SEMINARS
Updated: 2-20-2007
   
FEBRUARY 2007
   
Sato-Tate Seminar
Topic: Moduli spaces of matrices
Presenter: Brian Conrad, University of Michigan and Columbia University
Date:  Wednesday, February 21, 2007, Time: 1:30 p.m., Location: Fine 314
   
Discrete Mathematics Seminar
Topic: Counting connected graphs via Erdös magic
Presenter: Joel Spencer, NYU
Date:  Wednesday, February 21, 2007, Time: 2:15 p.m., Location: Fine 224
Abstract: See http://www.math.princeton.edu/~bsudakov/spencer2007-spring.pdf
   
Department Colloquium
Topic: A game interpretation of curvature flows and other nonlinear PDE's
Presenter: Sylvia Serfaty, New York University
Date:  Wednesday, February 21, 2007, Time: 4:30 p.m., Location: Fine 314
Abstract: Mean curvature flow is the motion of a curve (or hupersurface) with normal velocity equal to its mean curvature. In a joint work with Robert Kohn, we showed how an elementary two-person deterministic game converges to the viscosity solution of the mean curvature equation (in level set formulation). This gives a parallel to the optimal control interpretation of first order Hamilton-Jacobi equations. In recent progress, we are able to find analogous interpretations for all parabolic and elliptic nonlinear PDEs. I should add that the abstract has many technical words, but the talk is quite easy to follow for anyone with a very basic knowledge of PDEs (and maybe even for those who don't have it...)
   
Ergodic Theory and Statistical Mechanics Seminar
Topic: The two-dimensional Ising model and Stochastic Loewner Evolution
Presenter: Valentina Riva, Institute for Advanced Study
Date:  Thursday, February 22, 2007, Time: 2:00 p.m., Location: Fine 401
Abstract: I will introduce Stochastic Loewner Evolution by illustrating its application to the two-dimensional Ising model.
   
Princeton University and Institute for Advanced Study Number Theory Seminar
Topic: On the Computation of p-adic Height Pairings on Jacobians of hyperelliptic Curves
Presenter: Amnon Besser, Ben-Gurion University, Israel
Date:  Thursday, February 22, 2007, Time: 4:30 p.m., Location: SH-101
Abstract: p-adic height pairings are analogues of the real height pairings that show up for example in the Birch-Swinnerton Dyer conjectures on special values of L-functions of Abelian varieties. The p-adic pairings show up when one tries to formulate p-adic analogues of these conjectures. The work of Mazur, Stein and Tate from two years ago gives a managable algorithm for computing this pairing on elliptic curves. The talk will present an algorithm for the computation of p-adic height pairings on hyperelliptic curves over number fields. Our work is not directly related to the work of Mazur Stein and Tate, though there are some similarities in the difficulties that occur and in the use of Kedlaya's algorithm. I will first explain where this height pairing arise, and how it decomposes into a sum of local terms at the places of the field. The most interesting is for places above the prime p. We use a description of these local terms given by Coleman and Gross that uses the theory of Coleman integration that I will also sketch. I will also review how one computes Coleman integrals using Kedlaya's algorithm and explain some of the tricks that are used to complete the computation at these primes. Finally I will discuss the situation at other primes, where there are still some delicate issues to resolve.
   
Topology Seminar
Topic: Minimality, Kodaira dimension, and symplectic sums
Presenter: Micheal Usher
Date:  Thursday, February 22, 2007, Time: 4:30 p.m., Location: Fine 314
Abstract: I'll explain how pseudoholomorphic curves can be combined with several other techniques to give simple necessary and sufficient conditions for a symplectic four-manifold arising as a symplectic sum along surfaces of positive genus to be minimal, or to have nonpositive Kodaira dimension. Among other things, this gives a new way of showing that certain small four-manifolds are exotic, and proves a conjecture of Stipsicz about the minimality of fiber sums of Lefschetz fibrations.
   
Differential Geometry and Geometric Analysis Seminar
Topic: TBA
Presenter: Rosa Sena-Dias, MIT and IST
Date:  Friday, February 23, 2007, Time: 3:00 p.m., Location: Fine 314
   
Analysis Seminar
Topic: TBA
Presenter: Michael Weinstein, Columbia University
Date:  Monday, February 26, 2007, Time: 4:00 p.m., Location: Fine 110
   
PACM Colloquium
Topic: A Taste of Compressed Sensing
Presenter: Ron DeVore, Courant Institute, New York University
Date:  Monday, February 26, 2007, Time: 4:00 p.m., Location: Fine 214
Abstract:

The usual paradigm for encoding signals is based on the Shannon sampling theorem. If the signal is broad-banded then this requires a high sampling rate even though the information content in the signal may be small. Compressed Sensing is an attempt to get out of this dilemma and sample at close to the information rate. The fact that this may be possible is embedded in some old mathematical results in functional analysis, geometry and approximation. This talk will be an excursion into these topics which will focus on the relation between the number of samples we take of a signal and how well we can approximate the signal. It will take place in the discrete setting for vectors in Euclidean space. The talk should be understandable to graduate students and non specialists.

   
Algebraic Geometry Seminar
Topic: On Gabber's finiteness theorem in étale cohomology
Presenter: Luc Illusie, Université Paris-Sud and IAS
Date:  Tuesday, February 27, 2007, Time: 4:30 p.m., Location: Fine 322
Abstract: Gabber has recently proven the constructibility of direct images of constructible sheaves of torsion prime to the characteristics by morphisms of finite type between excellent schemes. The main new ingredient in the proof is a deep local resolution theorem. I will start with a brief historical sketch, give an outline of the proof and discuss some by-products and related questions.
   
Mathematical Physics Seminar
Topic: The Thomas-Fermi limit of rapidly rotating Bose gases
Presenter: Jakob Yngvason, University of Vienna
Date:  Tuesday, February 27, 2007, Time: 4:30 p.m., Location: Jadwin 343
Abstract: Starting from the many-body Hamiltonian we derive the leading order energy and density asymptotics for the ground state energy and density of a rotating Bose gas in an anharmonic trap, in the limit in which the coupling parameter and/or the rotation speed tend to infinity, but the gas remains dilute. Although the many-body wave function is expected to have a complicated phase, the leading order contribution to the energy can be computed by minimizing a simple functional of the density alone.
   
Operations Research and Financial Engineering Seminar
Topic:

Coherent risk measures and coherent acceptability indices

Presenter:

Alexander Cherney, Moscow State University

Date:  Tuesday, February 27, 2007, Time: 4:30 p.m., Location: E-219, E-Quad
Abstract: The frst part of the talk discusses which representatives of coherent risk measures have the best properties from the economic viewpoint. In particular, I will describe several coherent risks measures termed MINV@R, MAXV@R, MAXMINV@R, and MINMAXV@R. As an example, MINV@R is a risk measure of the form

ρ(X) = -E{X1,….., XN};

where N is a natural number and X1; : : : ;XN are independent draws of X.
The second part of the talk deals with the question: which axioms a proper measure of trade performance should satisfy and what is the description of the corresponding performance measures? I will describe a new notion of a coherent acceptability index introduced in a recent paper with D. Madan.

References
[1] A.S. Cherny.Weighted V@R and its properties. Finance and Stochastics, 10 (2006), p. 367{393.

[2] A.S. Cherny, D.B. Madan. On measuring the degree of market efficiency. Preprint, www.ssrn.com.
   
Discrete Mathematics Seminar
Topic: Graphs and games: every dense graph has a large Surplus
Presenter: Jozsef Beck, Rutgers University
Date:  Wednesday, February 28, 2007, Time: 2:15 p.m., Location: Fine 224
Abstract: See http://www.math.princeton.edu/~bsudakov/beck2007-spring.pdf
   
Geometry, Representation Theory, and Moduli Seminar
Topic: TBA
Presenter: Maryam Mirzakhani, Princeton University
Date:  Wednesday, February 28, 2007, Time: 3:00 p.m., Location: Fine 214
   
Department Colloquium
Topic: The problem of stability for black hole spacetimes in general relativity
Presenter: Mihalis Dafermos, University of Cambridge
Date:  Wednesday, February 28, 2007, Time: 4:30 p.m., Location: Fine 314
Abstract: The notion of black hole plays a central role in general relativity. Nonetheless, the most basic mathematical questions about black holes remain unanswered, in particular, the question of their stability with respect to perturbation of initial data. In this talk, I will discuss how this problem is mathematically formulated, emphasizing its relation to decay properties for solutions of wave equations. I will then discuss recent progress on various related problems.
   
MARCH 2007
   
Ergodic Theory and Statistical Mechanics Seminar
Topic: On the connection between Stochastic Loewner Evolution and Conformal Field Theory
Presenter: Valentina Riva, Institute for Advanced Study
Date:  Thursday, March 1, 2007, Time: 2:00 p.m., Location: Fine 401
Abstract: I will discuss the relation between Stochastic Loewner Evolution and Conformal Field Theory with examples from the Potts model and self avoiding walks.
   
Differential Geometry and Geometric Analysis Seminar
Topic: TBA
Presenter: Brian Weber, University of Wisconsin
Date:  Friday, March 2, 2007, Time: 3:00 p.m., Location: Fine 314
   
Analysis Seminar
Topic: TBA
Presenter: Jan Metzger, Stanford University
Date:  Monday, March 5, 2007, Time: 4:00 p.m., Location: Fine 110
   
PACM Colloquium
Topic: Linear stability of ring systems
Presenter: Robert Vanderbei, ORFE & PACM, Princeton University
Date:  Monday, March 5, 2007, Time: 4:00 p.m., Location: Fine 214
Abstract:

(Co-author: Egemen Kolemen) We give a self-contained modern linear stability analysis of a system of n equal mass bodies in circular orbit about a single more massive body. Starting with the mathematical description of the dynamics of the system, we form the linear approximation, compute all of the eigenvalues of the linear stability matrix, and finally derive inequalities that guarantee that none of these eigenvalues have positive real part. In the end, we rederive the result that J.C. Maxwell found for large n in his seminal paper on the nature and stability of Saturn’s rings, which was published 150 years ago. In addition, we identify the exact matrix that defines the linearized system even when n is not large. This matrix is then investigated numerically (by computer) to find stability inequalities. Furthermore, using properties of circulant matrices, the eigenvalues of the large 4n×4n matrix can be computed by solving n quartic equations, which further facilitates the investigation of stability. Finally, we have implemented an n-body simulator and we verify that the threshold mass ratios that we derived mathematically or numerically do indeed identify the threshold between stability and instability. Throughout the paper we consider only the planar n-body problem so that the analysis can be carried out purely in complex notation, which makes the equations and derivations more compact, more elegant and therefore, we hope, more transparent. The result is a fresh analysis that shows that these systems are always unstable for 2 <= n <= 6 and for n > 6 they are stable provided that the central mass is massive enough. We give an explicit formula for this mass-ratio threshold.

The full paper is posted here: orfe.princeton.edu/~rvdb/tex/saturn/ms.pdf (PDF)


   
Algebraic Geometry Seminar
Topic: TBA
Presenter: Jason Starr, SUNY Stony Brook and MIT
Date:  Tuesday, March 6, 2007, Time: 4:30 p.m., Location: Fine 322
   
Operations Research and Financial Engineering Seminar
Topic: A Filtering Approach to Tracking Volatility from Prices Observed at Random Times
Presenter: Boris Rozovsky, Brown University
Date:  Tuesday, March 6, 2007, Time: 4:30 p.m., Location: E-219, E-Quad
Abstract: See http://orfe.princeton.edu/papers/rozovsky-abstract.pdf
   
Discrete Mathematics Seminar
Topic: Sum-product and applications
Presenter: Jean Bourgain, IAS
Date:  Wednesday, March 7, 2007, Time: 2:15 p.m., Location: Fine 224
   
Geometry, Representation Theory, and Moduli Seminar
Topic: TBA
Presenter: R. Thomas, Imperial College
Date:  Wednesday, March 7, 2007, Time: 3:00 p.m., Location: Fine 214
   
Department Colloquium
Topic: TBA
Presenter: Jason Starr, SUNY Stony Brook and MIT
Date:  Wednesday, March 7, 2007, Time: 4:30 p.m., Location: Fine 314
   
Ergodic Theory and Statistical Mechanics Seminar
Topic: Baby-talk on Sato-Tate problem
Presenter: Nicholas Katz, Princeton University
Date:  Thursday, March 8, 2007, Time: 2:00 p.m., Location: Fine 401
   
Differential Geometry and Geometric Analysis Seminar
Topic: TBA
Presenter: Nicos Kapouleas, Brown University
Date:  Friday, March 9, 2007, Time: 3:00 p.m., Location: Fine 314
   
PACM Colloquium
Topic: Patterns of Turbulence
Presenter: Dwight Barkley, Mathematics, University of Warwick
Date:  Monday, March 12, 2007, Time: 4:00 p.m., Location: Fine 214
Abstract: Plane Couette flow -- the flow between two infinite parallel plates moving in opposite directions -- undergoes a discontinuous transition from laminar flow to turbulence as the Reynolds number is increased. Due to its simplicity, this flow has long served as one of the canonical examples for understanding shear turbulence and the subcritical transition process typical of channel and pipe flows. Only recently was it discovered in very large aspect ratio experiments that this flow also exhibits remarkable pattern formation near transition. Steady, spatially periodic patterns of distinct regions of turbulent and laminar flow emerges spontaneously from uniform turbulence as the Reynolds number is decreased. The length scale of these patterns is more than an order of magnitude larger than the plate separation. It now appears that turbulent-laminar patterns are inevitable intermediate states on the route from turbulent to laminar flow in many shear flows. I will explain how we have overcome the difficulty of simulating these large scale patterns and show results from studies of three types of patterns: periodic, localized, and intermittent.
   
Algebraic Geometry Seminar
Topic: TBA
Presenter: Stephen Lichtenbaum, Brown University
Date:  Tuesday, March 13, 2007, Time: 4:30 p.m., Location: Fine 322
   
Operations Research and Financial Engineering Seminar
Topic:

Equi-energy sampler: From statistical inference to protein folding

Presenter: Samuel Kou, Department of Statistics, Harvard University
Date:  Tuesday, March 13, 2007, Time: 4:30 p.m., Location: E-219, E-Quad
Abstract: We introduce a new sampling algorithm, the equi-energy sampler, for efficient statistical sampling and estimation. Complementary to the widely used temperature-domain methods, the equi-energy sampler, utilizing the temperature-energy duality, targets the energy directly. The focus on the energy function not only facilitates efficient sampling, but also provides a powerful means for statistical estimation, for example, the calculation of the density of states and microcanonical averages in statistical mechanics. The equi-energy sampler is applied to a variety of problems, including exponential regression in statistics, motif sampling in computational biology, and protein folding.

This work is joint with Qing Zhou and Wing Wong.
   
Department Colloquium
Topic: TBA
Presenter: Pavel Bleher, Indiana University and Purdue University, Indianapolis
Date:  Wednesday, March 14, 2007, Time: 4:00 p.m., Location: Fine 314
   
Ergodic Theory and Statistical Mechanics Seminar
Topic: Large N asymptotics in random matrix models
Presenter: Pavel Bleher, Indiana University and Purdue University Indianapolis
Date:  Thursday, March 15, 2007, Time: 2:00 p.m., Location: Fine 401
Abstract: We review recent results and methods on the large N asymptotics in unitary ensembles of random matrices. The main results concern with the universal scaling limits of eigenvalue correlation functions in the bulk of the spectrum, at the edge points, and at the critical points. We discuss the powerful Riemann-Hilbert approach to the problem.
   
Analysis Seminar
Topic: TBA
Presenter: Ovidiu Savin, Columbia University
Date:  Monday, March 26, 2007, Time: 4:00 p.m., Location: Fine 110
   
PACM Colloquium
Topic: Modeling Science: Topic models of Scientific Journals and Other Large Text Databases
Presenter: David Blei, Computer Science, Princeton University
Date:  Monday, March 26, 2007, Time: 4:00 p.m., Location: Fine 214
Abstract:

A surge of recent research in machine learning and statistics has developed new techniques for finding patterns of words in document collections using hierarchical probabilistic models. These models are called "topic models" because the word patterns often reflect the underlying topics that are combined to form the documents; however topic models also naturally apply also such data as images and biological sequences.

After reviewing the basics of topic modeling, I will describe two related lines of research in this field, which extend the current state of the art.

First, I will describe probabilistic models designed to capture the dynamics of topics as they evolve over time. Many document collections change over time: scientific articles, emails, and search queries reflect evolving content, and it is important to model the corresponding evolution of the underlying topics.

Second, I will describe a probabilistic topic model which can capture correlations between the hidden topics. Previous models assume that the occurrence of the different topics are independent. In many document collections, however, the presence of a topic may be correlated with the presence of another. For example, a document about sports is more likely to also be about health than international finance.

In addition to giving quantitative, predictive models of a corpus, topic models provide a qualitative window into the structure of a large document collection. This allows a user to explore a corpus in a topic-guided fashion. I will demonstrate the capabilities of these new models on the archives of the journal Science, founded in 1880 by Thomas Edison. The models are built on the noisy text from JSTOR, an online scholarly journal archive, resulting from an optical character recognition engine run over the original bound journals.

(joint work with M. Jordan, A. Ng, and J. Lafferty)


   
Algebraic Geometry Seminar
Topic: Desingularization of quasi-excellent Q-schemes
Presenter: Michael Temkin, University of Pennsylvania
Date:  Tuesday, March 27, 2007, Time: 4:30 p.m., Location: Fine 322
   
Geometry, Representation Theory, and Moduli Seminar
Topic: TBA
Presenter: B. Eynard, CEA/Saclay
Date:  Wednesday, March 28, 2007, Time: 3:00 p.m., Location: Fine 214
   
Differential Geometry and Geometric Analysis Seminar
Topic: TBA
Presenter: Simon Brendle, Stanford University
Date:  Friday, March 30, 2007, Time: 3:00 p.m., Location: Fine 314
   
APRIL 2007
   
Analysis Seminar
Topic: TBA
Presenter: Becca Thomases, Courant Institute
Date:  Monday, April 2, 2007, Time: 4:00 p.m., Location: Fine 110
   
PACM Colloquium
Topic: TBA
Presenter: Frans Pretorius, Physics, University of Alberta
Date:  Monday, April 2, 2007, Time: 4:00 p.m., Location: Fine 214
   
Algebraic Geometry Seminar
Topic: TBA
Presenter: Junecue Suh, Princeton University
Date:  Tuesday, April 3, 2007, Time: 4:30 p.m., Location: Fine 322
   
Department Colloquium
Topic: TBA
Presenter: Edward Frenkel, UC Berkeley
Date:  Wednesday, April 4, 2007, Time: 4:30 p.m., Location: Fine 314
   
Operations Research and Financial Engineering Seminar
Topic: TBA
Presenter: Rama Cont, Columbia University
Date:  Wednesday, April 4, 2007, Time: 4:30 p.m., Location: E-219, E-Quad
   
Special Department Colloquium
Topic: Layered lattices
Presenter: Hendrik Lenstra, Mathematisch Instituut, Universiteit Leiden
Date:  Thursday, April 5, 2007, Time: 4:30 p.m., Location: TBA
Abstract: Lattice basis reduction algorithms can be used for solving systems of linear equations over the ring of integers. An analysis of this application suggests that it is more appropriately handled by means of a "layered lattice". This is a new notion of lattice, for which the length function takes values in an ordered vector space of dimension greater than one.
   
Analysis Seminar
Topic: TBA
Presenter: Jared Wunsch, Northwestern University
Date:  Monday, April 9, 2007, Time: 4:00 p.m., Location: Fine 110
   
PACM Colloquium
Topic: TBA
Presenter: Jason W. Fleischer, Electrical Engineering, Princeton University
Date:  Monday, April 9, 2007, Time: 4:00 p.m., Location: Fine 214
   
Algebraic Geometry Seminar
Topic: TBA
Presenter: Jacob Lurie, Harvard and AIM
Date:  Tuesday, April 10, 2007, Time: 4:30 p.m., Location: Fine 322
   
Operations Research and Financial Engineering Seminar
Topic: TBA
Presenter: Paul Dupuis, Brown University
Date:  Tuesday, April 10, 2007, Time: 4:30 p.m., Location: E-219, E-Quad
   
Discrete Mathematics Seminar
Topic: TBA
Presenter: David Gamarnik, MIT
Date:  Wednesday, April 11, 2007, Time: 2:15 p.m., Location: Fine 224
   
Department Colloquium
Topic: TBA
Presenter: Curtis T McMullen, Harvard University
Date:  Wednesday, April 18, 2007, Time: 4:30 p.m., Location: Fine 314
   
PACM Colloquium
Topic: Heterogeneous Lipid Bilayers: Evolving Microstructures in Biology
Presenter: Mikko Haataja, MAE, Princeton University
Date:  Monday, April 23, 2007, Time: 4:00 p.m., Location: Fine 214
Abstract:

The design and processing of materials with novel physical and mechanical properties requires a fundamental understanding of the connections between processing, microstructure, and properties. For example, mechanical properties in pure metals and alloys can be varied by manipulating the polycrystalline grain size or the size of the compositional domains through heat treatment, while elastic strain provides a way to tune the optical properties of self-assembled quantum dots during growth. In an analogous manner, the biological function of cell membranes is strongly affected by the details of the local "microstructure".

Typically, microstructural evolution takes place across multiple length and time scales, ranging from atomistic to mesoscopic ones. In this talk I will describe our recent efforts in developing physically-based, coarse-grained continuum models, which bridge the atomistic and mesoscopic scales, to elucidate lateral organization and non-equilibrium dynamics of heterogeneous lipid bilayers. In particular, I will focus on spatially organized, dynamic heterogeneities in the local lipid composition ("lipid rafts") which have been implicated in many important cellular processes including signal transduction, membrane trafficking, cytoskeleton organization, and pathogen entry.

   
Algebraic Geometry Seminar
Topic: TBA
Presenter: David Harbater, University of Pennsylvania
Date:  Tuesday, April 24, 2007, Time: 4:30 p.m., Location: Fine 322
   
Operations Research and Financial Engineering Seminar
Topic: TBA
Presenter: Andreas Hamel, Princeton University
Date:  Tuesday, April 24, 2007, Time: 4:30 p.m., Location: E-219, E-Quad
   
Discrete Mathematics Seminar
Topic: TBA
Presenter: Assaf Naor, NYU
Date:  Wednesday, April 25, 2007, Time: 2:15 p.m., Location: Fine 224
   
MAY 2007
   
Operations Research and Financial Engineering Seminar
Topic: TBA
Presenter: Rong Chen, University of Illinois at Chicago
Date:  Tuesday, May 1, 2007, Time: 4:30 p.m., Location: E-219, E-Quad
   
Department Colloquium
Topic: TBA
Presenter: Tamar Ziegler, University of Michigan
Date:  Wednesday, May 2, 2007, Time: 4:30 p.m., Location: Fine 314
   
Operations Research and Financial Engineering Seminar
Topic: TBA
Presenter: Frank Heyde, MLU Halle-Wittenberg
Date:  Tuesday, May 8, 2007, Time: 4:30 p.m., Location: E-219, E-Quad