Current Seminars
updated 10/15/2003

 

OCTOBER 15-17, 2003

   
Discrete Mathematics Seminar  *** Please note change in date
Topic: Multicoloured extremal problems
Presenter:  Peter Keevash, Princeton University
Date:  Wednesday, October 15, 2003, Time: 2:15 p.m., Location: Fine Hall 322
Abstract: See http://www.math.princeton.edu/~bsudakov/keevash2003.ps
   
Geometry, Representation Theory, and Moduli Seminar
Topic: Simple geodesics on hyperbolic surfaces and the Witten-Kontsevich formula
Presenter:  Maryam Mirzakhani, Harvard University
Date:  Wednesday, October 15, 2003, Time: 3:00 p.m., Location: Fine Hall 214
Abstract: In this talk we discuss an algorithm for calculating the Weil-Petersson volume $V_{g,n}(\ell)$ of the moduli space $\mathcal{M}_{g,n}(\ell)$ of bordered Riemann surfaces with fixed boundary lengths $\ell_{1},\ldots, \ell_{n}$. We show that $V_{g,n}(\ell)$ is a polynomial in $\ell$.  We also relate the coefficients of $V_{g,n}(\ell)$ to the intersection numbers of tautological classes on $\overline{math{M}}_{g,n}$.
   
Department Colloquium
Topic: Asymptotics of discrete interfaces
Presenter:  Richard Kenyon, Princeton University and University Paris-Sud
Date:  Wednesday, October 15, 2003, Time: 4:30 p.m., Location: Fine Hall 314
Abstract: This is joint work with Andrei Okounkov.  We study a model of random interfaces arising in the dimer model (domino tiling model).  These can be viewed as a natural generalization of the simple random walk, where the domain is  (part of) Z^2 instead of Z.  Because we are in two dimensions the boundary conditions on the domain can be much more varied, leading to interesting behavior in the scaling limit (limit when the mesh tends to zero).  Specifically, there is a "law of large numbers" which says that at small mesh size a typical surface lies very close to its mean value. The mean value surface is obtained by solving a Dirichlet problem for a certain nonlinear PDE.  Remarkably, solutions to this PDE can be parametrized by analytic functions and one can see facets appearing in the limit shapes. 
   
Ergodic Theory and Statistical Analysis Seminar
Topic: Flat surfaces and Teichmuller dynamics
Presenter A. Zorich, University of Rennes
Date: Thursday, October 16, 2003, Time: 2:00 p.m., Location: Fine Hall 224
Abstract: Various dynamical systems in dimensions one and two (like interval exchange transformations, billiards in rational polygons, measured foliations on surfaces) lead naturally to dynamics along straight lines (geodesics) on ``flat surfaces'': compact surfaces equipped with a flat matric having several specific cone type singularities. Such flat structure is equivalent to a pair: complex structure plus a quadratic  differential. Thus, families of flat surfaces correspond to the moduli spaces of quadratic differentials.  It happens that the Teichmuller geodesics flow acting on the moduli space of quadratic differentials plays a role of a renormalisation procedure for the original dynamical system. In many cases some complicated properties of "simple" dynamics on a generic flat surface can be related to simple properties of more complicated dynamics on the moduli space. I want to suggest an elementary introduction to the subject, to give a short report on recent advances in this area, and to present briefly several key problems in Teichmuller dynamics.
   
Joint Analysis Seminar 
Topic: Recent perspectives on singular integrals
Presenter: Eli Stein, Princeton University
Date: Thursday, October 16, 2003, Time: 3:30 p.m., Location: Fine Hall 224
   
Ergodic Theory and Statistical Analysis Seminar  *** Please note special time and location
Topic: Growth of the number of simple closed geodesics on hyperbolic surfaces and ergodic theory on moduli space
Presenter Maryam Mirzakhani, Harvard University
Date: Thursday, October 16, 2003, Time: 4:00 p.m., Location: Fine Hall 214
Abstract: In this talk we discuss the problem of the growth of the number of simple closed geodesics on hyperbolic surfaces. We relate this problem to the ergodic properties of the earthquake flow on moduli space and the Weil-Petersson volumes of moduli spaces of bordered Riemann surfaces.
   
Joint Institute for Advanced Study/Princeton University Number Theory Seminar
Topic: Hilbert's Tenth Problem for function fields of surfaces over $\mathbf{C}$
Presenter: Kirsten Eisentrager, Institute for Advanced Study
Date: Thursday, October 16, 2003, Time: 4:15 p.m., Location: Fine Hall 322
Abstract: Hilbert's Tenth Problem in its original form is the following: Is there a uniform algorithm that determines, given a multivariate polynomial equation with integer coefficients, whether the equation has a solution over the integers?  Davis-Putnam-Robinson-Matiyasevich showed that there is no such algorithm, i.e. that Hilbert's Tenth Problem is undecidable. Since then the analogue of this question has been studied for various rings. I will discuss the result by Kim and Roush that Hilbert's Tenth Problem for $\mathbf{C}(t_1,t_2)$ is undecidable, and show how their result can be generalized to finite extensions of $\mathbf{C}(t_1,t_2)$, i.e. to function fields of surfaces over the complex numbers.
   
Topology Seminar
Topic: Smoothing loop spaces
Presenter: Erik Pedersen, SUNY Binghamton
Date: Thursday, October 16, 2003, Time: 4:30 p.m., Location: Fine Hall 314
Abstract: If X is a loop space with finitely generated homology, then X is homotopy equivalent to a closed, smooth, parallelisable manifold. This is joint work with Tilman Bauer, Nitu Kitchloo, and Dietrich Notbohm.
   
Ergodic Theory and Statistical Analysis Seminar  ***Note special date
Topic: Counting saddle connections on flat surfaces and description of the "cusps" of the moduli spaces of Abelian differentials
Presenter: A. Zorich, University of Rennes
Date: Friday, October 17, 2003, Time: 2:00 p.m., Location: Fine Hall 601
Abstract: A holomorphic 1-form on a compact Riemann surface S naturally defines a flat metric on S with cone-type singularities. We present the following surprising phenomenon: having found a geodesic segment (saddle connection) joining a pair of conical points one can find with a nonzero probability another saddle connection on S having the same direction and the same length as the initial one. A similar phenomenon is valid for the families  of parallel closed geodesics. We give a description of all possible configurations of parallel saddle connections (and of families of parallel closed geodesics) which might be found on a generic flat surface S and we count the  number of corresponding saddle connections of length less than L. To perform this computation we elaborate the detailed description of the "cusps" (i.e., of the principal part of the boundary) of the moduli space of holomorphic 1-forms and we find the volumes of these "cusps".
   
Joint Columbia University/Courant Institute/Princeton University Differential Geometry Seminar
Topic: Quasi-local mass in general relativity
Presenter: Hubert Bray, Columbia University
Date: Friday, October 17, 2003, Time: 2:00 p.m., Location: Fine Hall 314
   
Joint Columbia University/Courant Institute/Princeton University Differential Geometry Seminar
Topic: Estimates for the extinction time of the Ricci flow
Presenter: Toby Colding, Courant Institute
Date: Friday, October 17, 2003, Time: 3:30 p.m., Location: Fine Hall 314
   

OCTOBER 20-24, 2003

   
 Analysis Seminar
Topic: On the behavior of Feynman-Kac propagators
Presenter: Archie Gulisashvili, Ohio University
Date: Monday, October 20, 2003, Time: 4:00 p.m., Location: Fine Hall 314
   
PACM Seminar
Topic: Dynamic Properties of Biological Regulatory Networks
Presenter: Chao Tang, NEC Laboratories, Inc.
Date: Monday, October 20, 2003, Time: 4:00 p.m., Location: Fine Hall 214
Abstract: The interactions between proteins, DNA, and RNA in living cells constitute molecular networks that govern various cellular functions. To investigate the global dynamical properties and stabilities of such networks, we studied the cell-cycle regulatory network of the budding yeast. With the use of a simple dynamical model, it was demonstrated that the cell-cycle network is extremely stable and robust for its function. The biological stationary state-the G1 state-is a global attractor of the dynamics. The biological pathway-the cell-cycle sequence of protein states-is a globally attracting trajectory of the dynamics. These properties are largely preserved with respect to small perturbations to the network. These results suggest that cellular regulatory networks are robustly designed for their functions.
   
Algebraic Geometry Seminar
Topic: Semistable reduction for p-adic local systems
Presenter: Kiran S. Kedlaya, Institute for Advanced Study and MIT
Date: Tuesday, October 21, 2003, Time: 4:30 p.m., Location: Fine Hall 322
Abstract:

In complex analysis, a holomorphic local system arising from a variation of Hodge structures (e.g., the cohomology of a family of smooth projective varieties) always has quasi-unipotent monodromy; so after passing to a finite cover, the local system admits a canonical logarithmic extension. We describe a p-adic analogue of this situation: certain "local systems" (overconvergent isocrystals) equipped with extra analytic structure (action of Frobenius) have quasi-unipotent monodromy, and on some cover admit canonical logarithmic extensions. This makes it easier to handle the cohomology of said local systems.

   
Special Colloquium
Topic: Foundations of Quantum Mechanics and Quantum Gravity
Presenter: Sir Roger Penrose, Oxford University
Date: Tuesday, October 21, 2003, Time: 4:30 p.m., Location: Taplin Auditorium
   
Discrete Mathematics Seminar
Topic: Dimers, tilings and trees
Presenter:  Richard Kenyon, Princeton University and University Paris-Sud
Date:  Wednesday, October 22, 2003, Time: 2:15 p.m., Location: Fine Hall 322
Abstract: This is joint work with Scott Sheffield.  We describe a natural equivalence between three types of planar objects: bipartite planar graphs, tilings with convex polygons, and planar Markov chains.
 In particular a tiling gives a "discrete analytic function" on a bipartite planar graph as well as a harmonic function on the Markov chain.  Dimer configurations on the bipartite graph are in bijection with spanning trees on the Markov chain.
The result has some far-reaching consequences in the theory of random interfaces.
   
Department Colloquium
Topic: Full Regularity of Variational Solutions to Two Phase Free Boundary Problems in 3-Dimensions
Presenter:  Carlos Kenig, Institute for Advanced Study and University of Chicago
Date:  Wednesday, October 22, 2003, Time: 4:30 p.m., Location: Fine Hall 314
Abstract: See http://www.math.princeton.edu/~seminar/2003-04-sem/KenigAbstract10-22-2003.pdf
   
Ergodic Theory and Statistical Analysis Seminar
Topic: Random walks on nilpotent Lie groups
Presenter Emmanuel Breuillard, Yale University
Date: Thursday, October 23, 2003, Time: 2:00 p.m., Location: Fine Hall 224
Abstract: We generalize some well-known limit theorems of classical probability theory in the context of nilpotent Lie groups. In particular, we prove a local limit theorem for products of independent random variables which are identically distributed according to an arbitrary centered and compactly supported probability law $\mu$ on the Heisenberg group $H$. We also get a precise estimate of the behavior of $\mu^{n}$ on $H$ by comparing it to the associated heat kernel. Weaker estimates are also obtained on arbitrary nilpotent Lie groups. As an application, we show that symmetric unipotent random walks on homogeneous spaces &G/\Gamma$ are equidistributed, thus yielding a probabilistic version of Ratner's theorem.
   
Joint Analysis Seminar 
Topic: Convergence of the Yamabe flow for arbitrary initial energy
Presenter: Simon Brendle, Princeton University
Date: Thursday, October 23, 2003, Time: 3:30 p.m., Location: Fine Hall 224
   
Joint Institute for Advanced Study/Princeton University Number Theory Seminar
Topic: Reductions of an elliptic curve modulo primes
Presenter: Alina Cojocaru, Princeton University
Date: Thursday, October 23, 2003, Time: 4:15 p.m., Location: Fine Hall 322
   
Topology Seminar
Topic: Dehn surgery problems and Seiberg-Witten monopoles
Presenter: Peter Ozsvath, Columbia University and the Institute for Advanced Study
Date: Thursday, October 23, 2003, Time: 4:30 p.m., Location: Fine Hall 314
Abstract: I will discuss joint work with Peter Kronheimer, Tom Mrowka, and Zoltan Szabo, in which we use methods from gauge theory to verify a conjecture of Gordon, according to which if p/q Dehn surgery on a knot K is orientation preservingly diffeomorphic to p/q Dehn surgery along the unknot U, then K=U. The key technical device is a surgery long exact sequence for Seiberg-Witten monopole Floer homology. There are other applications of these techniques to problems of lens space surgeries, and also to the non-existence of taut foliations over certain three-manifolds.
   
NOVEMBER 3-7, 2003
   
PACM Seminar
Topic: Transport-limited aggregation in two dimensions
Presenter: Martin Bazant, Massachusetts Institute of Technology
Date: Monday, November 3, 2003, Time: 4:00 p.m., Location: Fine Hall 214
Abstract: Over the past two decades, Diffusion-Limited Aggregation (DLA) has become the canonical model of fractal growth controlled by bulk transport (as opposed to interfacial kinetics). A key feature of DLA, also arising in related phenomena of Laplacian growth such as viscous fingering, is the assumption of steady diffusion, governed by a harmonic concentration field. As first described by Hastings and Levitov (1998), this allows DLA in the plane to be recast in terms of a stochastic conformal map with ``bumps'' chosen according to the harmonic measure. Here, we apply conformal mapping to certain systems of transport equations [1] to generalize the Hastings-Levitov formalism to a new class of (discrete and continuous) non-Laplacian growth phenomena limited by nonlinear diffusion, advection-diffusion in a potential flow, and/or electrochemical transport [2]. Motivated by the viscous-fingering analysis of Entov and Etingov (1991), we also consider curved two-dimensional manifolds, including DLA on a sphere or pseudo-sphere [3]. Another interesting example is Advection-Diffusion-Limited Aggregation in a potential flow, which exhibits a universal crossover from DLA to a new advection-dominated regime, controlled by a time-dependent Peclet number. Remarkably, the fractal dimension is not affected by spatial curvature or advection, in spite of dramatic changes in anisotropy and growth rate. [1] M. Z. Bazant, to appear in Proc. Roy. Soc. A (2003). http://arXiv.org/abs/physics/0302086 [2] M. Z. Bazant, J. Choi, and B. Davidovitch, Phys. Rev. Lett. 91, 045503 (2003). http://arXiv.org/abs/cond-mat/0303234 [3] J. Choi, D. Crowdy, and M. Z. Bazant, in preparation.
   
Algebraic Geometry Seminar
Topic: Towards the McKay correspondence in all dimensions
Presenter: Alastair Craw, Stony Brook
Date: Tuesday, November 4, 2003, Time: 4:30 p.m., Location: Fine Hall 322
Abstract: For a finite subgroup G of SL(3,C), Bridgeland, King and Reid proved that a particular crepant resolution Y of the quotient C^3/G is "distinguished" in the sense that it is a moduli space of objects on C^3. In addition, they established the McKay correspondence for Y as an equivalence of derived categories. I'll describe recent joint work with Akira Ishii (Kyoto) proving that every crepant resolution of C^3/G is a moduli space of representations of the McKay quiver (for G Abelian), generalising a result by Kronheimer for finite subgroups of SL(2,C). I'll also describe a programme to appropriately generalise the McKay correspondence to higher dimensions.
Discrete Mathematics Seminar
Topic: Analysis of Algorithms and the Topology of Random Surfaces
Presenter:  Nicholas Pippenger, Princeton University
Date:  Wednesday, November 5, 2003, Time: 2:15 p.m., Location: Fine Hall 322
Abstract: See http://www.math.princeton.edu/~bsudakov/nick2003.ps
   
Topology Seminar
Topic: On groups generated by two positive multi-twists
Presenter: Christopher J. Leininger, Columbia University
Date: Thursday, November 6, 2003, Time: 4:30 p.m., Location: Fine Hall 314
Abstract: Following Thurston, we study subgroups of the mapping class group generated by two positive multi-twists. We classify the configurations of curves for which the corresponding groups exhibit certain exceptional behaviors.  We also identify a pseudo-Anosov automorphism whose dilatation is Lehmer's number, and show that this is minimal for the groups under consideration. Connections with Coxeter groups, billiards, and knot theory are also observed.
   
Geometric Analysis Seminar
Topic: Einstein metrics on spheres
Presenter: Janos Kollar, Princeton University
Date: Friday, November 7, 2003, Time: 3:00 p.m., Location: Fine Hall 314
   

NOVEMBER 10-14, 2003

   
PACM Seminar
Topic: A posteriori error estimates and adaptivity for convection dominated flow problems
Presenter: Mario Ohlberger, University of Maryland
Date: Monday, November 10, 2003, Time: 4:00 p.m., Location: Fine Hall 214
Abstract: We consider a class of implicit finite volume schemes on unstructured > grids to approximate solutions of convection dominated weakly coupled > non-linear convection--diffusion--reaction systems. An a posteriori > error estimate is proven. The L^1-error estimate obtained is robust in > the diffusion coefficient, i.e. it applies in particular in the > convection--dominated case and is even valid in the hyperbolic limit. > Numerical experiments with an associated grid-adaptive algorithm are > presented. Examples include environmental problems and combustion. From > the numerical results it can be seen that the first order adaptive > method is an adequate tool for non-linear convection with some > self-sharpening effect. However, it is not convincing for linear > advection problems because of its low order of convergence. To improve > the method we introduce a higher order discretization of the convective > part by MUSCL-type reconstruction. The improvement is demonstrated in > several numerical examples.
   
Algebraic Geometry Seminar
Topic: TBA
Presenter: Linda Chin, Columbia University
Date: Tuesday, November 11, 2003, Time: 4:30 p.m., Location: Fine Hall 322
   
Mathematical Physics Seminar
Topic: String-localized quantum fields from Wigner representations
Presenter: Jakob Yngvason, University of Vienna
Date: Tuesday, November 11, 2003, Time: 4:30 p.m., Location: Jadwin A06
Abstract: Among the irreducibe unitary representations of the Poincare group classified by Wigner in 1939 there are massless representations where the ``little group'' is represented faithfully and all (integer or half integer) helicity values occur. They are often referred to as ``infinite spin'' or ``continuous spin'' representations. It has been known since 1969 that such representations can not occur in the standard setting of quantum field theory with point-like localized fields.  In joint work with Jens Mund and Bert Schroer, free quantum fields have been constructed that are associated with these representations and localized in semi-infinite strings extending to spacelike infinity.  These fields comply with the causality and spectral principles of relativistic quantum field theory, in spite of their weaker localization properties. An interpretation of the directions of the strings as points in a de Sitter space is an important ingredient for the construction. Such objects, which are outside the Lagrangian framework, exist in every space-time dimension $D\geq 3$. They provide explicit examples of string localized relativistic quantum fields.
   
Discrete Mathematics Seminar
Topic: TBA
Presenter:  Peter Winkler, Bell Labs and the Institute for Advanced Study
Date:  Wednesday, November 12, 2003, Time: 2:15 p.m., Location: Fine Hall 322
   
Department Colloquium
Topic: Twisting in stringy orbitfold
Presenter:  Yongbin Ruan, University of Wisconsin
Date:  Wednesday, November 12, 2003, Time: 4:30 p.m., Location: Fine Hall 314
Abstract: Stringy orbifold is a new emerging field of mathematics for last a few years. It has its root in physics and connections to many branches of mathematics such as algebraic geometry, algebraic topology and representation theory. One important aspect of stringy orbifold is twisting process. The first twisting is discrete torsion invented by physcist C. Vafa. Recently, gerbe is emerging as a leading candidate. The talk will try to explain all these connections.
   

NOVEMBER 17-21, 2003

   
PACM Seminar
Topic: Biological Molecular Algorithms -- A Mathematician’s Perspective on Molecular Biology
Presenter: Barry Merriman, University of California, Los Angeles
Date: Monday, November 17, 2003, Time: 4:00 p.m., Location: Fine Hall 214
   
Mathematical Physics Seminar
Topic: Lieb-Thirring inequalities and absolutely continuous spectrum of Schroedinger operators
Presenter: Ari Laptev, Technical University Stockholm
Date: Tuesday, November 18, 2003, Time: 4:30 p.m., Location: Jadwin A06
Abstract: The aim of this talk is to extend a class of potentials for  which the absolutely continuous spectrum of the corresponding multidimensional Schroedinger operator is essentially supported by [0, infnity). Our main theorem states that this property is preserved for slowly decaying potentials provided that there are some oscillations with respect to one of the variables.
   
Discrete Mathematics Seminar
Topic: TBA
Presenter:  Avi Wigderson, the Institute for Advanced Study and Hebrew University
Date:  Wednesday, November 19, 2003, Time: 2:15 p.m., Location: Fine Hall 322
   
Joint Columbia University/Courant Institute/Princeton University Differential Geometry Seminar
Topic: The Ricci flow I
Presenter: Richard Hamilton, Columbia University
Date: Friday, November 21, 2003, Time: 2:00 p.m., Location: Courant Institute, New York
   
Joint Columbia University/Courant Institute/Princeton University Differential Geometry Seminar
Topic: The Ricci flow II
Presenter: Richard Hamilton, Columbia University
Date: Friday, November 21, 2003, Time: 3:30 p.m., Location: Courant Institute, New York
   

NOVEMBER 24-28, 2003

   
PACM Seminar
Topic: Eavesdropping on Synaptic Traffic
Presenter: Steve Cox, Rice University
Date: Monday, November 24, 2003, Time: 4:00 p.m., Location: Fine Hall 214
Abstract: Nerve cells communicate to one another across synapses. The receiver encodes this message as a change in local, in space and time, conductance. This change engenders a postsynaptic change in potential that actively diffuses through the dendritic tree and eventually may lead to the firing of a nervous impulse which may in turn lead to a long term change in the aforementioned synaptic conductance. To quantify this synaptic plasticity we propose a non invasive cocktail of optical imaging via voltage sensitive dyes and numerical determination of synapse location and conductance time course. In this talk we will focus on the mathematical and numerical study of the sideways Hodgkin-Huxley system that permits one to eavesdrop on synapses.
   
Algebraic Geometry Seminar
Topic: Simple Hironaka resolution
Presenter: Jaroslaw Wlodarczyk, Purdue University
Date: Tuesday, November 25, 2003, Time: 4:30 p.m., Location: Fine Hall 322
Abstract: Building upon works of O.Villamyor, Encinas-Villamayor and Bierstone-Milman we give a short proof of Hironaka resolution teorems. We put particular emphasis on canonicity and functoriality of the algorithm. Introduced here idea of "Homogenized ideals" gives apriorie canonicity of the resolution procedure and radically simplifies the proof.
   
Discrete Mathematics Seminar
Topic: TBA
Presenter:  Bela Bollobas, Memphis and Cambridge Universities
Date:  Wednesday, November 26, 2003, Time: 2:15 p.m., Location: Fine Hall 322
   

DECEMBER 1 - 5, 2003

   
Algebraic Geometry Seminar
Topic: TBA
Presenter: Sorin Popescu, Stony Brook
Date: Tuesday, December 2, 2003, Time: 4:30 p.m., Location: Fine Hall 322
   

DECEMBER 8 - 12, 2003

   
Discrete Mathematics Seminar
Topic: TBA
Presenter:  Jeff Kahn, Rutgers University
Date:  Wednesday, December 10, 2003, Time: 2:15 p.m., Location: Fine Hall 322
   
Joint Columbia University/Courant Institute/Princeton University Differential Geometry Seminar
Topic: Collapsing and non-collapsing
Presenter: Jeff Cheeger, Courant Institute
Date: Friday, December 12, 2003, Time: 2:00 p.m., Location: Columbia University, New York
   
Joint Columbia University/Courant Institute/Princeton University Differential Geometry Seminar
Topic: Extremal K\"ahler metrics and applications
Presenter: Gang Tian, Princeton University
Date: Friday, December 12, 2003, Time: 3:30 p.m., Location: Columbia University, New York