SEMINARS
Updated: 11-23-2005
 
NOVEMBER 23 - 25, 2005
 
Statistical Mechanics Seminar
Topic: Ultraviolet stability and multiscale analysis
Presenter: Giovanni Gallavotti, University of Rome
Date:  Wednesday, November 23, 2005, Time: 2:00 p.m., Location: Jadwin 343
Abstract: An exposition of the key ideas and methods used to establish the lower bound on the ground state energy in two and three dimensional scalar quantum field theories.
 
Discrete Mathematics Seminar
Topic: A book about tic-tac-toe like games
Presenter: 

Jozsef Beck, Rutgers University

Date:  Wednesday, November 23, 2005, Time: 2:15 p.m., Location: Fine Hall 224
Abstract: See http://www.math.princeton.edu/~bsudakov/beck2005-2006.pdf
 
NOVEMBER 28 - DECEMBER 2, 2005
 
Joint Princeton University and Institute for Advanced Study Number Theory Seminar *** Please note special day, time, and location
Topic: Elliptic curves, quadratic twists and p-(in)divisibility of L-values
Presenter: 

Kartik Prasanna, UCLA

Date:  Monday, November 28, 2005, Time: 2:00 p.m. , Location: Fine Hall 224
Abstract: Let E be an elliptic curve over the rationals and p a fixed prime. A (very hard) question of Kolyvagin asks if there exists a quadratic discriminant d such that the Tate-Shafarevich group of the quadratic twist E_d has order prime to p. I will explain some recent results that are related to this question, that are obtained by studying the p-adic properties of the Shimura correspondence.
 
PACM Colloquium
Topic: Thermally-driven rare events and large deviation theory
Presenter: 

Maria Reznikoff, Mathematics, Princeton University

Date:  Monday, November 28, 2005, Time: 4:00 p.m., Location: Fine Hall 214
Abstract:

Thermal or stochastic effects are prevalent in physical, chemical, and biological systems. Particularly in small systems, noise can overpower the deterministic dynamics and lead to "rare events", events which would never be seen in the absence of noise. One example is the thermally-driven switching of the magnetization in small memory elements. Wentzell-Freidlin large deviation theory is a mathematical tool for studying rare events. It estimates their probability and also the "most likely switching pathway," which is the pathway in phase space by which rare events are most likely to occur. We explain how large deviation theory and concepts from stochastic resonance may be applied to analyze thermally-activated magnetization reversal in the context of the spatially uniform Landau-Lifschitz-Gilbert equations. The time-scales of the experiment are critical. One surprising and physically relevant result is that in multiple-pulse experiments, nonconvential "short-time switching pathways" can dominate. The effect is dramatic: the usual pathway (connected with the Arrhenius-law) underestimates the probability of switching by an exponential factor.

An advantage of the method via large deviation theory is that it generalizes to systems with spatial variation. To discuss the complications and richness that emerge when spatial variation is taken into account, we consider the (simpler) Allen-Cahn equation. In this context, the rare event of interest is phase transformation from u = -1 to u = +1, and the most likely switching pathway is a pathway through function space. A natural reduced problem emerges in the "sharp-interface limit." We give a brief overview of some results (rigorous in d = 1, heuristic in d > 1.)

The first part of the talk is joint work with Bob Kohn and Eric Vanden-Eijnden. The second part includes work that is also joint with Felix Otto and Yoshihiro Tonegawa.

 
Algebraic Geometry Seminar
Topic: A_6 is of general type
Presenter: David Lehavi
Date:  Tuesday, November 29, 2005, Time: 4:30 p.m., Location: Fine Hall 322
Abstract: This is a joint work with S. Grushevsky. We construct new effective geometric divisors on the moduli spaces A_g of principally polarized complex abelian varieties. For g >= 5 we obtain a divisor of slope smaller than the currently known minimum. This in particular allows us to prove that A_g is of general type for g >= 6, thus settling the case of the Kodaira dimension of A_6 - since the 1980s the only dimension for which it has been unknown.
 
Mathematical Physics Seminar
Topic: Isoperimetric inequalities for eigenvalues of the Laplacian in the hyperbolic space H_n
Presenter: Rafael Benguria, Universidad Catolica Santiago, Chile
Date:  Tuesday, November 29, 2005, Time: 4:30 p.m., Location: Jadwin 343
Abstract: I will review several isoperimetric inequalities for eigenvalues of the laplacian on bounded, smooth domains of $H_n$ with Dirichlet boundary conditions. In particular, I will present our recent proof of an isoperimetric inequality for the second Dirichlet eigenvalue. This is joint work with Helmut Linde.
 
Operations Research and Financial Engineering Seminar
Topic:

Options embedded in variable annuities: GMDBs and GMWBs

Presenter: Tom Salisbury, York University and the Fields Institute
Date:  Tuesday, November 29, 2005, Time: 4:30 p.m., Location: Room E-219, Engineering Quad
Abstract: The Insurance industry is increasingly exposed to market risk, through retirement savings products such as variable annuities. These products frequently contain riders that can be viewed as embedded options. In the last market cycle, unhedged guaranteed minimum death benefit (GMDB) riders caused substantial losses across the industry. A variety of new riders have emerged in recent years such as guaranteed minimum withdrawal benefits (GMWBs). I will discuss some of the valuation, control and hedging issues associated with these products. This is joint work with Moshe Milevsky, of the Schulich School of Business.
 
Princeton University Graduate Student Seminar
Topic: The Face Numbers of a Simple Convex Polytope
Presenter: Balin Fleming, Princeton University
Date:  Wednesday, November 30, 2005, Time: 12:30 p.m., Location: Fine Hall 224
Abstract: A polytope $K$ is the convex hull of a finite collection of points in $R^n$. Let $f_i$ be the number of i-dimensional faces of $K$. We ask: what vectors $(f_0, ..., f_{n-1})$ arise as the face numbers of some $n$-dimensional $K$? For simplicial polytopes McMullen proposed a conjecture. This was proved by Billera and Lee (sufficiency) and Stanley (necessity). Stanley's proof uses deep results in algebraic geometry by tying the $f_i$ to the cohomology of an associated toric variety, but later McMullen gave another, more combinatorial proof. We'll discuss a variation on McMullen's argument, by passing from K to its normal fan, combinatorially constructing the cohomology as the ring of continuous conewise polynomial functions, and investigating the structure of this ring.
 
Statistical Mechanics Seminar
Topic: The Bose Gas, Part 2
Presenter: Eliot Lieb, Princeton University
Date:  Wednesday, November 30, 2005, Time: 2:00 p.m., Location: Jadwin 343
Abstract: This will be the second of several lectures on the theory of the Bose gas and its various properties at or near absolute zero temperature.
Reference: The Mathematics of the Bose Gas and its Condensation}, vol. 34, Oberwolfach Seminars Series, Birkhaeuser (2005).
 
Discrete Mathematics Seminar
Topic: What is known about Frieman's theorem?
Presenter: 

Ben Green, Clay Institute, University of Bristol and MIT

Date:  Wednesday, November 30, 2005, Time: 2:15 p.m., Location: Fine Hall 224
Abstract: See http://www.math.princeton.edu/~bsudakov/green2005-2006.pdf
 
Department Colloquium
Topic: Multiplier Ideal Sheaves and the Finite Generation of Canonical Rings
Presenter: 

Yum-Tong Siu, Harvard University

Date:  Wednesday, November 30, 2005, Time: 4:30 p.m., Location: Fine Hall 314
Abstract: Multiplier ideal sheaves identify the jet directions where estimates for partial differential equations fail.  The technique of multiplier ideal sheaves injects in a new way methods of algebraic geometry into problems of analysis.  It also opens new channels of applying analysis to problems in algebraic geometry.  We will discuss its application to the problem of the finite generation of canonical rings.
 
Operations Research and Financial Engineering Seminar
Topic:

Prospect Eleven: The making, testing, and running of Princeton's entry in the 2005 Darpa Grand Challenge

Presenter: Alain L. Kornhauser and Members of the Prospect Eleven Team
Date:  Wednesday, November 30, 2005, Time: 4:30 p.m., Location: Friend Bowl 008
Abstract: The DARPA Grand Challenge last October 8 was a field test intended to accelerate research and development in autonomous ground vehicles. Prospect Eleven was an "extreme" entry in that it was completely designed, built/modified and tested by a dedicated core of Princeton undergraduates and was only one of two entries that relied on stereo vision. Prospect Eleven performed flawlessly for the first ten miles before succumbing to a software bug.  Unsatisfied, part of the team returned to the desert during Fall Break.  After changing one line of code, Prospect Eleven autonomously completed what remained of the 132 mile course as well as the more difficult 143 mile 2004 course.  The talk will focus on Prospect Eleven's fundamental design concepts, experiences and lessons learned.
 
Operations Research and Financial Engineering Seminar
Topic:

Comprehensive Robust Optimization

Presenter: Aharon Ben-Tal, Minerva Optimization Center, Department of Industrial Engineering, Technion University
Date:  Thursday, December 1, 2005, Time: 4:30 p.m., Location: Room E-219, Engineering Quad
Abstract: We propose a new methodology for handling optimization problems under uncertainty.   Whereas in the standard Robust Optimization (RO) paradigm one seeks decisions ensuring a required performance for all realizations of the data belonging to a given bounded uncertainty set, in the new Comprehensive Robust Optimization (CRO) paradigm one requires also a  controlled deterioration in the performance for data outside the uncertainty set.  The CRO methodology opens up new possibilities to solve efficiently multi-stage finite horizon uncertain optimization problems, in particular to analyze and synthesize linear controllers for discrete time dynamical systems.
 
Topology Seminar
Topic:

Angles and volumes of degenerating hyperbolic polyhedra

Presenter: Igor Rivin, Temple University
Date:  Thursday, December 1, 2005, Time: 4:30 p.m., Location: Fine Hall 314
Abstract: J. W. Milnor had studied the possible angles of simplices in $\mathbb{H}^n,$ and conjectured that the volume function extends continuously to the closure of the set of possible angles, and tends to zero at those points which also lie in the closure of the set of angles of Euclidean simplices.  We will answer (affiirmatively) Milnor's conjecture, but also extend the question and the answer to arbitrary convex polyhedra (and polytopes), in process giving a description of the boundary of the set of dihedral angles of polyhedra and some estimates at the diameter growth of degenerating polyhedra.
 
Geometric Analysis Seminar
Topic: Quasilinear and Hessian equations with nonlinear source terms
Presenter: Igor Verbitsky, University of Missouri-Columbia
Date:  Friday, December 2, 2005, Time: 3:00 p.m., Location: Fine Hall 314
Abstract: We will give a characterization of removable singularities and present a solution to the existence problem for a class of quasilinear and fully nonlinear PDE with nonlinear source terms. Model problems involve the p-Laplacian or k-Hessian operators. Solutions, possibly singular, are understood in the renormalized (entropy) or viscosity sense. Sharp global and local estimates, and Liouville theorems will be discussed. Our approach is based on sharp forms of Harnack's inequality, nonlinear potential theory, and harmonic analysis methods. This work is joint with Nguyen Cong Phuc.
 
DECEMBER 5 - 9, 2005
 
PACM Colloquium
Topic: The Boosting Approach to Machine Learning
Presenter: 

Robert Schapire, Computer Science, Princeton University

Date:  Monday, December 5, 2005, Time: 4:00 p.m., Location: Fine Hall 214
Abstract: Machine learning studies the design of computer algorithms that automatically make predictions about the unknown based on past observations. Often, the goal is to learn to categorize objects into one of a relatively small set of classes. Boosting, one method for solving such learning problems, is a general technique for producing a very accurate classification rule by combining rough and moderately inaccurate "rules of thumb." While rooted in a theoretical framework of machine learning, boosting has been found to perform quite well empirically. After introducing the boosting algorithm AdaBoost, I will explain the underlying theory of boosting, including our explanation of why boosting often does not suffer from overfitting. I also will touch on some of the other theoretical perspectives on boosting, and describe some recent applications and extensions.
 
Analysis Seminar *** Please note special time, date, and location
Topic: A new characterization of Sobolev spaces
Presenter: Hoai-Minh Nguyen, University Paris 6
Date:  Monday, December 5, 2005, Time: 4:30 p.m., Location: Fine Hall 314
 
Algebraic Geometry Seminar
Topic: TBA
Presenter: R. Guralnick, University of Southern California
Date:  Tuesday, December 6, 2005, Time: 4:30 p.m., Location: Fine Hall 322
 
Operations Research and Financial Engineering Seminar
Topic:

Consistent prices and face-lifting pricing under transaction costs

Presenter: Paolo Guasoni, Boston University
Date:  Tuesday, December 6, 2005, Time: 4:30 p.m., Location: Room E-219, Engineering Quad
Abstract:

Consistent Price Systems (CPS) are the counterparts of martingale measures for models with transaction costs, as they guarantee the absence of arbitrage, and allow to characterize superreplication prices of contingent claims. Unfortunately, and especially for non semimartingale models, the explicit calculation of CPS may not be easy.

We first establish the existence of CPS for price processes endowed with their natural filtration from a condition on their topological support, which can often be easily verified. In particular, we see that any two nonatomic continuous processes with full support have the same set of consistent price systems.

We then exploit this result to characterize the superreplication prices of a class of contingent claims as the backward recursive concave envelope (face-lifting) of their payoff. For European calls and puts, we obtain a very simple proof that their prices are trivial.

(Joint work with W. Schachermayer)

 
Princeton University Graduate Student Seminar
Topic: The Prime Number Theorem on the Nose
Presenter: Alex Kontorovich, Columbia University
Date:  Wednesday, December 7, 2005, Time: 12:30 p.m., Location: Fine Hall 224
Abstract: When Gauss was a little boy, he did many wonderful things. One of them was conjecture the asymptotic formula for the number of primes less than some fixed bound, which of course implies an asymptotic formula for the size of the n-th prime. About a century later, his conjecture was answered affirmatively and is now known as the Prime Number Theorem. We will describe (read: handwave) a recent result on how many primes are exactly equal to their average value (we call these "primes on the nose"). No prior knowledge is assumed.
 
Discrete Mathematics Seminar
Topic: The quantum adversary method and classical formula size lower bounds
Presenter: 

Mario Szegedy, Rutgers University

Date:  Wednesday, December 7, 2005, Time: 2:15 p.m., Location: Fine Hall 224
Abstract: See http://www.math.princeton.edu/~bsudakov/szegedi2005-2006.pdf
 
Department Colloquium
Topic: Nonlocal instability of the planar 3 body problem
Presenter:  Vadim Kaloshin, Caltech/Penn State
Date:  Wednesday, December 7, 2005, Time: 4:30 p.m., Location: Fine Hall 314
Abstract: The Restricted Planar Circular 3 Body Problem (RPC3BP) which is the simplest nonintegrable 3 body problem. Usually it is viewed as a model for planar either Sun-Jupiter-Asteriod or Sun-Earth-Moon system. Stability v.s. instability of such a system is one of long standing problems. Using Aubry-Mather
theory, Mather variational method, and numerical analysis, we managed to prove existence of rich variety of unstable motions. For example, an Asteriod could have a nearly elliptic orbit of say eccenticity 0.76 in the past and escape to infinity along nearly parabolic orbit of eccentricity more than 1 in the future. These motions could be interpreted as Arnold diffusion for this system. Instability results for RPC3BP imply instability for more general planar 3 body problems. This is a joint work with T. Nguyen and D. Pavlov.
 
Analysis Seminar
Topic: TBA
Presenter: Joachim Krieger, Harvard University
Date:  Thursday, December 8, 2005, Time: 4:00 p.m., Location: Fine Hall 214
 
Geometric Analysis Seminar
Topic: TBA
Presenter:

Pierre Albin, MIT

Date:  Friday, December 9, 2005, Time: 3:00 p.m., Location: Fine Hall 314
 
Joint Princeton University and Institute for Advanced Study Number Theory Seminar *** Please note special day
Topic: Serre's modularity conjecture
Presenter: 

Chandrashekhar Khare, University of Utah

Date:  Friday, December 9, 2005, Time: TBA, Location: TBA
Abstract: The title refers to a conjecture that Serre made in the early 1970's, that has proved to be very influential. I will sketch the main ideas of the proof of the level 1 case of Serre's conjecture. If time permits, I will indicate how these ideas can be extended to prove almost all of Serre's conjecture.  The latter is joint work with J-P. Wintenberger.
 
Special Topology & Geometry Meeting in Honor of Wu-chung Hsiang
Presenters: Tobias Colding, MIT and NYU
Michael Hopkins, Harvard University
Dennis Sullivan, Suny at Stony Brook
Zoltan Szabo, Princeton University
Date: 
Location:
Saturday, December 10, 2005
A01 McDonnell Hall, Princeton University
See http://www.math.princeton.edu/HsiangTopologyDay/ for more information.
 
DECEMBER 12 - DECEMBER 16, 2005
 
PACM Colloquium
Topic: The General Circulation of the Ocean and Atmosphere as a Problem in Turbulence
Presenter: 

Geoff Vallis, Geosciences/Atmospheric & Oceanic Sciences, Princeton University

Date:  Monday, December 12, 2005, Time: 4:00 p.m., Location: Fine Hall 214
Abstract: The large-scale circulation is not only affected but is essentially effected by turbulent flows. This turbulence is not the small-scale turbulence that is (unfortunately) sometimes connoted by the word turbulence, but is turbulence up to the scale of the large-scale flow itself. This is largely two-dimensional, so-called geostrophic turbulence. We will discuss what is known and what is unknown about such flow, the problems of both simulating it and of understanding it, and whether these two are the same.
 
Princeton University Graduate Student Seminar
Topic: Tell Me Your Values and I Will Tell You What You Are!
Presenter: Boris Bukh, Princeton University
Date:  Wednesday, December 14, 2005, Time: 12:30 p.m., Location: Fine Hall 224
Abstract: Suppose you know the values a rational function; can you tell what the rational function is? When the ground field is the the rational numbers, the answer is almost yes. I will prove this and other cheerful facts about images of polynomials and rational functions.
 
Discrete Mathematics Seminar
Topic: Spectral profile and Markov chain mixing
Presenter: 

Prasad Tetali, Georgia Tech

Date:  Wednesday, December 14, 2005, Time: 2:15 p.m., Location: Fine Hall 224
Abstract: See http://www.math.princeton.edu/~bsudakov/tetali2005-2006.pdf