polyconvex stored energy. The assumption of polyconvexity is instrumental in the existence theory for the equations of elastostatics, and the purpose is to investigate its role for the equations of elastodynamics. The scheme is motivated by embedding the equations of elastodynamics into a larger system consisting of the equation of motion and some geometric evolutions of the null Lagrangians (the determinant and cofactor matrix). The scheme decreases the mechanical energy, and its solvability is reduced to the solution of a constrained convex minimisation problem. We will survey certain results on stability and convergence of such approximations of the equations of elastodynamics in the 3-d and in the 1-d setting. (joint work with S. Demoulini (Oxford) and D. Stuart (Cambridge)).
Topology Seminar Monday 4:30 Fine 322
Topic: TBA April 3
Presenter: Mark Gross, University of Warwick
Algebraic Geometry Seminar Tuesday 4:15 Fine 322
Topic: Lifting projective l-adic representations April 4
Presenter: D. Prasad
Abstract: It is a theorem of Tate that a complex projective representation of the Galois group of a global field can be lifted to an ordinary representation. In this talk we will formulate a conjectural version of this theorem for compatible family of projective l-adic representations. We will give a natural context where these projective l-adic representations arise, and show that in these `Geometric contexts' these projective representations can be compatibly lifted.
Colloquium Wednesday 4:30 Fine 314
Topic: Random Colorings of a Cayley Tree April 5
Presenter: Peter Winkler, Bell Labs
Abstract: Probability measures on the space of proper colorings of a Cayley tree (that is, an infinite regular connected graph with no cycles) are of interest not only in combinatorics but also in statistical physics, as states of the antiferromagnetic Potts model at zero temperature, on the ``Bethe lattice''. We concentrate on a particularly nice class of such measures which remain invariant under parity-preserving automorphisms of the tree. Using branching random walks, we determine when more than one such measure exists. This talk (on joint work with Graham Brightwell, of the London School of Economics) will provide, we hope, a helpful glimpse into the rapidly expanding intersection of combinatorics and statistical physics.
Week of April 10 - 14, 2000
Analysis Seminar Monday 4:00 Fine 314
Topic: TBA April 10
Presenter: Hart Smith, University of Washington
PACM Colloquium Monday 4:00 Fine 224
Topic: How are Protein Structures Selected in Nature? April 10
Presenter: Chao Tang, Physical Sciences Research, NEC Inc.
Abstract: Natural protein sequences and structures are very special classes among all possible sequences and structures.
A protein sequence has, as its folded native state, a distinct global minimum of free energy well separated from other
misfolded states--a property not shared by random sequences. Protein structures often exhibit a high degree of regularity,
with a wealth of secondary structures, preferred motifs, and tertiary symmetries. With the use of simple models of protein
folding, we demonstrate that these special properties of proteins are related to high "designability" and evolutionary
and thermodynamic stability. The designability of each structure is measured by the number of sequences that can design
the structure--that is, sequences that possess the structure as their unique ground state. Structures differ drastically in
terms of their designability; highly designable structures emerge with a number of associated sequences much larger than
the average. These highly designable structures possess "proteinlike" secondary structures, motifs, and even tertiary
symmetries. In addition, they are thermodynamically more stable than other structures. These results suggest that protein
structures are selected in nature because they are readily designed and stable against mutations, and that such a selection
simultaneously leads to thermodynamic stability.
Ergodic Theory & Statistical Mechanics Tuesday 5:00 Fine 110
Topic: Instanton for probability of the signal lost in optical fibers April 11
Presenter: Vladimir Lebedev, Landau Institute of Theoretical Physics, Russia
Abstract: We find the probability distribution of the parameters of a soliton propagating through a noisy medium. Even though a weak noise is considered, we are interested in probabilities of large fluctuations which are beyond perturbation theory. Our method is a modification of the instanton formalism (method of optimal fluctuation) based on a saddle-point approximation in the path integral. We first solve consistently a fundamental problem of soliton propagating within the framework of noisy Nonlinear Schroedinger Equation. Then we consider possible modifications.
Algebraic Geometry Seminar Tuesday 4:15 Fine 322
Topic: TBA April 11
Presenter: Sándor Kovács, Chicago
Mathematical Physics Seminar Tuesday 4:30 Jadwin A06
Topic: Short-Range Spin Glasses: A Guide for the Perplexed April 11
Presenter: C.M. Newman, Courant Institute
Colloquium Wednesday 4:30 Fine 314
Topic: Some Insights of Computational Complexity Theory April 12
Presenter: Avi Wigderson, I.A.S. & Hebrew University, Jerusalem
Abstract: Computational complexity theory has been one of the most exciting fields of scientific research over the last few decades. This research studies the power of feasible computation, and is guided by a few clear and focused questions, deeply motivated on scientific, practical and philosophical grounds, like the P vs NP problem, and the questions on the power of randomized and quantum computation. While these problems are far from resolved, Complexity Theory was able to offer fresh rigorous definitions to some central notions which naturally (or less so) arise from these questions, and unveil many rich and beautiful connections between them. In this general survey, I would like to probe some of the unique features and insights of the complexity theory viewpoint. This will be done by considering how (and why) notions which intrigued people for centuries or even millenia (like Knowledge, Randomness, Cryptography, Learning, Proof, and naturally, Computation), reveal new dimensions, and are suprisingly linked together, when viewed from our special Computational Complexity glasses.
Topology Seminar Thursday 4:00 Fine 314
Topic: Strong form of Poincare duality April 13
Presenter: Edgar Brown, Brandeis University
Week of April 17 - 21, 2000
Analysis Seminar Monday 4:00 Fine 314
Topic: TBA April 17
Presenter: Jim Colliander, UC Berkley
Colloquium Wednesday 4:30 Fine 314
Topic: TBA April 19
Presenter: N. Higson, Pennsylvania State University
Topology Seminar Thursday 4:00 Fine 314
Topic: TBA April 20
Presenter: Casim Abbas, University of Pennsylvania
Week of April 24 - 28, 2000
Analysis Seminar Monday 4:00 Fine 314
Topic: TBA April 24
Presenter: Chris Sogge, John Hopkins University
PACM Colloquium Monday 4:00 Fine 224
Topic: 0-1 Laws for Single Molecules April 24
Presenter: Bud Mishra, Courant Institute, New York University
Abstract: Single molecule methods (e.g., optical mapping, molecular combing, fluorescent flow cytometry, ion channels, etc.) for genomics and proteomics rely on the statistical properties of a large number of identical molecules. We will use ideas from probabilistic methods to show existence of 0-1 laws governing the behavior of the group of molecules and how we exploit it in devising powerful algorithmic and automation tools to create restriction maps and sequence information from parsimonious and noisy data from single DNA molecules.
The set of tools underlying our "Computational Optical Mapping Project" have been used in making clone maps (BACS and cosmids, Y-DAZ locus), microbial genomic maps (P. falciparum, D. radiodurans, E. coli, etc.), and a partial human genome map.
Mathematical Physics Seminar Tuesday 4:30 Jadwin A06
Topic: Phase Separation and the Wulff Problem in Ising-Potts Models April 25
Presenter: Agoston Pisztora, Carnegie Mellon University
Topology Seminar Thursday 4:00 Fine 314
Topic: "New" geometry and topology of orbifolds April 27
Presenter: Y. B. Ruan, University of Wisconsin at Madison
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