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NOVEMBER 23 - 25, 2005 |
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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. |
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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 |
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NOVEMBER 28 - DECEMBER 2, 2005 |
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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. |
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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. |
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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. |
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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. |
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Operations Research and Financial Engineering Seminar |
Topic: |
Options embedded in variable annuities: GMDBs and GMWBs
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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. |
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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. |
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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). |
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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 |
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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. |
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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. |
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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. |
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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. |
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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. |
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DECEMBER 5 - 9, 2005 |
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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. |
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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 |
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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 |
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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) |
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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. |
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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 |
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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. |
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Analysis Seminar |
Topic: |
TBA |
Presenter: |
Joachim Krieger, Harvard University |
Date: |
Thursday, December 8, 2005, Time: 4:00 p.m., Location: Fine Hall 214 |
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Geometric Analysis Seminar |
Topic: |
TBA |
Presenter: |
Pierre Albin, MIT |
Date: |
Friday, December 9, 2005, Time: 3:00 p.m., Location: Fine Hall 314 |
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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. |
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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. |
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DECEMBER 12 - DECEMBER 16, 2005 |
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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. |
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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. |
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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 |
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