Current Seminars
updated 2/10/2004

   
   
FEBRUARY 9 - 13, 2004
   
   
Algebraic Geometry Seminar
Topic: Asymptotic intersection numbers and restricted volumes
Presenter:  Mihnea Popa, Harvard University
Date:  Tuesday, February 10, 2004, Time: 4:30 p.m., Location: Fine Hall 322
Abstract: I will describe work (partly in progress) on defining asymptotic intersection numbers of big (or pseudoeffective) line bundles on smooth projective varieties. Intuition is provided by intersecting with the positive part of a Zariski decomposition in case it exists. The technical tool is a notion of volume for restrictions of linear series. One shows that the asymptotic intersection numbers and the restricted volumes define continuous functions on the big cone of the ambient variety, and obtain an interesting decomposition of this cone given by their zero-locus. This is joint work with Ein, Lazarsfeld, Mustata and Nakamaye.
   
Mathematical Physics Seminar
Topic: Flow-line geometries and Gaussian loop ensembles
Presenter: Scott Sheffield, Microsoft Research
Date: Tuesday, February 10, 2004, Time: 4:30 p.m., Location: Jadwin A06
Abstract: Given a real function h on the complex plane, consider the flow lines of a complex vector field of the form e^{i(h+c)}, with c  in [0, 2pi).  If h is constant, these paths are the straight lines of Euclidean geometry.  If h is harmonic, they are the image of Euclidean lines under a conformal map.  If h is a well-behaved function with non-zero Laplacian, the flow lines are the rays of a sort of "twisted geometry" that is still reasonably tame (parallel lines do not intersect, non-parallel lines intersect at most once, triangle angles sum to 180 degrees, etc.)
If, however, h is a constant C times the Gaussian free field the story is very different.  Rays circle and "bounce off" themselves, 'parallel rays' converge, and non-parallel rays have multiple intersections.  Individual rays look locally like Schramm-Loewner evolution with a parameter kappa that depends on C.  In fact, the rays determine the boundaries of the Gaussian loop ensembles, GLE_{kappa}, which we conjecture to be the scaling limits of the O(n) loop models and other two-dimensional loop ensembles from statistical physics.
   
Discrete Mathematics Seminar
Topic: Equidistant sets under the 1-norm
Presenter:  Noga Alon, Tel Aviv University and the Institute for Advanced Study
Date:  Wednesday, February 11, 2004, Time: 2:30 p.m., Location: Fine Hall 224
Abstract: See http://www.math.princeton.edu/~bsudakov/noga2004.ps
   
Geometry, Representation, and Moduli Seminar
Topic: The determinant of the Laplacian on a Riemann surface
Presenter: 

Ezra Getzler, Northwestern University

Date:  Wednesday, February 11, 2004, Time: 3:00 p.m., Location: Fine Hall 214
   
Ergodic Theory and Statistical Mechanics Seminar
Topic: Cluster swapping and domino tilings
Presenter: 

Scott Sheffield, Microsoft Research

Date:  Thursday, February 12, 2004, Time: 2:00 p.m., Location: Fine Hall 322
Abstract: We classify the ergodic Gibbs measures on the space of domino tilings of the plane.  These measures are indexed by the asymptotic slopes of the corresponding height functions.  Our proof uses a technique called "cluster swapping" which generalizes to other random surface models (e.g., square ice, anharmonic crystals, linear solid-on-solid models).
   
Joint Columbia University/Courant Institute/Princeton University Differential Geometry Seminar
Topic: Mean curvature flow in $R^3$ and related questions
Presenter: 

Tom Ilmanen, ETH

Date:  Friday, February 13, 2004, Time: 2:00 p.m., Location: Fine Hall 314
   
Joint Columbia University/Courant Institute/Princeton University Differential Geometry Seminar
Topic: Gauge Theory Scattering And Twistor Space
Presenter: 

Edward Witten, Institute for Advanced Study

Date:  Friday, February 13, 2004, Time: 3:30 p.m., Location: Fine Hall 314
   
FEBRUARY 16 - 20, 2004
   
PACM Colloquium
Topic: Design of Semiconductor and Nano Devices
Presenter: 

Martin Burger, University of California, Los Angeles and Johannes Kepler University

Date:  Monday, February 16, 2004, Time: 4:00 p.m., Location: Fine Hall 214
Abstract:

The subject of this talk is the solution of mathematical problems related to the design of classical semiconductor and novel nano-scale devices. For the first class, we present optimization problems related to the drift-diffusion model, whose solution allows to improve the characteristics of currently produced devices. In particular, we discuss a novel design approach recently introduced in collaboration with Rene Pinnau (TU Darmstadt), which allows to optimize a device with a computational effort compareable to three direct simulations. For nano-scale devices, which are still in a pre-technological phase, we discuss some mathematical models of self-organized growth by elastic relaxation and surface diffusion, and their numerical solution, which might be used for design tasks in the future.

   
Algebraic Geometry Seminar
Topic: K3 sections and the effective cone of the moduli space of curves
Presenter:  Gavril Farkas, Princeton University
Date:  Tuesday, February 17, 2004, Time: 4:30 p.m., Location: Fine Hall 322
   
Mathematical Physics Seminar
Topic: Localization lengths and Boltzmann limit for the Anderson model in dimension 3
Presenter: Thomas Chen, Courant Institute
Date: Tuesday, February 17, 2004, Time: 4:30 p.m., Location: Jadwin A06
Abstract: We prove lower bounds on the localization length of eigenfunctions in the three-dimensional Anderson model at weak disorders, which are similar to those obtained by Shubin, Schlag and Wolff for dimensions one and two. In addition, we show that the macroscopic limit of the corresponding lattice random Schr\"odinger dynamics is governed by the linear Boltzmann equations. The proof comprises an extension of methods due to Erdoes and Yau.
   
Discrete Mathematics Seminar
Topic: A topological colorful Helly theorem
Presenter:  Roy Meshalum, Technion
Date:  Wednesday, February 18, 2004, Time: 2:30 p.m., Location: Fine Hall 224
Abstract: See http://www.math.princeton.edu/~bsudakov/meshulam2004.ps
   
Geometry, Representation, and Moduli Seminar
Topic: Hypergeometric functions and homological mirror symmetry
Presenter: 

Paul Horja, University of Michigan

Date:  Wednesday, February 18, 2004, Time: 3:00 p.m., Location: Fine Hall 214
   
Ergodic Theory and Statistical Mechanics Seminar
Topic: On the Ergodicity of the 2-D Dissipative Boussinesq system
Presenter: 

Jinhoo Lee , PACM, Princeton University

Date:  Thursday, February 19, 2004, Time: 2:00 p.m., Location: Fine Hall 322
Abstract: We study the stationary measure for the 2-D dissipative Boussinesq system with random forcing. We follow the strategy of E-Mattingly-Sinai's paper for the 2-D Navier-Stokes equations (Comm. Math. Phys. vol.224(2001) pp. 83--106). 
   
Joint Analysis Seminar *** Please note change in room from last semester
Topic: On the interaction of nearly parallel vortex filaments
Presenter:  Gustavo Ponce, UC Santa Barbara
Date:  Thursday, February 19, 2004, Time: 3:30 p.m., Location: Fine Hall 214
   
Topology Seminar
Topic: Bounded cohomology and hyperbolic groups
Presenter: Igor Mineyev, University of Illinois, Urbana and the Institute for Advanced Study
Date: Thursday, February 19, 2004, Time: 4:00 p.m., Location: Fine Hall 314
Abstract: Gromov hyperbolic groups generalize fundamental groups of closed negatively curved manifolds. Bounded cohomology, due to B. E. Johnson, is defined as the usual (singular or bar-construction) cohomology with the additional boundedness assumption on cochains. I will remind both definitions and will discuss the construction of homological bicombings on hyperbolic graphs.
   
Geometric Analysis Seminar
Topic: Local $C^0$ estimates for solutions of the $\sigma_k$-Yamabe problem under small volume condition
Presenter: 

Zheng-Chao Han, Rutgers University

Date:  Friday, February 20, 2004, Time: 3:00 p.m., Location: Fine Hall 314
   
FEBRUARY 23 - 27, 2004
   
PACM Colloquium
Topic:

Testable New Theory about Early-Universe Density Fluctuations and Origins of Cosmic Structure, with Focus on Mathematical-Probability and Computational Aspects

Presenter: 

Erik H. VanMarcke, Civil and Environmental Engineering, Princeton University

Date:  Monday, February 23, 2004, Time: 4:00 p.m., Location: Fine Hall 214
Abstract: The talk will summarize the main findings, predictions and interdisciplinary research opportunities stemming from a new probabilistic model of how complex patterns of extreme density fluctuations may have emerged from the inflation phase of the Big Bang. Based on quantum-physical principles and requiring a minimum number of (observationally-accessible) parameters, the "embryonic inflation model" yields a coherent set of testable hypotheses about the formation, evolution and composition of galaxies, stars and planets. Implying a robust (and testable, hence falsifiable) alternative to the dual paradigm of spatially-uniform light-element primordial nucleosynthesis and stellar "recycling" of matter as the sole mechanism of heavy-element production, it integrates astrophysical and planetary sciences with cosmology and galaxy formation in a coherent evolutionary framework. Overall cosmic flatness, an accelerating component, dark matter and dark energy all fit, in quantifiable and testable ways, into the framework of the theory. (Prof. VanMarcke's book on the subject, Quantum Origins of Cosmic Structure, was published in Nov. 1997, before the observation-based discovery of the "accelerating universe", which fits the theory.)
   
Algebraic Geometry Seminar
Topic: TBA
Presenter:  Andrei Caldararu, University of Pennsylvania
Date:  Tuesday, February 24, 2004, Time: 4:30 p.m., Location: Fine Hall 322
   
Mathematical Physics Seminar
Topic: Coherency effects in the multiple scattering of photons by cold atoms
Presenter: Eric Akkerman, Technion
Date: Tuesday, February 24, 2004, Time: 4:30 p.m., Location: Jadwin A06
   
Discrete Mathematics Seminar
Topic: TBA
Presenter:  Jozsef Beck, Rutgers University
Date:  Wednesday, February 25, 2004, Time: 2:30 p.m., Location: Fine Hall 224
   
Geometry, Representation, and Moduli Seminar
Topic: TBA
Presenter: 

Paul Seidel, University of Chicago

Date:  Wednesday, February 25, 2004, Time: 3:00 p.m., Location: Fine Hall 214
   
Department Colloquium
Topic: Seiberg-Witten theory and random partitions
Presenter:  Nikita Nekrasov, IHES
Date:  Wednesday, February 25, 2004, Time: 4:30 p.m., Location: Fine Hall 314
   
MARCH 1-5, 2004
   
Analysis Seminar
Topic: Asymptotics for the measure invariant with respect to a diffusion related to $NA$ groups
Presenter: 

Andrzej Hulanicki , Wroclaw University and CUNY

Date:  Monday, March 1, 2004, Time: 4:00 p.m., Location: Fine Hall 314
   
PACM Colloquium
Topic:

TBA

Presenter: 

Jianqing Fan, Operations Research and Financial Engineering, Princeton University

Date:  Monday, March 1, 2004, Time: 4:00 p.m., Location: Fine Hall 214
   
Algebraic Geometry Seminar
Topic: TBA
Presenter:  Jim Bryan, University of British Columbia
Date:  Tuesday, March 2, 2004, Time: 4:30 p.m., Location: Fine Hall 322
   
Mathematical Physics Seminar
Topic: Conformal restriction properties
Presenter: Wendelin Werner, Universite Paris Sud, Orsay
Date: Tuesday, March 2, 2004, Time: 4:30 p.m., Location: Jadwin A06
Abstract: This talk is based on joint work with Greg Lawler, Oded Schramm, and Roland Friedrich. We will describe the so-called restriction properties and give various equivalent descriptions of the various random sets that do satisfy this property. We will then outline how they are related to the (conjectural) scaling limit of simple two dimensional models, to representation theory and to some aspects of conformal field theory.
   
Discrete Mathematics Seminar
Topic: The intersection of a matroid and a simplicial complex
Presenter:  Eli Berger , Princeton University
Date:  Wednesday, March 3, 2004, Time: 2:30 p.m., Location: Fine Hall 224
Abstract: See http://www.math.princeton.edu/~bsudakov/berger2004.ps
   
Geometry, Representation, and Moduli Seminar
Topic: TBA
Presenter: 

Christopher Woodward, Rutgers University

Date:  Wednesday, March 3, 2004, Time: 3:00 p.m., Location: Fine Hall 214
   
Department Colloquium
Topic: Critical phenomena in two dimensions, conformal invariance and Schramm-Loewner Evolutions
Presenter:  Wendelin Werner, Universite Paris Sud, Orsay
Date:  Wednesday, March 3, 2004, Time: 4:30 p.m., Location: Fine Hall 314
   
Ergodic Theory and Statistical Mechanics Seminar
Topic: Reinforced Random Walk
Presenter: 

Michael Keene, Wesleyan University

Date:  Thursday, March 4, 2004, Time: 2:00 p.m., Location: Fine Hall 322
Abstract:

One of the distinguishing properties of the present scientific method is reproducibility.

In one of its guises, probability theory is based on statistical reproduction, near certainty being obtained of truth of statements  by averaging over long term to remove randomness occurring in individual experiments.

When one assumes, as is often the case, that events farther and farther in the past have less and less influence on the present, the probabilistic paradigm is currently well understood and is successful in many scientific and technological applications.

Recently, however, we have come to realize that precisely in these applications important stocahstic processes occur whose present
outcomes are significantly influenced by events in the remote past.

This behaviour is not at all well understood and some of the simplest questions remain today irritatingly beyond reach.

A salient example occurs in the theory of random walks, where there  is a dichotomy between recurrent and transient behaviour.

After explaining this classical dichotomy, we present a very simple example with infinite memory which is neither known to be transient  nor recurrent.

Then, using a reinforcement mechanism due to POLYA, we explain the nature of a particular infinite memory process in terms of spontaneous emergence of opinions.

Finally we would like to discuss briefly some of our recent results towards understanding the recurrence-transience dichotomy for
reinforced random walks, and indicate an application to universal coding used in optical CD technology.

   
Joint Analysis Seminar
Topic: TBA
Presenter:  Tristan Riviere, ETH
Date:  Thursday, March 4, 2004, Time: 3:30 p.m., Location: Fine Hall 214
   
Topology Seminar
Topic: On classifying simply connected 7-manifolds.
Presenter: Diarmuid J. Crowley, Pennylvania State University
Date: Thursday, March 4, 2004, Time: 4:00 p.m., Location: Fine Hall 314
Abstract: I shall present a program for the classification of simply connected, closed, smooth 7-manifolds.
   
Joint Analysis Seminar *** Please note special time
Topic: Brownian loop soups and conformal field theory
Presenter:  Wendelin Werner, Universite Paris Sud, Orsay
Date:  Thursday, March 4, 2004, Time: 4:45 p.m., Location: Fine Hall 214
   
Geometric Analysis Seminar
Topic: On scalar-flat Kaehler surfaces
Presenter:  Yann Rollin, MIT
Date:  Friday, March 5, 2004, Time: 3:00 p.m., Location: Fine Hall 314
   
MARCH 8-12, 2004
   
PACM Colloquium - Distinguished Lecture Series *** Please note special time and location
Topic:

Time reversal, imaging and communications in richly scattering environments

Presenter:  George Papanicolaou, Department of Mathematics, Stanford University
Date:  Monday, March 8, 2004, Time: 8:00 p.m., Location: A02 McDonnell Hall
Abstract:

Signals received by an array, time reversed and re-emitted into the environment will pack-propagate to the vicinity of the sources that produced them. It is remarkable that the focusing resolution in time reversal is much better in a strongly scattering medium than in a homogeneous one, assuming dissipation is negligible. This interesting phenomenon has many surprising applications in imaging and communications through clutter. I will describe time reversal and its properties, explain mathematically how super-resolution occurs in random media and introduce some imaging methods that deal effectively with clutter. I will also describe how time reversal can be used in communications.

 
Algebraic Geometry Seminar
Topic: TBA
Presenter:  Fabrizio Catanese, Bayreuth
Date:  Tuesday, March 9, 2004, Time: 4:30 p.m., Location: Fine Hall 322
   
Geometry, Representation, and Moduli Seminar
Topic: TBA
Presenter: 

Thomas Nevins , University of Michigan

Date:  Wednesday, March 10, 2004, Time: 3:00 p.m., Location: Fine Hall 214
 
Department Colloquium
Topic: TBA
Presenter:  Charlie Fefferman, Princeton University and the Courant Institute
Date:  Wednesday, March 10, 2004, Time: 4:30 p.m., Location: Fine Hall 314
   
Joint Analysis Seminar *** Please note change in room from last semester
Topic: Solving free boundary problems by variational and maximum principle methods
Presenter:  David Jerison, MIT
Date:  Thursday, March 11, 2004, Time: 3:30 p.m., Location: Fine Hall 214
   
Geometric Analysis Seminar
Topic: Energy of solutions of Yamabe type problems and their Morse index
Presenter:  Mohameden Ahmedou, University of Bonn
Date:  Friday, March 12, 2004, Time: 3:00 p.m., Location: Fine Hall 314
   
SPRING BREAK MARCH 13 - 21, 2004
   
MARCH 22 - 26, 2004
   
PACM Colloquium - Please note special time and location

Lewis-Sigler Topical Seminar Series 2004, Functional Genomics

Topic: Engineered Gene Networks: A Reductionist Approach to Systems Biology
Presenter:  James Collins, Center for BioDynamics, Boston University
Date:  Monday, March 22, 2004, Time: 4:00 p.m., Location: Room 101, Carl Icahn Lab
   
Algebraic Geometry Seminar
Topic: TBA
Presenter:  Steven Sperber, University of Minnesota and Princeton University
Date:  Tuesday, March 23, 2004, Time: 4:30 p.m., Location: Fine Hall 322
   
Mathematical Physics Seminar
Topic: Dynamics of magnetic Bloch electrons
Presenter: Herbert Spohn, Zentrum Mathematik and Physics Department, Technical University, Munich
Date: Tuesday, March 23, 2004, Time: 4:30 p.m., Location: Jadwin A06
Abstract: As a standard model of solid state physics we consider independent electrons subject to a periodic lattice potential and a strong uniform magnetic field with rational flux per unit cell. We then explain the first order corrections to the effective Hamiltonian from the Peierls substitution.
   
Geometry, Representation, and Moduli Seminar
Topic: TBA
Presenter: 

Michael Shapiro, Michigan State University

Date:  Wednesday, March 24, 2004, Time: 3:00 p.m., Location: Fine Hall 214
   
MARCH 29 - APRIL 2, 2004
   
PACM Colloquium
Topic:

Upper bounds on coarsening rates

Presenter: 

Robert Kohn, Courant Institute of Mathematics, New York University

Date:  Monday, March 29, 2004, Time: 4:00 p.m., Location: Fine Hall 214
Abstract: I will discuss surface-energy-driven coarsening of two-phase microstructures. Such coarsening is observed in many physical systems; two basic examples are motion by surface diffusion and Mullins-Sekerka (evaporation-condensation) dynamics. Experiments and simulations suggest that solutions are in some sense statistically self-similar. There is, however, virtually nothing known with mathematical rigor. I will briefly introduce this topic, then present recent joint work with Felix Otto (Comm. Math. Phys. 2002). Our main accomplishment is an upper bound on the coarsening rate, consistent with the conjectured self-similar behavior. Our work is also interesting for its viewpoint, which is new and potentially applicable to many other problems. I will close with one such application, to epitaxial growth -- joint work with Xiaodong Yan (Comm. Pure Appl. Math. 2003).
   
Algebraic Geometry Seminar
Topic: TBA
Presenter:  Jun-Muk Hwang, KIAS and Harvard University
Date:  Tuesday, March 30, 2004, Time: 4:30 p.m., Location: Fine Hall 322
   
Mathematical Physics Seminar
Topic: Ferromagnetism in the Hubbard model --- a constructive approach
Presenter: H. Tasaki, Gakushuin University
Date: Tuesday, March 30, 2004, Time: 4:30 p.m., Location: Jadwin A06
Abstract: It is believed that strong ferromagnetic order in some solids is generated by a subtle interplay between quantum many-body effects and the spin-independent Coulomb interactions between electrons.  I will describe our constructive approach to ferromagnetism in the Hubbard model, which is a standard idealized model for strongly interacting electrons in a solid.  I present nonsingular models of itinerant electrons with only spin-independent interactions where the low energy behavior is proved to be that of a ``healthy'' ferromagnetic insulator.  I will also discuss some open problems and conjectures regarding metallic ferromagnetism.
   
Geometry, Representation, and Moduli Seminar
Topic: TBA
Presenter: 

C. C. Liu, Harvard University

Date:  Wednesday, March 31,2004, Time: 3:00 p.m., Location: Fine Hall 214
   
Department Colloquium
Topic: TBA
Presenter:  Maciej Zworski, University of California, Berkeley
Date:  Wednesday, March 31, 2004, Time: 4:30 p.m., Location: Fine Hall 314
   
Joint Analysis Seminar
Topic: TBA
Presenter:  Maciej Zworski, Berkeley University
Date:  Thursday, April 1, 2004, Time: 3:30 p.m., Location: Fine Hall 214
   
APRIL 5- APRIL 9, 2004
   
PACM Colloquium
Topic: TBA
Presenter:  Fernando Reitich, University of Minnesota
Date:  Monday, April 5, 2004, Time: 4:00 p.m., Location: Fine Hall 214
   
Algebraic Geometry Seminar
Topic: TBA
Presenter:  Olivier Debarre, Strasbourg
Date:  Tuesday, April 6, 2004, Time: 4:30 p.m., Location: Fine Hall 322
   
Discrete Mathematics Seminar
Topic: TBA
Presenter:  Michael Krivelevich, Tel Aviv University
Date:  Wednesday, April 7, 2004, Time: 2:30 p.m., Location: Fine Hall 224
   
APRIL 12- APRIL 18, 2004
   
PACM Colloquium
Topic:

Vorticity and Wave Confinement A Rotationally Invariant Limiter Approach to Modeling Small Scales

Presenter:  John Steinhoff, University of Tennessee Space Institute
Date:  Monday, April 12, 2004, Time: 4:00 p.m., Location: Fine Hall 214
Abstract:

A new computational method, Vorticity/Wave Confinement, (V/WC), is described. V/WC has been shown to efficiently treat thin features in complex fluid flow and time domain wave equation problems involving vortices and acoustic pulses. The method allows them to be propagated over arbitrarily long distances with no spreading due to numerical errors. It has also been shown to be effective in representing boundary layers on surfaces as thin vortical layers “immersed” in uniform Cartesian grids. We define these thin vortical or wave regions as “features.” Outside these features, where the flow is irrotational or the wave amplitude vanishes, the method automatically reduces to a conventional finite difference approximation to the correct continuum partial differential equation (pde). The features are treated as a type of weak solution and, within the features, a nonlinear difference equation, as opposed to finite difference approximation, is solved that does not necessarily represent a Taylor expansion discretization of a simple pde. The approach is similar to artificial compression and shock capturing schemes, where conservation laws are satisfied across discontinuities. For propagating features, the result of this conservation is that integral quantities such as total momentum and amplitude, and centroid motion are accurately computed. Effectively, the features are treated as multi-dimensional nonlinear discrete solitary waves that “live” on the computational lattice. These obey a “confinement” relation that is a generalization to multiple dimensions of 1-D discontinuity capturing schemes. A major point is that the method involves a rotationally invariant limiter – a single limiter that is a function of rotationally invariant variables. This is in contrast to conventional discontinuity capturing schemes which may involve a concatenation of separate 1-D limiters, each a function of variables along each axis.

Results will be shown for convection of thin convecting vortex filaments, flow over complex surfaces “immersed” in uniform grids, and thin acoustic pulses scattering from complex surfaces.

   
Algebraic Geometry Seminar
Topic: TBA
Presenter:  Ravi Vakil, Stanford University
Date:  Tuesday, April 13, 2004, Time: 4:30 p.m., Location: Fine Hall 322
   
Geometry, Representation, and Moduli Seminar
Topic: TBA
Presenter: 

Alexander Braverman, Brown University

Date:  Wednesday, April 14, 2004, Time: 3:00 p.m., Location: Fine Hall 214
   
APRIL 19- APRIL 23, 2004
   
PACM Colloquium
Topic:

TBA

Presenter: 

Nicholas J. Pippenger, Computer Science, Princeton University

Date:  Monday, April 19, 2004, Time: 4:00 p.m., Location: Fine Hall 214
   
Algebraic Geometry Seminar
Topic: TBA
Presenter:  Mikhail Kapranov, Yale University
Date:  Tuesday, April 20, 2004, Time: 4:30 p.m., Location: Fine Hall 322