Current Seminars
updated 10/24/ 2001
As of October 24-26
Department Colloquium
Topic: Embedded minimal surfaces in 3-manifolds
Presenter: Tobias Colding, Princeton University
Date: Wednesday, October 24, 2001, Time: 4:30 p.m., Location: Fine Hall 314
Abstract: I will discuss the description of the space of all embedded minimal surfaces in a 3-manifold. (This is joint work with Bill Minicozzi).
Ergodic Theory and Statistical Mechanics Seminar
Topic: Sample path properties of the stochastic flow and the dynamics of an oil spill (joint work with Dima Dolgopyat and
Vadim Kaloshin) Part II
Presenter: Leonid Koralov, Princeton University
Date: Thursday, October 25, 2001, Time: 2:00 p.m., Location: Fine 224
Abstract: We consider a stochastic flow driven by a finite dimensional Brownian motion. We show that almost every realization of such a flow exhibits strong statistical properties such as the exponential convergence of an initial measure to the equilibrium state and the central limit theorem. The proof uses new estimates of the mixing rates of the multi point motion. An application of these results allows us to describe the limiting shape of a domain in $\R^2$ (say, an oil spill on the surface of the ocean) carried by the stochastic flow. This is a continuation of the talk from Thursday, October 18, 2001.
Discrete Mathematics Seminar
Topic: Local density in graphs with forbidden subgraphs
Presenter: Peter Keevash, Cambridge University and Princeton University
Date: Thursday, October 25, 2001, Time: 4:00 p.m., Location: Fine Hall 224
Topology Seminar *** Note change in speaker ***
Topic: Gromov-Witten Invariants and Symplectic Sums
Presenter: Eleny Ionel, Institute for Advanced Study
Date: Thursday, October 25, 2001, Time: 4:00 p.m., Location: Fine Hall 314
Princeton/IAS Number Theory Seminar
Topic: Boundary Value Distributions of Automorphic Forms and Constructions of L-functions
Presenter: Stephen Miller, Rutgers University
Date: Thursday, October 25, 2001, Time: 4:30 p.m., Location: Institute for Advanced Study, SH-101
Abstract: We study the boundary values of automorphic forms, which can be viewed as automorphic distributions on nilpotent groups. For example, the distributions for classical automorphic forms are distributions in one-variable. Since the smaller dimensions and easier structure of nilpotent groups makes them quite tractable, this point of view has certain advantages, especially in studying automorphic L-functions. I will highlight computations of gamma factors for automorphic L-functions on GL(n) as well as how a new proof of the Jacquet-Piatetski-Shapiro-Shalika GL(3) converse theorem can be obtained using the co-adjoint orbit method on the Heisenberg group. I will also address what other potential converse theorems and instances of Langlands functorality might be accesible from this point of view. Joint work with Wilfried Schmid, Harvard University.
Graduate Student Seminar
Topic: Regulators on Milnor K-theory
Presenter: Matt Kerr, Princeton University
Date: Friday, October 26, 2001, Time: 12:30 p.m., Location: Fine Hall 1201
Abstract: We'll discuss how a generalization of Liouville's theorem leads directly into arithmetic phenomena related to the Beilinson conjectures (e.g. polylogarithms and special values of L-functions), via elementary complex algebraic geometry and hodge theory. Pizza will be provided.
Geometric Analysis Seminar
Topic: Estimates for embedded minimal disks
Presenter: Tobias Colding, Princeton University
Date: Friday, October 26, 2001, Time: 3:00 p.m., Location: Fine Hall 314
Week of October 29-November 2
Analysis Seminar
Topic: Interpolating between conservation laws and small date theory for semilinear evolution PDEs
Presenter: Fabrice Planchon, Université Pierre et Marie Curie
Date: Monday, October 29, 2001, Time: 4:00 p.m., Location: Fine Hall 314
Abstract: We present a method to utilize both small data or local in time theory and conservation laws to obtain global results for solutions which do not verify the conservation laws. We provide 3 examples: a semilinear wave equation, for which the method provides a approach to global well-posedness below H^1 different from Bourgain's approach; the incompressible Navier-Stokes equations, for which it yields global infinite energy solutions in 2D as well as stability for 3D global solutions (assuming we have one).
PACM Colloquium
Topic: Modeling Cell Communication in Drosophila Oogenesis
Presenter: Stanislav Shvartsman, Chemical Engineering, Princeton University
Date: Monday, October 29, 2001, Time: 4:00 p.m., Location: Fine Hall 214
Abstract: Until recently, cell communication in tissues was studied using exclusively biochemical and genetic approaches. As a rule, mechanisms deduced from these studies are difficult to evaluate without the aid of mathematical models. I will present our recent work on modeling of cell communication in Drosophila oogenesis (egg development). The model focuses on autocrine loops - a mode of cell signaling that is established when soluble ligands released by cells stimulate receptors on their surfaces. Autocrine signaling through the Epidermal Growth Factor Receptor (EGFR) is highly conserved across species and operates at various stages of development, patterning the developing tissues and organs1. A recent hypothesis suggested that a distributed network of positive and negative EGFR autocrine feedback loops in Drosophila oogenesis is capable of spatially modulating a simple single-peaked input into a more complex two-peaked signaling pattern, specifying the formation of a pair organ (a pair of respiratory appendages)2. To test this hypothesis, we have integrated genetic and biochemical information about the EGFR network into a mechanistic model of transport and signaling3. Computational analysis of the model enables the evaluation of the proposed mechanism and the interpretation of the phenotypic transitions observed in this system4. 1. Casci, T. & Freeman, M. Control of EGF receptor signalling: Lessons from fruitflies. Cancer And Metastasis Reviews 18, 181-201 (1999). 2. Wasserman, J.D. & Freeman, M. An autoregulatory cascade of EGF receptor signaling patterns the Drosophila egg. Cell 95, 355-364 (1998). 3. Shvartsman, S.Y., Muratov, C.B. & Lauffenburger, D.A. Modeling and Computational Analysis of EGFR Autocrine Loops in Drosophila Oogenesis. in preparation (2001). 4. Nilson, L. & Schupbach, T. EGF receptor signaling in Drosophila oogenesis. Current topics in developmental biology 44, 203-243 (1999).
Special Analysis Seminar *** Note special date ***
Topic: Carleson's theorem with quadratic phase
Presenter: Michael Lacey, Georgia Tech
Date: Thursday, November 1, 2001, Time: 4:00 p.m., Location: Fine Hall 314
Week of November 5-9
PACM Colloquium
Topic: Complex fluids: liquid crystals, mixtures and polymeric materials
Presenter: Chun Liu, Penn State University
Date: Monday, November 5, 2001, Time: 4:00 p.m., Location: Fine Hall 214
Abstract: In this talk, several dynamical systems modeling specific types of complex fluids are introduced. The relation between these and other existing models will be discussed. We will also study the relations between the variational procedure; the basic energy law; stability; and the higher order energy estimates. The different non-Newtonian properties such systems exhibit is of particular interest. Finally we will study a differential-integral equation system that allows us to consider couplings and interactions of different spatial length scales.
Algebraic Geometry Seminar
Topic: p-adic representations and differential equations
Presenter: L. Berger, Brandeis University
Date: Tuesday, November 6, 2001, Time: 4:30 p.m., Location: Fine Hall 314
Abstract: I will explain how to associate objects of a differential nature to a p-adic representation. Using recent results of Andr\'e on the structure of p-adic differential equations, these constructions allow us to give a proof of Fontaine's monodromy conjecture: every "de Rham" p-adic representation is potentially semi-stable.
Tuesdays Lecture Series
Topic: Quantum Information Theory Part II
Presenter: Peter Shor, AT&T
Date: Tuesday, November 6, 2001, Time: 4:30 p.m., Location: Fine Hall 110
Abstract: We discuss entanglement, the property of quantum mechanics that Einstein called "spooky action at a distance." Entanglement between two parties is what leads to the violation of Bell's inequality, and also it appears to be one of the properties of quantum mechanics that speeds up quantum computers. Entanglement between two parties lets them perform a number of interesting tasks, one of which is "quantum teleportation," where a quantum state can be transfered using only classical communication and entanglement. We discuss these uses of entanglement, and then discuss how to quantify it. This is Part Two of a three part series.
Department Colloquium
Topic: TBA
Presenter: Bjorn Engquist, Princeton University
Date: Wednesday, November 7, 2001, Time: 4:30 p.m., Location: Fine Hall 314
Ergodic Theory and Statistical Mechanics Seminar
Topic: Classical and quantum scattering for random decaying potentials.
Presenter: Wilhelm Schlag, Institute for Advanced Study
Date: Thursday, November 8, 2001, Time: 2:00 p.m., Location: Fine 224
Princeton/IAS Number Theory Seminar
Topic: TBA
Presenter: Fernando Rodriguez-Villegas, University of Texas and Harvard University
Date: Thursday, November 8, 2001, Time: 4:30 p.m., Location: TBA
Geometric Analysis Seminar
Topic: Singular Yamabe metrics, explosion for superprocess, and thinness
Presenter: D. Labutin, ETH
Topic: Multi-valued minimal graphs and properness of embedded disks
Presenter: Tobias Colding, Princeton University
Date: Friday, November 9, 2001, Time: 3:00 p.m., Location: Fine Hall 314
Week of November 12-16
PACM Colloquium
Topic: Eukaryotic Cell Cycle Controls: An Example of the 'Last Step' in Computational Molecular Biology
Presenter: John Tyson, Virginia Polytechnic, Institute and State University
Date: Monday, November 12, 2001, Time: 4:00 p.m., Location: Fine Hall 214
Abstract: The cell cycle is the sequence of events by which a growing cell duplicates all its components and partitions them more-or-less evenly between two daughter cells. In the last 15 years, molecular biologists have made great progress in identifying the genes, proteins and molecular interactions that control the basic events of the cell cycle (DNA synthesis and mitosis). The control system is so complex that its behavior cannot be understood by casual, hand-waving arguments. We use biochemical kinetics and dynamical systems theory to convert hypothetical molecular mechanisms of cell cycle control into quantitative computational models. By testing our models against experimental observations, we gain new insights into how the control system works. The approach is generally applicable to any complex gene-protein network that regulates some physiological characteristics of a living cell.
Algebraic Geometry Seminar
Topic: TBA
Presenter: V. Vatsal, University of British Columbia
Date: Tuesday, November 13, 2001, Time: 4:30 p.m., Location: Fine Hall 314
Statistical Mechanics Seminar
Topic: Thomas Fermi theory for matter in strong magnetic fields at nonzero temperatures
Presenter: Jakob Yngvason, University of Vienna
Date: Wednesday, November 14, 2001, Time: 2 p.m., Location: Jadwin 343
Abstract: Rigorous results are presented on the validity of Thomas Fermi theory for the computation of the equation of state of matter in the surface layers of neutron stars.
Department Colloquium
Topic: Diophantine geometry over groups and the elementary theory of a free group
Presenter: Zlil Sela, Institute for Advanced Study
Date: Wednesday, November 14, 2001, Time: 4:30 p.m., Location: Fine Hall 314
Abstract: We study the structure of sets of solutions to equations defined over a free group, projections of such sets, and the structure of elementary sets defined over a free group. The structure theory we obtain, enable us to answer some questions of A. Tarski's, and classify those finitely generated groups that are elementary equivalent to a free group. Connections with low dimensional topology, and some generalizations, extensions, and possible future directions will also be discussed.
Ergodic Theory and Statistical Mechanics Seminar
Topic: Markov operators and ergodic theorems for actions of free groups
Presenter: Alexander I. Bufetov, Princeton University
Date: Thursday, November 15, 2001, Time: 2:00 p.m., Location: Fine 224
Abstract: A measure-preserving action of a free group on a probability space can be considered as a stationary Markov process. This approach allows to give a short proof of the Nevo-Stein theorem and to obtain more general ergodic theorems for actions of free groups.
Geometric Analysis Seminar
Topic: Geometry and Soliton equations
Presenter: C. L. Terng, Northeastern University
Date: Friday, November 16, 2001, Time: 3:00 p.m., Location: Fine Hall 314
Week of November 19-23
PACM Colloquium
Topic: Protein folding by all-atom simulations
Presenter: Yong Duan, University of Delaware
Date: Monday, November 19, 2001, Time: 4:00 p.m., Location: Fine Hall 214
Abstract: Elucidation of the mechanisms of protein folding has challenged the scientific community for decades. It has also been termed as the second half of genomics. The challenge lies at the detailed description of the processes. Our approach is to apply all-atom molecular dynamics simulations to accurately replicate the folding processes of small proteins on computer. I will discuss the status of the field and use a few examples to demonstrate how one can effectively use such an approach in the studies of protein folding.
Algebraic Geometry Seminar
Topic: TBA
Presenter: B. de Oliveira, University of Pennsylvania
Date: Tuesday, November 20, 2001, Time: 4:30 p.m., Location: Fine Hall 314
Week of November 26-30
Mathematical Physics Seminar
Topic: Stable and unstable directions for nonlinear Schroedinger equations
Presenter: H.T. Yau, Courant Institute
Date: Tuesday, November 27 2001, Time: 4:30 p.m., Location: Jadwin A06
Abstract: We consider a nonlinear Schroedinger equation in R^3 with a bounded local potential so that the linear Hamiltonian has two bound states and the eigenvalues satisfy some resonance condition. Suppose that the initial data is small and is near some nonlinear *excited* state. Then we give a sufficient condition on the initial data so that the solution of the nonlinear Schroedinger equation approaches a certain nonlinear *ground* state as the time tends to infinity. On the other hand, for certain finite codimensional subset in the space of initial data, we construct solutions converging to the excited states in both non-resonant and resonant cases.
Tuesdays Lecture Series
Topic: Quantum Information Theory Part III
Presenter: Peter Shor, AT&T
Date: Tuesday, November 27, 2001, Time: 4:30 p.m., Location: Fine Hall 110
Abstract: The classical theorem of Shannon from 1948 gives a simple formula for how much information can be sent through a communication channel. When we try to extend this formula to the quantum regime, we find that there is no longer a unique way to define channel capacity. We can define one capacity of a channel for transmitting classical information, and another for transmitting quantum information. To further complicate the situation, these quantum channel capacities can sometimes be changed by giving the sender and receiver additional capabilities which do not change classical capacity (e.g., shared entanglement or a back channel from the receiver to the sender). However, as we discuss, there do seem to be a small number of interesting quantum channel capacities, and several of them seem to be quantifiable by analogs of Shannon's formula. This is Part Three of a three part series.
Princeton/IAS Number Theory Seminar
Topic: TBA
Presenter: Ted Chinburg, University of Pennsylvania
Date: Thursday, November 29, 2001, Time: 4:30 p.m., Location: TBA
Geometric Analysis Seminar
Topic: Rolling stones with flat sides: all time regularity of the interface
Presenter: Panagiota Daskalopoulos, Columbia University
Date: Friday, November 30, 2001, Time: 3:00 p.m., Location: Fine Hall 314
Week of December 3-7
PACM Colloquium
Topic: Lattice Boltzmann Method for fluid flows
Presenter: Shiyi Chen, Johns Hopkins University
Date: Monday, December 3, 2001, Time: 4:00 p.m., Location: Fine Hall 214
Algebraic Geometry Seminar
Topic: TBA
Presenter: T. Pantev, University of Pennsylvania
Date: Tuesday, December 4, 2001, Time: 4:30 p.m., Location: Fine Hall 314
Department Colloquium
Topic: TBA
Presenter: Yakov Eliashberg, Institute for Advanced Study
Date: Wednesday, December 5, 2001, Time: 4:30 p.m., Location: Fine Hall 314
Princeton/IAS Number Theory Seminar
Topic: TBA
Presenter: Mak Trifkovic, Harvard University
Date: Thursday, December 6, 2001, Time: 4:30 p.m., Location: TBA
Geometric Analysis Seminar
Topic: TBA
Presenter: Samuel Grushevsky, Harvard University
Date: Friday, December 7, 2001, Time: 3:00 p.m., Location: Fine Hall 314
Week of December 10-14
Department Colloquium
Topic: Universal covering spaces of closed 3 manifolds are simply connected at infinity
Presenter: Valentin Poenaru, Université de Paris-Sud (Orsay)
Date: Wednesday, December 12, 2001, Time: 4:30 p.m., Location: Fine Hall 314