SEPTEMBER 2005 

PACM Colloquium  
Topic:  Collective Motion in Engineered and Natural MultiAgent Systems 
Presenter:  Naomi Leonard, Mechanical & Aerospace Engineering, Princeton University 
Date:  Monday, September 19, 2005, Time: 4:00 p.m., Location: Fine Hall 214 
Abstract:  The collective control of mobile, multiagent systems is motivated by a range of engineering applications that require the coordination of a group of individually controlled systems. A closely related problem focuses on the role of feedback and interconnection in the collective motion of animal groups. Tools from control and dynamical systems can be used to study both engineered and natural mobile networks in a systematic and scalable way. One goal is to prove stability and robustness of designed patterns or emergent behaviors. In this talk I will describe recent collaborative work on models for collective motion based on a planar group of selfpropelled particles with steering control. We extend phase models of coupled oscillators to include spatial dynamics and use these models to stabilize and control collective motion patterns. The patterns can be parametrized, in part, by the extent of oscillator synchrony. I will conclude the talk with some discussion of open problems in the area of cooperative control. 
Operations Research and Financial Engineering Seminar  
Topic:  Semiparametric methods for geneenvironment casecontrol studies 
Presenter:  Raymond Carroll, Texas A&M University 
Date:  Tuesday, September 20, 2005, Time: 4:30 p.m., Location: Room E219, Engineering Quad 
Abstract:  We consider casecontrol studies of gene and environment interactions using prospective logistic regression models. In a typical casecontrol study, neither the intercept of the logistic regression nor the population probability of disease can be identified. However, in many cases it is reasonable to assume that genotype and environment are independent in the population, possibly conditional on covariates to account for population stratification. In such as case, we show that the intercept and population probability of disease are identified. We develop a semiparametric likelihood approach for this problem, showing that it leads to more efficient estimates of geneenvironment interaction parameters than the standard approach. In addition, if the probability of disease is known in the population, we show efficiency gains for estimating geneenvironment interactions, again in contrast to the standard approach. Multiple extensions are discussed, including to missing genotype data, haplotype data, and measurement error in genotypes or environmental variables. Applications to two important data sets are discussed. This is joint work with Nilanjan Chatterjee (National Cancer Institute). 
Operations Research and Financial Engineering Seminar *** Please note special date  
Topic:  Portfolio Theory: Past, Present and Future 
Presenter:  Harry Markowitz, Rady School at the University of California, San Diego 
Date:  Wednesday, September 21, 2005, Time: 4:30 p.m., Location: Room E219, Engineering Quad 
Abstract:  This talk will discuss: What was financial theory and practice like before 1952? What did portfolio theory add? How is portfolio theory used in practice today? What may we expect from portfolio theory in the future? 
Operations Research and Financial Engineering Seminar  
Topic:  Hedging and portfolio optimization in Levy market models 
Presenter:  David Nualart, Kansas University 
Date:  Tuesday, September 27, 2005, Time: 4:30 p.m., Location: Room E219, Engineering Quad 
Abstract:  Suppose the stock price process is described by a geometric Levy process. Except for the Brownian and Poisson cases, this model is not complete and there are many equivalent martingale measures. In this talk we will show that this model can be completed by adding a series of assets related to the powerjump processes of the underlying Levy process, and we will discuss the maximization of the expected utility of a portfolio, assuming that we can invest in these additional powerjump assets. As particular cases we obtain the optimal portfolios based in stocks and bonds, showing that the new assets are superfluous for certain martingale measures that depend on the utility function we use. 
Statistical Mechanics Seminar  
Topic:  Microscopic models and mesoscopic free energies 
Presenter:  Joel Lebowitz, Rutgers University 
Date:  Wednesday, September 28, 2005,Time: 2:00 p.m., Location: Jadwin 343 
Abstract:  I will describe the statistical mechanical derivation of mesoscopic free energy functionals for systems interacting via both short range and long range (Kac) potentials. These functionals are useful for describing the spatial structure of components in various types of phase transitions. I will then consider the phenomenological Cahn Hilliard free energy functional and derive criteria for stability of droplets of the minority phase just inside the coexistence region. 
Discrete Mathematics Seminar  
Topic:  Product representations of polynomials 
Presenter:  Jacques Verstraete, University of Waterloo 
Date:  Wednesday, September 28, 2005, Time: 2:15 p.m., Location: Fine Hall 224 
Abstract:  See http://www.math.princeton.edu/~bsudakov/verstraete20052006.pdf 
Department Colloquium  
Topic:  Eigenvalue statistics and lattice points 
Presenter:  Zeev Rudnick, Tel Aviv 
Date:  Wednesday, September 28, 2005, Time: 4:30 p.m., Location: Fine Hall 314 
Abstract:  One of the more challenging problems in spectral theory and mathematical physics today is to understand the statistical distribution of eigenvalues of the Laplacian on a compact manifold. Among the most studied quantities is the counting function for eigenvalues in a window, with the position of the window chosen at random and the window size depending on its position. I will describe what is known about the statistics of this counting function for the very simple case of the flat torus, where the problem reduces to counting lattice points in annuli. In various regimes this case has been intensively studied since the early 1990's by HeathBrown, Bleher, Dyson, Lebowitz, Sinai, Sarnak, Eskin, Mozes, Margulis and others. I will explain some recent progress, by Hughes and myself and by Wigman. Time permitting, I will also discuss the case of the modular surface. 
OCTOBER 2005 

Operations Research and Financial Engineering Seminar  
Topic:  TBA 
Presenter:  Andrew Barron, Yale University 
Date:  Tuesday, October 4, 2005, Time: 4:30 p.m., Location: Room E219, Engineering Quad 
Statistical Mechanics Seminar  
Topic:  Is entropy production local in an infinite classical system? 
Presenter:  David Ruelle, IHES France 
Date:  Wednesday, October 5, 2005,Time: 2:00 p.m., Location: Jadwin 343 
Discrete Mathematics Seminar  
Topic:  TBA 
Presenter:  Van Vu, UCSD and Rutgers University 
Date:  Wednesday, October 5, 2005, Time: 2:15 p.m., Location: Fine Hall 224 
Department Colloquium  
Topic:  TBA 
Presenter:  Terence Tao, UCLA 
Date:  Wednesday, October 5, 2005, Time: 4:30 p.m., Location: Fine Hall 314 
PACM Colloquium  
Topic:  Loworder models for control of fluids 
Presenter:  Clancy Rowley, Mechanical & Aerospace Engineering, Princeton University 
Date:  Monday, October 10, 2005, Time: 4:00 p.m., Location: Fine Hall 214 
Abstract:  The ability to effectively control a fluid would enable many exciting technological advances, including the design of quieter, more efficient aircraft. Most of the flow control strategies tried so far have been largely ad hoc, and have not used many of the available tools from control theory and dynamical systems, which can guide controller design as well as placement of sensors and actuators. These tools require knowledge of a model of the system in terms of a system of differential equations, and the equations governing a fluid, though known, are too complex for these tools to apply. This talk addresses model reduction techniques, which are used to simplify existing models, to obtain loworder models tractable enough to be used for analysis and control, while retaining the essential physics. These techniques provide a bridge between complex problems and the mathematical tools useful for their analysis. Specifically, the talk will focus on recent developments of two techniques, Proper Orthogonal Decomposition (POD) and balanced truncation. Each of these techniques has strengths and weaknesses, and we show how ideas from both techniques may be combined, to exploit their strengths. We illustrate the methods by obtaining reducedorder models for a compressible flow past a cavity, and an incompressible channel flow. 
Operations Research and Financial Engineering Seminar  
Topic:  TBA 
Presenter:  Robert Almgren, University of Toronto/Bank of America 
Date:  Tuesday, October 11, 2005, Time: 4:30 p.m., Location: Room E219, Engineering Quad 
Discrete Mathematics Seminar  
Topic:  Algebraic techniques for Turan problems 
Presenter:  Peter Keevash, Caltech 
Date:  Wednesday, October 12, 2005, Time: 2:15 p.m., Location: Fine Hall 224 
Abstract:  See http://www.math.princeton.edu/~bsudakov/keevash20052006.pdf 
PACM Colloquium  
Topic:  Algebraic topology and the statistics of natural images 
Presenter:  Gunnar Carlsson, Mathematics, Stanford University 
Date:  Monday, October 17, 2005, Time: 4:00 p.m., Location: Fine Hall 214 
Abstract:  Natural images taken with a digital camera can be viewed as vectors in a highdimensional vector space whose dimension is the number of pixels. To understand the set of natural images within this vector space is a very interesting problem, but as stated it is very difficult and likely intractable. A. Lee, D. Mumford, and K. Pedersen have created a data set consisting of small (3 by 3) patches, and one can then ask questions about this set. We (V. de Silva, T. Ishkanov, and myself) have used algebraic topological techniques to obtain information about this set, and I will discuss this application of topological methods in this talk. I will also discuss potential applications in compression and in the neuroscience of vision. 
Discrete Mathematics Seminar  
Topic:  TBA 
Presenter:  Jan Vondrak, Microsoft Research 
Date:  Wednesday, October 19, 2005, Time: 2:15 p.m., Location: Fine Hall 224 
Department Colloquium  
Topic:  TBA 
Presenter:  Assaf Naor, Microsoft Research 
Date:  Wednesday, October 19, 2005,Time: 4:30 p.m., Location: Fine Hall 314 
Operations Research and Financial Engineering Seminar *** Please note special date  
Topic:  TBA 
Presenter:  Jaksa Cvitanic, University of Southern California 
Date:  Thursday, October 20, 2005, Time: 4:30 p.m., Location: Room E219, Engineering Quad 
PACM Colloquium  
Topic:  Sparse recovery 
Presenter:  Terence Tao, Mathematics, University of California, Los Angeles 
Date:  Monday, October 24, 2005, Time: 4:00 p.m., Location: Fine Hall 214 
Abstract:  Suppose one is given a small number of (possibly noisy) linear measurements of a signal. If the number of measurements is less than the number of degrees of freedom of the signal, then one of course cannot reconstruct the signal from the measurements in general. But if one makes the additional hypothesis that the signal is sparse, or at least compressible, then it does become possible to recover the signal accurately, stably, and quickly. The key is decoherence: the measurement basis has to be very "skew" with respect to the sparsity basis. We will survey a number of recent theoretical developments of this idea by several groups and in several contexts (Fourier reconstruction, linear codes, statistical selection.) 
Operations Research and Financial Engineering Seminar  
Topic:  TBA 
Presenter:  Mark Broadie, Columbia University 
Date:  Tuesday, October 25, 2005, Time: 4:30 p.m., Location: Room E219, Engineering Quad 
Discrete Mathematics Seminar  
Topic:  Hyperbolic van der Warden and Valiant Schrijver conjectures 
Presenter:  Leonid Gurvits, Los Alamos Laboratory 
Date:  Wednesday, October 26, 2005, Time: 2:15 p.m., Location: Fine Hall 224 
Abstract:  See http://www.math.princeton.edu/~bsudakov/gurvitz.pdf 
NOVEMBER 2005 

PACM Colloquium  
Topic:  Bounds on the Optimal Density of Sphere Packings in High Dimensions 
Presenter:  Sal Torquato, Chemistry, Princeton University 
Date:  Monday, November 7, 2005, Time: 4:00 p.m., Location: Fine Hall 214 
Operations Research and Financial Engineering Seminar  
Topic:  TBA 
Presenter:  Kharen Musaelian, JP Morgan 
Date:  Tuesday, November 8, 2005, Time: 4:30 p.m., Location: Room E219, Engineering Quad 
Discrete Mathematics Seminar  
Topic:  TBA 
Presenter:  Dhruv Mubayi, University of Illinois at Chicago 
Date:  Wednesday, November 9, 2005, Time: 2:15 p.m., Location: Fine Hall 224 
Department Colloquium  
Topic:  TBA 
Presenter:  Christopher Hacon, University of Utah 
Date:  Wednesday, November 9, 2005, Time: 4:30 p.m., Location: Fine Hall 314 
PACM Colloquium  
Topic:  Homological Methods for Sensor Networks 
Presenter:  Robert Ghrist, Mathematics, University of Illinois 
Date:  Monday, November 14, 2005, Time: 4:00 p.m., Location: Fine Hall 214 
Abstract:  As sensor engineering and manufacturing evolve to produce smaller devices, we will have the problem of dealing with large numbers of very localized objects. What types of global problems can be solved by a swarm of local sensors? Topologists solved a similar problem nearly a century ago. This talk will demonstrate the surprising effectiveness of homology theory in sensor networks. 
Operations Research and Financial Engineering Seminar  
Topic:  TBA 
Presenter:  Adrian Lewis, Cornell University 
Date:  Tuesday, November 15, 2005, Time: 4:30 p.m., Location: Room E219, Engineering Quad 
PACM Colloquium  
Topic:  TBA 
Presenter:  Guust Nolet, Geosciences, Princeton University 
Date:  Monday, November 21, 2005, Time: 4:00 p.m., Location: Fine Hall 214 
Discrete Mathematics Seminar  
Topic:  TBA 
Presenter:  Jozsef Beck, Rutgers University 
Date:  Wednesday, November 23, 2005, Time: 2:15 p.m., Location: Fine Hall 224 
Operations Research and Financial Engineering Seminar  
Topic:  TBA 
Presenter:  Tom Salisbury, York University 
Date:  Tuesday, November 29, 2005, Time: 4:30 p.m., Location: Room E219, Engineering Quad 
Discrete Mathematics Seminar  
Topic:  TBA 
Presenter:  Ben Green, Clay Institute, University of Bristol and MIT 
Date:  Wednesday, November 30, 2005, Time: 2:15 p.m., Location: Fine Hall 224 
DECEMBER 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. 
Operations Research and Financial Engineering Seminar  
Topic:  TBA 
Presenter:  Paolo Guasoni, Boston University 
Date:  Tuesday, December 6, 2005, Time: 4:30 p.m., Location: Room E219, Engineering Quad 
PACM Colloquium  
Topic:  Turbulence and Largescale Geophysical Circulations 
Presenter:  Geoff Vallis, Geosciences/Atmospheric & Oceanic Sciences, Princeton University 
Date:  Monday, December 12, 2005, Time: 4:00 p.m., Location: Fine Hall 214 
Operations Research and Financial Engineering Seminar  
Topic:  TBA 
Presenter:  PierreLouis Lions 
Date:  Tuesday, December 13, 2005, Time: 4:30 p.m., Location: Room E219, Engineering Quad 