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| Joint Institute for Advanced Study/Princeton University Number Theory Seminar | |
| Topic: | Constructing semisimple Galois representations with prescribed properties |
| Presenter: | Ravi Ramakrishna, Princeton University and Cornell University |
| Date: | Thursday, September 25, 2003, Time: 4:15 p.m., Location: IAS SH-101 |
| Topology Seminar | |
| Topic: | Instanton Floer homology with Lagrangian boundary conditions |
| Presenter: | Katrin Wehrheim, Princeton University |
| Date: | Thursday, September 25, 2003, Time: 4:30 p.m., Location: Fine Hall 314 |
| Geometric Analysis Seminar | |
| Topic: | The J-flow and the Mabuchi energy |
| Presenter: | Ben Weinkove, Columbia University |
| Date: | Friday, September 26, 2003, Time: 3:00 p.m., Location: Fine Hall 314 |
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SEPTEMBER 29 - OCTOBER 3, 2003 |
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| PACM Seminar | |
| Topic: | Heterogeneous Multiscale Methods for the Modeling of Fluids |
| Presenter: | Weiqing Ren, Princeton University |
| Date: | Monday, September 29, 2003, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: | We apply the framework of the heterogeneous multiscale methods to develop numerical methods for the study of macroscale dynamics of fluids in situations where either the constitutive relation is not explicitly available or the macroscopic model is invalid in part of the computational domain. The methods rely on an efficient coupling between the macroscopic and microscopic models. The continuum hydrodynamics is employed as the macroscopic model while molecular dynamics serves as the microscopic model and is used to supply the necessary data for the macroscopic model. Scale separation is exploited so that macroscopic variables can be evolved in macroscopic spatial/temporal scales using data that are predicted based on molecular dynamics on microscale spatial/temporal domains. Applications to complex fluids and contact line dynamics are presented. |
| Algebraic Geometry Seminar | |
| Topic: | On the arithmetic of K3 surfaces |
| Presenter: | Yuri Tschinkel, Uni. Goettingen |
| Date: | Tuesday, September 30, 2003, Time: 4:30 p.m., Location: Fine Hall 322 |
| Abstract: | I will explain some results and constructions on K3 surfaces over countable fields. |
| Mathematical Physics Seminar | |
| Topic: | Deformations of Tiling Spaces, or -- Can You Hear the Shape of a Tile? |
| Presenter: | Lorenzo Sadun, University of Texas at Austin |
| Date: | Tuesday, September 30, 2003, Time: 4:30 p.m., Location: Jadwin A06 |
| Joint Institute for Advanced Study/Princeton University Complex Geometry Seminar | |
| Topic: | Algebraic cycles on compact Kahler manifolds |
| Presenter: | C. Voisin, Paris |
| Date: | Wednesday, October 1, 2003, Time: 1:00 p.m., Location: IAS SH-101 |
| Discrete Mathematics Seminar | |
| Topic: | Classifying uniform tilings of the hyperbolic plane |
| Presenter: | John Conway, Princeton University |
| Date: | Wednesday, October 1, 2003, Time: 2:15 p.m., Location: Fine Hall 322 |
| Abstract: | Archimedes found all convex
polyhedra whose faces are regular polygons, and whose symmetry group is
transitive on the vertices; in modern language all the uniform polyhedra.
The analogous tessellations of the Euclidean plane have been known at least
since the 19th century. Recently, Chaim Goodman-Strauss and I have completely classified the uniform tessellations of the hyperbolic plane (which were previously known only to degree 5). Surprisingly, our argument is utterly trivial; it involves a new "permutation" symbol and diagram. I'll start with a brief description of the Archimedean polyhedra and uniform Euclidean tessellations, mention some new ideas about them, and apply those to give a new proof of the classification of the polyhedra that can be used as dice. Then I'll describe the new symbol, and will finish by showing how it relates to the only slightly-less-new "generalised Schlafi symbol" for an arbitrary polytope or tessellation. |
| Department Colloquium | |
| Topic: | Kahler geometry and holomorphic foliations |
| Presenter: | Gang Tian, Princeton University |
| Date: | Wednesday, October 1, 2003, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: | This talk concerns my recent joint work with Xiuxiong Chen on the geometry of the space of Kahler metrics. I will discuss a new result on special maps into the space of Kahler metrics and explain how it is related to holomorphic foliations. I will also discuss its applications to Kahler geometry, including the uniqueness of Calabi's extremal metrics and stability of underlying manifolds. |
| Ergodic Theory and Statistical Analysis Seminar | |
| Topic: | The Conference on Dynamics in Teichmuller spaces, Marseille, July 2003 |
| Presenter | Corinna Ulcigrai, Princeton University |
| Date: | Thursday, October 2, 2003, Time: 2:00 p.m., Location: Fine Hall 224 |
| Joint Institute for Advanced Study/Princeton University Number Theory Seminar | |
| Topic: | Different types of Galois representations |
| Presenter: | Chandrashekhar Khare, University of Utah |
| Date: | Thursday, October 2, 2003, Time: 4:15 p.m., Location: Fine Hall 322 |
| Topology Seminar | |
| Topic: | Spherical CR Geometry and Dehn Surgery |
| Presenter: | Richard Schwartz, Institute for Advanced Study and University of Maryland |
| Date: | Thursday, October 2, 2003, Time: 4:30 p.m., Location: Fine Hall 314 |
| OCTOBER 6-10, 2003 | |
| PACM Seminar | |
| Topic: | Signal transmission by autocrine cells in model epithelial layers |
| Presenter: | Cyrill Muratov, NJIT |
| Date: | Monday, October 6, 2003, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: | Autocrine signaling induced by growth factors is crucial in various stages of development and in adult multicellular organisms across species. At the present level of complexity, systematic evaluation of cell communication mechanisms is next to impossible without mathematical modeling of cell signaling networks. In this talk, I will discuss recent results of our mechanistic modeling and analysis of Epidermal Growth Factor Receptor (EGFR)-mediated cell communication. I will first introduce a modeling framework which is relevant to the development and physiology of epithelial layers and to a number of in-vitro experimental formats. Mathematically, this leads to a series of interesting nonlocal/discrete nonlinear problems. I will then concentrate on the mechanism in which autocrine positive feedback loops are established by ligand-activated ligand release regulated by EGFR via a signaling network consisting of an autocrine switch (an intracellular protease) and a messenger (a secreted EGFR ligand). Such autocrine relays are found to be capable of supporting traveling waves with a number of unusual properties, such as a non-monotone dependence of the wave speed on the ligand-receptor binding rate. I will then consider the effect of cell discreteness in a physiologically relevant context and obtain the characteristics of discrete traveling waves and propagation failure. The analysis allows to characterize signal transmission in epithelial layers in terms of the biophysical and geometric parameters of the problem. |
| Algebraic Geometry Seminar | |
| Topic: | A canonical bundle formula |
| Presenter: | O. Fujino, Nagoya and Institute for Advanced Study |
| Date: | Tuesday, October 7, 2003, Time: 4:30 p.m., Location: Fine Hall 322 |
| Abstract: | Kodaira's canonical bundle formula for elliptic surfaces is a useful and important tool for the classification of surfaces. We treat various generalizations of Kodaira's formula. Roughly speaking, let $f:X\to Y$ be a surjective morphism between non-singular complex projective varieties with connected fibers. We compare $K_X$ with $K_Y$ on the assumption that the Kodaira dimension of the generic fiber of $f$ is zero. Our formula has many applications to birational geometry. |
| Discrete Mathematics Seminar | |
| Topic: | Multicoloured extremal problems |
| Presenter: | Peter Keevash, Princeton University |
| Date: | Wednesday, October 8, 2003, Time: 2:15 p.m., Location: Fine Hall 322 |
| Abstract: | See http://www.math.princeton.edu/~bsudakov/keevash2003.ps |
| Department Colloquium | |
| Topic: | TBA |
| Presenter: | Igor Rodnianski, Princeton University |
| Date: | Wednesday, October 8, 2003, Time: 4:30 p.m., Location: Fine Hall 314 |
| Joint Institute for Advanced Study/Princeton University Number Theory Seminar | |
| Topic: | TBA |
| Presenter: | Alexandru Popa, Princeton University |
| Date: | Thursday, October 9, 2003, Time: 4:15 p.m., Location: IAS SH-101 |
| Topology Seminar | |
| Topic: | Refined Seiberg-Witten invariants: Gluing in the positive curvature case |
| Presenter: | Stefan Bauer, Institute for Advanced Study |
| Date: | Thursday, October 9, 2003, Time: 4:30 p.m., Location: Fine Hall 314 |
| Geometric Analysis Seminar | |
| Topic: | The anatomy of a Ricci flow neckpinch |
| Presenter: | Dan Knopf, University of Iowa |
| Date: | Friday, October 10, 2003, Time: 3:00 p.m., Location: Fine Hall 314 |
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OCTOBER 13-17, 2003 |
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| PACM Seminar | |
| Topic: | Coarse-grained stochastic processes and Monte Carlo simulations in lattice systems |
| Presenter: | Markos Katsoulakis, University of Massachusetts |
| Date: | Monday, October 13, 2003, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: | In this talk we present a new class
of coarse-grained stochastic processes and corresponding Monte Carlo simulation
methods capable of describing efficiently much larger scales than conventional
Monte Carlo simulations, as well as providing a tool for direct hierarchical
modeling across space/time scales. Our work mainly addresses microscopic models
for the adsorption, desorption and diffusion of interacting molecules between a
surface and an overlying gas phase, while this methodology is also applied on
prototype stochastic models for unresolved features of moist atmospheric
convection. We demonstrate analytically and numerically that the new coarse-grained stochastic models can capture large scale structures while retaining significant microscopic information, such as particle/particle interactions and random fluctuations. Furthermore, computational comparisons of coarse-grained and microscopic MC simulations along with accompanying rigorous estimates on the loss of information (i.e. relative entrop) between the coarse-grained and the microscopic probability distribution functions (PDF), highlight the regimes where microscopic and coarse-grained processes and MC simulations are asymptotically identical. Finally we discuss adaptive Monte Carlo algorithms constructed using the coarse-grained stochastic processes tools we have already developed. The adaptivity criterion is based, in analogy to PDE finite element methods, on a posteriori estimates which in our stochastic context take the form of a posteriori estimations on the loss of information between the coarse-grained and the microscopic PDFs. |
| 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. |
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OCTOBER 20-24, 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 |
| Joint Institute for Advanced Study/Princeton University Number Theory Seminar | |
| Topic: | TBA |
| Presenter: | Alina Cojocaru, Princeton University |
| Date: | Thursday, October 23, 2003, Time: 4:15 p.m., Location: TBA |
| 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. |
| Discrete Mathematics Seminar | |
| Topic: | TBA |
| Presenter: | Nicholas Pippenger, Princeton University |
| Date: | Wednesday, November 5, 2003, Time: 2:15 p.m., Location: Fine Hall 322 |
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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. |
| 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 |
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NOVEMBER 17-21, 2003 |
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| PACM Seminar | |
| Topic: | TBA |
| Presenter: | Barry Merriman, University of California, Los Angeles |
| Date: | Monday, November 17, 2003, Time: 4:00 p.m., Location: Fine Hall 214 |
| 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 |
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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. |