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OCTOBER 22-24, 2003 |
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| 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 |
| Ergodic Theory and Statistical Mechanics Seminar | |
| Topic: | Stochastic Loewner equations (tutorial talks) |
| Presenter: | Leonid Koralov, Princeton University |
| Date: | Thursday, November 6, 2003, Time: 2:00 p.m., Location: Fine Hall 224 |
| 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 |
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NOVEMBER 10-14, 2003 |
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| 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. |
| Ergodic Theory and Statistical Mechanics Seminar | |
| Topic: | Stochastic Loewner equations (tutorial talks) |
| Presenter: | Leonid Koralov, Princeton University |
| Date: | Thursday, November 13, 2003, Time: 2:00 p.m., Location: Fine Hall 224 |
| Joint Institute for Advanced Study/Princeton University Number Theory Seminar | |
| Topic: | On some singular exponential sums |
| Presenter: | Steven Sperber, University of Minnesota and Princeton University |
| Date: | Thursday, November 13, 2003, Time: 4:15 p.m., Location: Fine Hall 322 |
| Geometric Analysis Seminar | |
| Topic: | On the positivity of mass for asymptotically Anti-de Sitter spacetimes |
| Presenter: | Greg Galloway, University of Miami |
| Date: | Friday, November 14, 2003, Time: 3:00 p.m., Location: Fine Hall 314 |
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NOVEMBER 17-21, 2003 |
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| 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 |
| Department Colloquium | |
| Topic: | TBA |
| Presenter: | Chris Skinner, University of Michigan |
| Date: | Wednesday, November 19, 2003, Time: 4:30 p.m., Location: Fine Hall 314 |
| Ergodic Theory and Statistical Mechanics Seminar | |
| Topic: | Dyadic models for the equations of fluid motion |
| Presenter: | Natasa Pavlovic, Princeton University |
| Date: | Thursday, November 20, 2003, Time: 2:00 p.m., Location: Fine Hall 224 |
| Abstract: | In this talk we shall introduce dyadic models for the Euler and the Navier-Stokes equations and will discuss some results that were obtained for these models. For the scalar dyadic Euler equations we prove finite time blow-up, and in the context of the scalar dyadic Navier-Stokes equations with hyper-dissipation we prove finite time blow-up in case when the degree of dissipation is sufficiently small (joint work with Nets Katz). These results can be generalized to analogous results for a vector dyadic model (recent joint work Susan Friedlander), and we shall present them in the talk. |
| 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 |
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NOVEMBER 24-28, 2003 |
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| 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 |
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DECEMBER 1 - 5, 2003 |
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| Algebraic Geometry Seminar | |
| Topic: | TBA |
| Presenter: | Sorin Popescu, Stony Brook |
| Date: | Tuesday, December 2, 2003, Time: 4:30 p.m., Location: Fine Hall 322 |
| Department Colloquium | |
| Topic: | Homological mirror symmetry for Fano surfaces |
| Presenter: | Denis Auroux, MIT |
| Date: | Wednesday, December 3, 2003, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: | This talk will be an attempt, aimed at non-specialists, to explain the statement of the homological mirror symmetry conjecture, and describe a procedure for its verification on concrete examples, in a special case where essentially no understanding of symplectic topology is required. |
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DECEMBER 8 - 12, 2003 |
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| Discrete Mathematics Seminar | |
| Topic: | TBA |
| Presenter: | Jeff Kahn, Rutgers University |
| Date: | Wednesday, December 10, 2003, Time: 2:15 p.m., Location: Fine Hall 322 |
| Department Colloquium | |
| Topic: | TBA |
| Presenter: | Hillel Furstenberg, Yale University and Hebrew University of Jerusalem |
| Date: | Wednesday, December 10, 2003, Time: 4:30 p.m., Location: Fine Hall 314 |
| 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 |
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