| OCTOBER 8-10, 2003 | |
| Joint Institute for Advanced Study/Princeton University Complex Geometry Seminar | |
| Topic: | Canonical Ka"hler metrics and Geometric stability: A survey of results and open problems |
| Presenter: | S. Paul, Columbia University |
| Date: | Wednesday, October 8, 2003, Time: 1:30 p.m., Location: Fine Hall 401 |
| Discrete Mathematics Seminar | |
| Topic: | Chromatic number of the plane |
| Presenter: | Alexander Soifer, DIMACS, Princeton University and University of Colorado |
| Date: | Wednesday, October 8, 2003, Time: 2:15 p.m., Location: Fine Hall 322 |
| Abstract: | See http://www.math.princeton.edu/~bsudakov/soifer2003.pdf |
| Geometry, Representation Theory, and Moduli Seminar | |
| Topic: | Partitions & algebraic curves II |
| Presenter: | Rahul Pandharipande, Princeton University |
| Date: | Wednesday, October 8, 2003, Time: 3:00 p.m., Location: Fine Hall 214 |
| Department Colloquium | |
| Topic: | On local and global aspects of the Einstein evolution |
| Presenter: | Igor Rodnianski, Princeton University |
| Date: | Wednesday, October 8, 2003, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: | I will discuss recent progress on the L^2-curvature conjecture obtained in joint work with S. Klainerman. In particular, this will include the question on existence and regularity of null hypersurfaces in an Einstein vacuum space-time. The "global" part of the talk will focus on the question of stability of the "harmonic gauge" in general relativity (joint work with H. Lindblad) and the proof of the Price law (or the "no hair theorem") in the collapse of a self-graviatitng scalar field (joint work with M. Dafermos.) |
| Ergodic Theory and Statistical Analysis Seminar | |
| Topic: | Statistic Properties of the Rauzy-Veech-Zorich Induction for Interval Exchanges of Four Intervals |
| Presenter | Alexander I. Bufetov, Princeton University |
| Date: | Thursday, October 9, 2003, Time: 2:00 p.m., Location: Fine Hall 224 |
| Abstract: | An interval exchange transformation is a piecewise increasing piecewise isometric bijective self-map of the unit interval. The space of all such maps with a fixed number of discontinuities is endowed with a natural renormalization map, the Rauzy--Veech--Zorich induction, which preserves a natural absolutely continuous finite invariant measure. In the talk, we shall consider the case of four intervals. In that case, I shall obtain the correlation decay rates for the Rauzy--Veech--Zorich induction map. The proof relies on the Tower Method of Lai-Sang Young. If time permits, I shall also discuss connections to the Teichmueller flow on the space of moduli of quadratic differentials. |
| Noetherian Ring Mini-Course in Symplectic Geometry *** Special Seminar | |
| Topic: | Symplectic Geometry: An Introduction |
| Presenter: | Rebecca Goldin, George Mason University |
| Date: | Thursday, October 9, 2003, Time: 2:30 p.m., Location: Professor's Lounge |
| Abstract: | I will outline some of the basic constructions and results discovered in the early 1980s about symplectic manifolds with Hamiltonian group actions. I will define the basic objects that people study, including symplectic manifolds, Hamiltonian T-actions, toric varieties, moment maps, and symplectic reduction. I will illustrate these concepts with several examples, and show how these group actions lead to combinatorial questions. |
| Non-Linear Analysis Seminar | |
| Topic: | Controllability of nonlinear systems |
| Presenter: | J. M. Coron, Orsay and Insti. Univ. de France |
| Date: | Thursday, October 9, 2003, Time: 3:30 p.m., Location: Fine Hall 224 |
| Joint Institute for Advanced Study/Princeton University Number Theory Seminar | |
| Topic: | Special values of Rankin L-series over real quadratic fields |
| 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 |
| Noetherian Ring Mini-Course in Symplectic Geometry *** Special Seminar | |
| Topic: | Symplectic Geometry in Equivariant Cohomology |
| Presenter: | Rebecca Goldin, George Mason University |
| Date: | Friday, October 10, 2003, Time: 10:00 a.m., Location: Fine Hall 110 |
| Abstract: | I will define equivariant cohomology, state some fundamental results about equivariant cohomology as it pertains to Hamiltonian T-spaces (where T is a compact torus), and give a few examples. I will pose some open questions about the underlying geometry of Hamiltonian T-spaces as it relates to their equivariant cohomology ring. Time permitting we will discuss how at least one of these questions is related to a well-known question in linear algebra and representation theory. |
| Geometric Analysis Seminar | |
| Topic: | Poincare metrics and conformal geometry |
| Presenter: | Robin Graham, University of Washington |
| Date: | Friday, October 10, 2003, Time: 3:00 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: 4:15 p.m., Location: Fine Hall 314 |
|
OCTOBER 13-17, 2003 |
|
| Noetherian Ring Mini-Course in Symplectic Geometry *** Special Seminar | |
| Topic: | The Image of the Moment Map for Hamiltonian T-spaces, and the Jeffrey-Kirwan Residue Formula |
| Presenter: | Rebecca Goldin, George Mason University |
| Date: | Monday, October 13, 2003, Time: 10:00 a.m., Location: Professor's Lounge |
| Abstract: | Let M be a compact Hamiltonian T-space (where T is a compact torus) with isolated fixed points. Let u be a moment map for M. Then the image u(M) is a convex polytope. I will discuss how to obtain geometric data from the image of the moment map using a formula due to L. Jeffrey and F. Kirwan called the Residue Formula. I will present the abelian version of this formula and show how it can be used to distinguish chambers of the moment map polytope (joint work by myself, T. Holm and L. Jeffrey). I will also discuss why these techniques suggest that other questions about the "calculus" of equivariant cohomology for Hamiltonian T-spaces may be addressed using similar methods. Time permitting, I will dicuss how the same methods can be applied to find the volume of the symplectic reduction of a product of toric varieties. In fact, I conjecture that these techniques can be used to integrate any cohomology class on the reduction of a product of any compact Hamiltonian T-spaces. This last topic is work in progress. |
| Analysis Seminar | |
| Topic: | Phenomena arising from high dimensionality |
| Presenter: | Vitali Milman, Tel-Aviv University |
| Date: | Monday, October 13, 2003, Time: 4:00 p.m., Location: Fine Hall 314 |
| Graduate Student Seminar *** Please note change in date and room | |
| Topic: | Arithmetic Quantum Chaos: Semiclassical Limits of Automorphic Forms |
| Presenter: | Lior Silberman, Princeton University |
| Date: | Monday, October 13, 2003, Time: 4:00 p.m., Location: Fine Hall 322 |
| Abstract: |
I will attempt to explain the title of the talk in three stages. The first part will introduce the "Quantum Unique Ergodicity" problem, a question of Harmonic analysis on a dynamical system. After a brief introduction to the ergodic (chaotic) behaviour of a classical system, we will define the quantum mechanical version of that system (a process known as "quantization"). At high energies ("semi-classical" domain) we will expect the motion of the quantum particle to reflect the behaviour of the classical particle. There has been some (limited) success attacking the problem in this generality.At the second part we will see how a related version of this problem arises in analytic number theory ("Arithmetic QUE") as a question about analytic properties of automorphic forms. In the terminology of the first part, these systems have multiple "time directions" as well as additional "symmetries", and we are concerned with quantum states which respect these. Time permitting, I will conclude with a brief discussion of the recent proof due to Lindenstrauss of Arithmetic QUE on the upper half-plane. |
| 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. |
| Algebraic Geometry Seminar | |
| Topic: | Isotropy of quadratic forms over function fields of p-adic curves |
| Presenter: | R. Parimala, Tata Institute |
| Date: | Tuesday, October 14, 2003, Time: 4:30 p.m., Location: Fine Hall 322 |
| Abstract: | Kaplansky defined the u-invariant of a field k to be the maximum of the dimensions of ansiotropic quadratic forms over k. It is an open question if u(k) is finite implies u(k(t)) finite, where k(t) is the rational function field in one vairable over k. We shall discuss the bounds for the u-invariant of function fields of p-adic curves. |
| 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 *** Please note time | |
| 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: | TBA |
| Presenter: | Kirsten Eisentrager, Institute for Advanced Study |
| Date: | Thursday, October 16, 2003, Time: 4:15 p.m., Location: Fine Hall 322 |
| 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 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: | 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 |
| 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. |
| 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: | TBA |
| 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, October 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, October 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. |
| 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 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 |