Current Seminars
updated 4/3/ 2002
April 3-5, 2002
Department Colloquium
Topic: Evolution of Language
Presenter: Stephen Smale, University of California at Berkeley
Date: Wednesday, April 3, 2002, Time: 4:30 p.m., Location: Fine Hall 314
Abstract: A mathematical model is presented which helps to understand how languages are formed. A theorem in this setting is the convergence to a common language under a hypothesis on linguistic encounters.
Discrete Mathematics Seminar
Topic: Electrical Circuit Theory Generalized to Matroids
Presenter: Alan Sokal, New York University
Date: Thursday, April 4, 2002, Time: 2:00 p.m., Location: Fine Hall 224
Ergodic Theory and Statistical Analysis Seminar
Topic: Bernoulli diffeomorphisms with non-zero exponents on any manifold
Presenter: Yakov Pesin, Penn State University
Date: Thursday, April 4, 2002, Time: 2:00 p.m., Location: Fine Hall 601
Abstract: In the talk I will describe a solution of a long-standing problem to construct a Bernoulli diffeomorphism with nonzero Lyapunox exponents on any compact smooth Riemannian manifold.
Joint Princeton University/IAS/Rutgers University Non-Linear Analysis Seminar
Topic: Energy Growth for Schrodinger Equations with Markovian Forcing
Presenter: Mehmet Erdogan, Institute for Advanced Study
Date: Thursday, April 4, 2002, Time: 4:00 p.m., Location: Fine Hall 214
Topology Seminar
Topic: Lefschetz fibrations on compact Stein surfaces
Presenter: Burak Ozbacgi, Michigan State University
Date: Thursday, April 4, 2002, Time: 4:00 p.m., Location: Fine Hall 314
Graduate Student Seminar
Topic: Explicit construction of expanding graphs and Kazhdan's Property T.
Presenter: Lior Silberman, Princeton University
Date: Friday, April 5, 2002, Time: 1:00 p.m., Location: Fine Hall 1001
Abstract: An "expander" is a highly connected sparse graph, which is a useful tool for many problem in theoretical computer science. While the existence of expanders follows from counting arguments (a.k.a. the probabilistic method), for many applications an explicit construction is needed. This was first achieved by Margulis using a result on the representation theory of lattices in Lie groups, known as Kazhdan's "property T". I will first define expanders and discuss some of their properties. Turning to representation theory, I will explain the definition of property T, and show Margulis' construction, assuming Kazhdan's result. In future talks this semester (not at the GSS) I will discuss recent papers by Zuk and Gromov detailing randomized constructions of discrete groups with property T using expanders.
Princeton University/IAS Number Theory Seminar *** Please note special day and time
Topic: Moments of L-functions and Random Matrix Theory
Presenter: Michael Rubinstein, American Institute of Mathematics
Date: Friday, April 5, 2002, Time: 4:00 p.m., Location: Fine Hall 322
April 8 - 12, 2002
Analysis Seminar
Topic: TBA
Presenter: Diego Cordoba, Princeton University
Date: Monday, April 8, 2002, Time: 4:00 p.m., Location: Fine Hall 314
Algebraic Geometry Seminar
Topic: The Elliptic Curve Discrete Logarithm
Presenter: Joseph Silverman, Brown University
Date: Tuesday, April 9, 2002, Time: 4:30 p.m., Location: Fine Hall 314
Abstract: Let E be an elliptic curve defined over a finite field k and let S and T be points of E(k). The elliptic curve discrete logarithm problem (ECDLP) asks for the integer m such that T = mS. ECDLP is difficult to solve in general if k is large, a fact that has been used as the basis of a number of modern cryptographic constructions. In this survey talk I will discuss the various methods that have been developed to solve ECDLP, with an emphasis on those methods that use tools (albeit fairly elementary ones) from algebraic geometry.
Department Colloquium
Topic: Hyper-Encryption and Provably Everlasting Secrecy
Presenter: Michael Rabin, Harvard University and Columbia University
Date: Wednesday, April 10, 2002, Time: 4:30 p.m., Location: Fine Hall 314
Abstract:
Modern encryption is based on unproven assumptions concerning the intractability of certain
computational tasks. We present a novel encryption method and prove its security
against an adversary with unlimited computing power. The encryption remains secure even if the adversary mounts
an adaptive attack and later on obtains the secret decryption key. Hence the property of everlasting secrecy.
The main mathematical tool is an ergodic type theorem. The presentation is self
contained.
Joint Princeton University/IAS/Rutgers University Non-Linear Analysis Seminar
Topic: $L_p$-bounds on curvature and rectifiability of singular setsy
Presenter: Jeff Cheeger, Courant Instititue, NYU
Date: Thursday, April 11, 2002, Time: 4:00, Location: Fine Hall 214
Topology Seminar
Topic: Progress and prospects in controlled topology
Presenter: Frank Quinn, Virginia Polytechnic Institute
Date: Thursday, April 11, 2002, Time: 4:00 p.m., Location: Fine Hall 314
Princeton University/IAS Number Theory Seminar
Topic: Galois groups and geometry of modular varieties
Presenter: Alexander Goncharov, Brown University
Date: Thursday, April 11, 2002, Time: 4:30, Location: Fine Hall 322
Geometric Analysis Seminar
Topic: TBA
Presenter: Rina Rotman, University of Toronto and the Courant Institute of Mathematics
Date: Friday, April 12, 2002, Time: 3:00 p.m., Location: Fine Hall 314
April 15 - 19, 2002
PACM Colloquium
Topic: Structure Prediction in Protein Folding
Presenter: Christodolous Floudas, Chemical Engineering, Princeton University
Date: Monday, April 15, 2002, Time: 4:00 p.m., Location: Fine Hall 214
Abstract: Proteins serve as vital components in our cellular makeup and perform many biological functions that are essential for sustaining life. An important feature which determines the functionality of a protein is the form of its three-dimensional structure. The structure is in turn related to the protein sequences encoded by our genes, and these sequences were identified as part of the data from the human genome project. Therefore, a logical undertaking upon completion of the human genome project, and an important step in understanding and treating disease, would be to develop a method to predict the structure of a protein given its sequence information. Accurate prediction of the three-dimensional structure of a protein relies on both the mathematical model used to mimic the protein system and the technique used to identify the correct structure. In this presentation, a novel ab initio approach for the protein folding problem is introduced. The models are based solely on first principles, as opposed to the myriad of techniques relying on information from statistical databases. In addition, the search techniques rely on the foundations of deterministic global optimization, methods which can guarantee the correct identification of a protein's structure. The multistage approach begins with the identification of helical secondary structure elements, which is followed by the prediction of beta sheet and disulfide bridge configurations from a set of postulated beta strands. In the final stage the aforementioned predictions are used to derive structural restraints for the determination of the overall three-dimensional structure.
Special Topology Seminar
Topic: Laminations and groups of homeomorphisms of S^1 Part I (Part II is scheduled for Thursday, April 18)
Presenter: Danny Calegari, Harvard University
Date: Tuesday, April 16, 2002, Time: 3:00 p.m., Location: Fine Hall 601
Algebraic Geometry Seminar
Topic: Singularities of formal arc spaces and automorphic L-functions
Presenter: Alexander Braverman, Harvard University
Date: Tuesday, April 16, 2002, Time: 4:30 p.m., Location: Fine Hall 314
Abstract: Given an algebraic variety X (over some field) one may consider the (infinite-dimensional) scheme of formal arcs L(X) paramtetrising maps from the formal disc to X. We shall begin by describing a theorem due to Drinfeld and Grinberg-Kazhdan which says that the singularities of L(X) are in some sense finite-dimensional. We shall then explain how to compute these singularities when $X$ is any normal toric variety or (more generally) when X is a reductive algebraic semigroup (this notion is due to Vinberg and it will be explained in the lecture). If time permits we shall also discuss how these results may be applied in order to the study of some automorphic L-functions (for global field of positive characteristic).
Mathematical Physics Seminar *** Please note change in date from March 19, 2002
Topic: Binding of Matter in Strong Magnetic Fields
Presenter: Jakob Yngvason, University of Vienna
Date: Tuesday, April 16, 2002, Time: 4:30 p.m., Location: Jadwin A06
Abstract: The magnetic field at the surface of a neutron star, typically of the order $10^8$ Tesla and higher, has drastic effects on the properties of matter. One of the important and still only partially answered questions concerns the enhanced binding of Coulomb matter at the surface into molecules and chaines. The lecture brings a review of what is known and what one would like to know about this problem as well as some new results on a density matrix functional for infinite chains of heavy atoms in strong magnetic fields.
Department Colloquium
Topic: TBA
Presenter: Dusa McDuff, SUNY at Stony Brook
Date: Wednesday, April 17, 2002, Time: 4:30 p.m., Location: Fine Hall 314
Special Topology Seminar
Topic: Laminations and groups of homeomorphisms of S^1 Part II
Presenter: Danny Calegari, Harvard University
Date: Thursday, April 18, 2002, Time: 1:00 p.m., Location: Fine Hall 110
Discrete Mathematics Seminar
Topic: TBA
Presenter: Tibor Szabo, ETH Zurich
Date: Thursday, April 18, 2002, Time: 2:00 p.m., Location: Fine Hall 224
Topology Seminar
Topic: Bounded cochains on 3-manifolds
Presenter: Danny Calegari, Harvard University
Date: Thursday, April 18, 2002, Time: 4:00 p.m., Location: Fine Hall 314
Princeton University/IAS Number Theory Seminar
Topic: Discrete moments of the Riemann zeta function
Presenter: Nathan Ng, Institute for Advanced Study
Date: Thursday, April 18, 2002, Time: 4:30, Location: IAS SH-101
Geometric Analysis Seminar
Topic: Bifurcations of $J$-holmorphic maps
Presenter: Tom Parker, Michigan State University and the Institute for Advanced Study
Date: Friday, April 19, 2002, Time: 3:00 p.m., Location: Fine Hall 314
April 22 - 26, 2002
Algebraic Geometry Seminar *** Please note special day, time, and room
Topic: Supersingular abelian varieties and applications to cryptography
Presenter: Alice Silverberg, Ohio State University
Date: Monday, April 22, 2002, Time: 3:00 p.m., Location: Fine Hall 322
Abstract: Elliptic curves were introduced into cryptography in the mid-1980's. Supersingular elliptic curves were considered "weak" for cryptography until very recently, when some interesting new cryptographic applications were found for which supersingular elliptic curves were the best elliptic curves to use. In this talk we explain some of these applications, show how they can be done with supersingular abelian varieties, and use Honda-Tate theory and the theory of complex multiplication to construct supersingular abelian varieties that have properties that are optimal for the cryptographic applications.
Analysis Seminar
Topic: The lost proof of Loewner's theorem
Presenter: Barry Simon, Caltech
Date: Monday, April 22, 2002, Time: 4:00 p.m., Location: Fine Hall 314
Abstract: A real-valued function, F, on an interval (a,b) is called matrix monotone if F(A) < F(B) whenever A and B are finite matrices of the same order with eigenvalues in (a,b) and A < B. In 1934, Loewner proved the remarkable theorem that F is matrix monotone if and only if F is real analytic with continuations to the upper and lower half planes so that Im F > 0 in the upper half plane. This deep theorem has evoked enormous interest over the years and a number of alternate proofs. There is a lovely 1954 proof that seems to have been "lost" in that the proof is not mentioned in various books and review article presentations of the subject, and I have found no references to the proof since 1960. The proof uses continued fractions. I'll provide background on the subject and then discuss the lost proof and a variant of that proof which I've found, which avoids the need for estimates, and proves a stronger theorem.
PACM Colloquium
Topic: The chance of Two Noriegas is Closer to p/2 than p^2: Implications for Language Modeling, Information
Retrieval and Gzip
Presenter: Ken Church, AT&T Labs - Research
Date: Monday, April 22, 2002, Time: 4:00 p.m., Location: Fine Hall 214
Abstract: Bag-of-word independence models are commonly found in many language modeling applications including information retrieval, speech recognition and data compression. But, because repetition is so common, the speech literature has recently become interested in adaptive language models. Adaptive models allow probabilities to change or adapt after seeing just a few words of a text. Using a novel method for estimating adaptation, we find that adaptation effects are surprisingly large. The first Noreiga in a document has probability 0.006, two orders of magnitude more surprising than the second (0.75). Using query expansion methods borrowed from Information Retrieval, the method is generalized to account for priming. In this way, the first mention not only increases the chance of a second, but it also primes related words like "Bush" and "Panama." A wide range of applications will be discussed, mostly related to language. Interestingly, there are also non-language applications: gzipping binary tables (of telephone call detail) often works better if the table is enumerated in a convenient order that makes it easier for Lempel-Ziv compression methods to take advantage of the adaptation possibilities.
Mathematical Physics Seminar
Topic: Sum Rules and Spectral Properties of Jacobi Matrices
Presenter: Barry Simon, Caltech
Date: Tuesday, April 23, 2002, Time: 4:30 p.m., Location: Jadwin A06
Department Colloquium
Topic: TBA
Presenter: Karen Uhlenbeck, University of Texas at Austin
Date: Wednesday, April 24, 2002, Time: 4:30 p.m., Location: Fine Hall 314
Discrete Mathematics Seminar
Topic: Partitions with bounded components
Presenter: Penny Haxell, University of Waterloo
Date: Thursday, April 25, 2002, Time: 2:00 p.m., Location: Fine Hall 224
Princeton University/IAS Number Theory Seminar
Topic: TBA
Presenter: Wee Teck Gan, Princeton University
Date: Thursday, April 25, 2002, Time: 4:30, Location: Fine Hall 322
April 29 -May 3, 2002
PACM Colloquium
Topic: TBA
Presenter: Herb Keller, California Institute of Technology
Date: Monday, April 29, 2002, Time: 4:00 p.m., Location: Fine Hall 214
Department Colloquium
Topic: TBA
Presenter: Manjul Bhargava, Institute for Advanced Study
Date: Wednesday, May 1, 2002, Time: 4:30 p.m., Location: Fine Hall 314
Discrete Mathematics Seminar
Topic: TBA
Presenter: Igor Pak, MIT
Date: Thursday, May 2, 2002, Time: 2:00 p.m., Location: Fine Hall 224
Topology Seminar
Topic: TBA
Presenter: Ko Honda, USC
Date: Thursday, May 2, 2002, Time: 4:00 p.m., Location: Fine Hall 314
Princeton University/IAS Number Theory Seminar
Topic: TBA
Presenter: Brooks Roberts, University of Idaho
Date: Thursday, May 2, 2002, Time: 4:30, Location: Fine Hall 322
May 6 -May 10, 2002
Algebraic Geometry Seminar
Topic: Points of low canonical height on elliptic curves and surfaces
Presenter: Noam Elkies, Harvard University
Date: Tuesday, May 7, 2002, Time: 4:30 p.m., Location: Fine Hall 314