Current Seminars
updated 4/10/ 2002
As of April 10 - 12, 2002
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.
Ergodic Theory and Statistical Mechanics Seminar
Topic: Domino Tilings and the Gaussian Free Field
Presenter: Leonid Koralov, Princeton University
Date: Thursday, April 11, 2002, Time: 2:00 p.m., Location: Fine Hall 601
Abstract: We shall discuss recent results of Kenyon, who showed that a scaling limit of the height function of the domino tiling model is the "massless free field".
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
Graduate Student Seminar
Topic: Uniform Approximate Functional Equation for Principal L-functions
Presenter: Gergely Harcos, Princeton University
Date: Friday, April 12, 2002, Time: 1:00 p.m., Location: Fine Hall 1001
Abstract: I shall describe an approximate functional equation for central values of L-functions attached to cusp forms (with unitary central character) on GL_m over number fields. The formula generalizes a classical theorem of Hardy and Littlewood (for the Riemann zeta function) and is useful for establishing subconvexity or nonvanishing results in certain families. It is somewhat unexpected that the best known bounds for the Ramanujan-Selberg conjectures (due to Luo, Rudnick and Sarnak) are utilized in the proof.
Geometric Analysis Seminar
Topic: Some Estimates of the Length of a Shortest Closed Geodesic
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
Abstract: We will discuss some upper bounds for the length of a shortest closed geodesic 1(M) on a closed Riemannian manifold M: First, we will talk about the upper bounds for 1(M) that involve either an upper or a lower bound for the sectional curvature of M. Then we will present curvature-free upper bounds on 1(M) in the case when M is diffeomorphic to the 2-dimensional sphere. Finally we will discuss curvature-free estimates for the minimal mass of a stationary 1-cycle on an arbitrary closed Riemannian manifold.
April 15 - 19, 2002
Analysis Seminar
Topic: New Results and Analytic Methods in the Study of the Time-Dependent Schrödinger Equation
Presenter: Ovidiu Costin, Rutgers University
Date/Time Monday, April 18
Location: Fine Hall 314
Abstract: We study the Schrödinger equation with time periodic external forcing, when the forcing is not necessarily small, and perturbation theory does not apply; our results reflect substantial departures from the behavior exhibited in the perturbative regime (and are in accord with experimental results). The talk will focus on the results as well as on the methods we developed to analyze the equation nonperturbatively. (Work in collaboration with R. D. Costin, L. L. Lebowitz and A. Rokhlenko.)
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: Topological properties of Groups of Symplectomorphisms
Presenter: Dusa McDuff, SUNY at Stony Brook and the Institute for Advanced Study
Date: Wednesday, April 17, 2002, Time: 4:30 p.m., Location: Fine Hall 314
Abstract: A symplectomorphism is a diffeomorphism of a manifold that preserves a symplectic form. Ever since Gromov showed that the group of symplectomorphisms of the product of two 2-spheres of equal size has the homotopy type of an extension of SO(3) x SO(3) by Z/2Z, people have been interested in understanding the special properties of groups of symplectomorphisms. This survey talk will describe some ways in which the structure of a group of symplectomorphisms differs from that of an arbitrary diffeomorphism group.
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
PACM Colloquium *** Please note special date and room
Topic: Coordination of Groups of Mobile Autonomous Agents Using Nearest Neighbor Rules
Presenter: Steve Morse, Yale University
Date: Thursday, April 18, 2002, Time: 4:00 p.m., Location: Fine Hall 110
Abstract: In a recent Physical Review Letters paper, Vicsek et. al. propose a simple but compelling discrete-time model of n autonomous agents {i.e., points or particles} all moving in the plane with the same speed but with different headings. Each agent’s heading is updated using a local rule based on the average of its own heading plus the headings of its “neighbors.” Agent i’s neighbors at time t, are those agents which are either in or on a circle of pre-specified radius r centered at agent i’s current position. In their paper, Viscek et. al. provide a variety of interesting simulation results which demonstrate that the nearest neighbor rule they are studying can cause all agents to eventually move in the same direction despite the absence of centralized coordination and despite the fact that each agent’s set of nearest neighbors change with time as the system evolves. In this presentation we provide a theoretical explanation for this observed behavior. In addition, convergence results are given for several other similarly inspired models. The results to be presented provide a graphic example of a switched linear system which is stable, but for which there does not exist a common quadratic Lyapunov function. This research was done in collaboration with A. Jadbabaie and J. Lin.
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
Topology Seminar
Topic: An intersection theory on G_2 manifolds
Presenter: Conan Leung, University of Minnesota
Date: Thursday, April 25, 2002, Time: 4:00 p.m., Location: Fine Hall 314
Princeton University/IAS Number Theory Seminar
Topic: Multiplicities of cusp forms
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: The Three Body Problem and Space Mission Design
Presenter: Herb Keller, California Institute of Technology
Date: Monday, April 29, 2002, Time: 4:00 p.m., Location: Fine Hall 214
Abstract: The circular restricted three body problem (CR3BP) of gravitational dynamics governs the motion of satellites near the earth and moon and in many other configurations. The determination of periodic, homoclinic and heteroclinic orbits and indeed unstable orbits of satellites in this configuration is important in mission planning. We show how the code AUTO 2000 has been used to calculate such orbits. A bifurcation diagram showing how most of the known and some new families of periodic orbits are related and connect all the five libration points of the CR3BP. We also treat the new exact three body figure eight solution of Montgomery and Chenciner and show how by reducing the mass of one of the bodies a homotopy to a periodic CR3BP solution results. AUTO is software for continuation and bifurcation of solutions of parameter dependent nonlinear systems of equations. In particular it solves two point boundary value problems with great speed and accuracy. We show how it is adapted to the periodic N-body problem of gravitational dynamics.
CR Seminar
Topic: Flat connections over (Riemann) surfaces
Presenter: William Goldman, University of Maryland
Date: Tuesday, April 30, 2002, Time: 4:00 p.m., Location: Fine Hall 401
Abstract: I will discuss the geometry and symmetry of the moduli space of representations of the fundamental group of a closed oriented surface in a semisimple Lie group. The action of the mapping class group, the symplectic geometry of the moduli space, and the function defined by the energy of the harmonic section of the associated flat bundle of symmetric spaces will be related.
Mathematical Physics Seminar
Topic: Enhanced binding in non-relativistic QED
Presenter: Christian Hainzl, University of Munich
Date: Tuesday, April 30, 2002, Time: 4:30 p.m., Location: Jadwin A06
Abstract: Consider an electron in an external potential V, such that the Schroedinger operator p^2 + V has a ground state. We will show that, as soon as the quantized radiation field is turned on, the binding energy increases. For some short-range potentials V it is even possible that binding occurs, although the corresponding Schroedinger operator does not have an eigenstate. The results presented hold for small values of the coupling parameter alpha, which represents the fine structure constant. Moreover, we will comment on non-perturbative mass-renormalization in the limit of small alpha.
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: L and epsilon factors for some representations of GSp(4)
Presenter: Brooks Roberts, University of Idaho
Date: Thursday, May 2, 2002, Time: 4:30, Location: Fine Hall 322
Abstract: In a previous work we proved an analogue for GSp(4) of the dihedral case of the Langlands-Tunnell Theorem. This involved defining some L-packets for GSp(4). In this talk we will discuss the L and epsilon factors associated to the generic elements of these local nonarchimedean L-packets by the Novodvorsky integral representation. We will also discuss the problem of finding canonical vectors in such generic representations which represent their L-factors.
May 6 -May 10, 2002
Algebraic Geometry Seminar *** Please note special day, time, and location
Topic: TBA
Presenter: Robert Guralnick, USC
Date: Monday, May 6, 2002, Time: 3:00 p.m., Location: TBA
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
PACM Colloquium *** Please note the special day and time
Topic: Architecture and Dynamics of the Primary Visual Cortex
Presenter: David McLaughlin, Courant Institute of Mathematical Sciences, NYU
Date: Thursday, May 9, 2002, Time: 4:30 p.m., Location: Fine Hall 214