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| Discrete Mathematics Seminar | |
| Topic: | Long arithmetic progressions in sumsets and Erdos-Folkman conjecture |
| Presenter: | Van Vu, University of California, San Diego |
| Date: | Wednesday, March 12, 2003, Time: 2:15 p.m., Location: Fine Hall 224 |
| Abstract: | Click here to see abstract |
| Department Colloquium | |
| Topic: | Homology manifolds |
| Presenter: | Frank Quinn, Virginia Polytechnic Institute and State University |
| Date: | Wednesday, March 12, 2003, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: | We describe the development, complete with misadventures, of homology manifolds from Poincare to the present day. A new construction giving low-dimensional examples will be sketched, and the status of the major open problems will be discussed. |
| Ergodic Theory and Statistical Analysis Seminar | |
| Topic: | Ergodic and stochastic properties of Hénon and Hénon-like maps |
| Presenter: | Michael Benedicks, Royal Institute of Technology, Stockholm |
| Date: | Thursday, March 13, 2003, Time: 2:00 p.m., Location: Fine Hall 214 |
| Abstract: | We will indicate the fairly recent progress on the understanding of ergodic and statistical properties of the Henon maps with "strange attractors" constructed by L. Carleson and M. Benedicks around 1990 and the corresponding Henon-like map studied by Mora and Viana. We will discuss such topics as the existence of SRB-measures, decay of correlation, the metric basin property (there are no holes in the metric basin of the attractor) and stability under random perturbations. This is exclusively joint work with either L-S Young or M. Viana. |
| Joint Institute for Advanced Study /Princeton University/Rutgers University Non-Linear Analysis Seminar | |
| Topic: | Causal Structure of rough solutions to the Einstein equations |
| Presenter: | Sergiu Klainerman, Princeton University |
| Date: | Thursday, March 13, Time: 4:00 p.m., Location: Fine Hall 214 |
| Joint Institute for Advanced Study/Princeton University/Rutgers University Number Theory Seminar | |
| Topic: | Exceptional zero and prime numbers |
| Presenter: | Henryk Iwaniec, Rutgers University |
| Date: | Thursday, March 13, Time: 4:15 p.m., Location: IAS SH-101 |
| Topology Seminar | |
| Topic: | Mu transpososome: a knot-theoretic look at an experiment by Pathania, Jayaram, and Harshey |
| Presenter: | John Luecke, University of Texas at Austin |
| Date: | Thursday, March 13, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: | The Mu transpososome is a bringing-together of three separate segments of a DNA molecule. We describe a recent experiment by Pathania, Jayaram, Harshey (Cell, Vol. 109, 425-436) which discovers the architecture of this complex (thinking of it as a 3-string tangle) by coupling it with the recombination enzyme CRE and observing the resulting knotted products which arise. We will give a knot-theoretic analysis of the results of this experiment. We show that there are other possible architectures, and then classify these architectures in terms of certain kinds of knotted graphs. Using this description, we shot that the PJH solution is the only rational (3-string) tangle solution for the architecture, and furthermore show that any other solution must have at least 11 crossings (where the PJH solution has only 6). This is joint work with Isabel Darcy and Mariel Vasquez. |
| Geometric Analysis Seminar | |
| Topic: | Dehn surgery and Einstein metrics in higher dimensions |
| Presenter: | Michael Anderson, SUNY at Stony Brook |
| Date: | Friday, March 14, 2003, Time: 3:00 p.m., Location: Fine Hall 314 |
| Abstract: | We will describe a construction of a large class of Einstein metrics of negative scalar curvature on compact n-manifolds, for any n > 2. These metrics are obtained by performing Dehn surgery on toral ends of a complete non-compact hyperbolic n-manifold, exactly as in Thurston's cusp closing theorem in dimension 3. (The construction gives a new proof of Thurston's theorem). A key ingredient is the use of "twisted" toral black hole metrics discussed in connection with the AdS/CFT correspondence. |
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| Mathematical Physics Seminar | |
| Topic: | Scaling limit for the stationary two-point function of the noisy Burgers equation |
| Presenter: | Herbert Spohn, TU München |
| Date: | Tuesday, March 18, 2003, Time: 4:30 p.m., Location: Jadwin A06 |
| Geometric Analysis Seminar | |
| Topic: | Analytic torsion on Calabi-Yau moduli |
| Presenter: | Hao Fang, Courant Institute, New York University |
| Date: | Friday, March 21, 2003, Time: 3:00 p.m., Location: Fine Hall 314 |
| Abstract: | Viewed as a function of the Kaehler metrics of Calabi-Yau manifolds, a special analytic torsion purposed by Bershadsky, Cecotti, Ooguri and Vafa is our subject of study. We illustrate its relations to the Weil-Peterson metric and Hodge metric on the moduli space and prove the effectiveness of the boundary of the moduli for a large class of Calabi-Yau. Furthermore, we analyze its variation in the Kaehler Cone, and its asymptotic behavior near the "nice" boundary of moduli space. As a result, for many examples (including Calabi-Yau quintic), we compute explicitly this torsion invariant as a modular function and confirm a Mirror Symmetry prediction. (joint work with Zhiqin Lu). |
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| PACM Colloquium *** Please note special time | |
| Topic: | Weird Phase Transition in a Randomly Grown Graph |
| Presenter: | Steven Strogatz, Cornell University |
| Date: | Monday, March 24, 2003, Time: 12:30 p.m., Location: Fine Hall 214 |
| Abstract: | We analyze a minimal model of a growing network. At each time step, a new vertex is added; then, with probability $\delta$, two vertices are chosen uniformly at random and joined by an undirected edge. This process is repeated for $t$ time steps. In the limit of large $t$, the resulting graph displays surprisingly rich characteristics. In particular, it appears that a giant component emerges in an infinite-order phase transition at $delta = 1/8,$ but it's still an open problem to prove this rigorously. This is joint work with Duncan Callaway, John Hopcroft, Jon Kleinberg, and Mark Newman. |
| PACM Colloquium | |
| Topic: | New high-order, high-frequency methods in computational electromagnetism |
| Presenter: | Oscar Bruno, California Institute of Technology |
| Date: | Monday, March 24, 2003, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: | We present a new set of algorithms and methodologies for the numerical solution of problems of scattering by complex bodies in three-dimensional space. These methods, which are based on integral equations, high-order integration, fast Fourier transforms and highly accurate high-frequency methods, can be used in the solution of problems of electromagnetic and acoustic scattering by surfaces and penetrable scatterers --- even in cases in which the scatterers contain geometric singularities such as corners and edges. In all cases the solvers exhibit high-order convergence, they run on low memories and reduced operation counts, and they result in solutions with a high degree of accuracy. In particular, our algorithms can evaluate accurately in a personal computer scattering from hundred-wavelength-long objects by direct solution of integral equations --- a goal, otherwise achievable today only by supercomputing. A new class of high-order surface representation methods will be discussed, which allows for accurate high-order description of surfaces from a given CAD representation. A class of high-order high-frequency methods which we developed recently, finally, are efficient where our direct methods become costly, thus leading to a general and accurate computational methodology which is applicable and accurate for the whole range of frequencies in the electromagnetic spectrum. |
| Department Colloquium | |
| Topic: | List decoding of error-correcting codes |
| Presenter: | Madhu Sudan, MIT |
| Date: | Wednesday, March 26, 2003, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: | The task of dealing with errors (or correcting them) lies at the very heart of communication and computation. The mathematical foundations for this task were laid in two concurrent and interdependent works by Shannon and Hamming in the late 1940s. The two theories are strikingly powerful and distinct in their modelling of the error. Shannon's theory models errors as effected by a probabilistic/stochastic process, while Hamming envisions them as being introduced by an adversary. While the two theories share a lot in the underlying tools, the quantitative results are sharply diverging. Shannon's theory shows that a channel that corrupt (arbitrarily) close to 50% of the transmitted bits can still be used for transmission of information. Hamming's theory in contrast has often been interpreted to suggest it can handle at most 25% error on a binary channel. So what can we do if an adversary is given the power to introduce more than 25% errors? Can we protect information against this, or do we just have to give up? The notion of list-decoding addresses precisely this question, and shows that under a relaxed notion of "decoding" (or recovering from errors), the quantitative gaps between the Shannon and Hamming theories can be bridged. In this talk, we will describe this notion and some recent algorithmic developments. |
| Ergodic Theory and Statistical Analysis Seminar | |
| Topic: | Universality of discrete orthogonal polynomial ensemble |
| Presenter: | Jinho Baik, Princeton University |
| Date: | Thursday, March 27, 2003, Time: 2:00 p.m., Location: Fine Hall 214 |
| Abstract: | In the random matrix theory, it is known that in the bulk scaling limit, the correlation functions of the scaled eigenvalues are universal (sine kernel) for a general class of unitary invariant measure on Hermitian matrices. The density function of the eigenvalues of unitary invariant measure is given by the Coulomb gas of beta=2 with certain external (continuous) potential. In this talk, we replace the potential by pure point measure. We prove the universality for a general class of pure point measures when we take continuum limit and bulk scaling limit simultaneously. An application of this result is the computation of the local correlation functions of random hexagon tiling. This is a joint work with Thomas Kriecherbauer, Ken McLaughlin and Peter Miller. |
| Joint Institute for Advanced Study /Princeton University/ Rutgers University Non-Linear Analysis Seminar | |
| Topic: | Topological Singularity in some Non-linear PDE Problems |
| Presenter: | Fang-Hua Lin, Courant Institute, New York University |
| Date: | Thursday, March 27, 2003, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: |
Many
interesting natural phenomena contain some sort of singular behavior and are
often manifested through energy concentrations. Singularities of
solutions of Partial Differential Equations which describe these phenomena
are, therefore, an important part of facets. One can divide these
singularities into two basic categories: topological and
non-topological. There are many examples of non-topological
singularities such as spikes in the reaction-diffusion systems, concentrated
vorticities in the Euler or the Navier-Stokes equations. Singularities
in these examples may or may not carry quantified amounts of energy. On
the other hand, the topological singularities often not only carry a definite
topological information but also a quantified amount of energy. Because
of this, they are often more stable energetically and dynamically. The
purpose of this lecture is to describe some recent works on analysis of
topological singularity in some variational and evolution problems.
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| Joint Institute for Advanced Study /Princeton University/ Rutgers University Number Theory Seminar | |
| Topic: | On the class number one problem for some special real quadratic fields |
| Presenter: | Andras Biro, Budapest |
| Date: | Thursday, March 27, 2003, Time: 4:15 p.m., Location: Fine Hall 322 |
| Topology Seminar | |
| Topic: | Hyperbolic Manifolds with Convex Boundary |
| Presenter: | Jean-Marc Schlenker, Université Paul Sabatier |
| Date: | Thursday, March 27, 2003, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: |
Let
M be a compact 3-manifold with boundary, which admits a convex co-compact
hyperbolic metric. One can describe the hyperbolic metrics on M for which
the boundary is smooth and strictly convex.
Theorem A: the induced metrics have curvature K>-1, and each is obtained for a unique hyperbolic metric on M. Theorem B: the third fundamental forms of the boundary have curvature K<1, and their closed geodesics which are contractible in M have length L>2\pi. Each is obtained for a unique hyperbolic metric on M. Theorem B has analogs when the boundary is supposed to look locally like an ideal or a hyperideal polyhedron. As a consequence, we find an extension of the Koebe circle packing theorem when the sphere is replaced by the boundary of M. |
| Geometric Analysis Seminar | |
| Topic: | TBA |
| Presenter: | Jie Qing, UC at Santa Cruz |
| Date: | Friday, March 28, 2003, Time: 3:00 p.m., Location: Fine Hall 314 |
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| PACM Colloquium | |
| Topic: | TBA |
| Presenter: | Anna-Karin Tornberg, Courant Institute, New York University |
| Date: | Monday, March 31, 2003, Time: 4:00 p.m., Location: Fine Hall 214 |
| Algebraic Geometry Seminar | |
| Topic: | TBA |
| Presenter: | Gavril Farkas, University of Michigan, Ann Arbor |
| Date: | Tuesday, April 1, 2003, Time: 4:30 p.m., Location: Fine Hall 322 |
| Mathematical Physics Seminar | |
| Topic: | Lifshits tails in magnetic fields |
| Presenter: | Simone Warzel, Univ. Erlangen-Nuernberg |
| Date: | Tuesday, April 1, 2003, Time: 4:30 p.m., Location: Jadwin A06 |
| Department Colloquium | |
| Topic: | TBA |
| Presenter: | Stanislav Smirnov, Royal Institute of Technology, Stockholm |
| Date: | Wednesday, April 2, 2003, Time: 4:30 p.m., Location: Fine Hall 314 |
| Ergodic Theory and Statistical Analysis Seminar | |
| Topic: | Ergodic properties of boundary actions |
| Presenter: | Tatiana Nagnibeda, Royal Institute of Technology, Stockholm |
| Date: | Thursday, April 3, 2003, Time: 2:00 p.m., Location: Fine Hall 214 |
| Abstract: | We shall discuss ergodic properties of the action of a subgroup H of a free group F on the Poisson boundary of the simple random walk on F. The action is ergodic if and only if the quotient F/H admit no non-constant bounded harmonic function. Methods from combinatorial group theory allow us to identify the conservative and the dissipative part of the action. We also present necessary and sufficient conditions of conservativity of the action in terms of geometry of the quotient. This is a joint work with R. Grigorhcuk and V. Kaimanovich. |
| Topology Seminar | |
| Topic: | TBA |
| Presenter: | John Morgan, Columbia University |
| Date: | Thursday, April 3, 2003, Time: 4:30 p.m., Location: Fine Hall 314 |
| Geometric Analysis Seminar | |
| Topic: | Regularity of biharmonic maps into Riemannian manifolds |
| Presenter: | Changyou Wang, University of Kentucky |
| Date: | Friday, April 4, 2003, Time: 3:00 p.m., Location: Fine Hall 314 |
| Abstract: | In this talk, I will consider both intrinsic and extrinsic biharmonic maps into general Riemannian manifolds. I will sketch the ideas to prove smoothness of biharmonic maps from domains of dimension four and partial regularity for stationary biharmonic maps from domains of dimensions five or above. The same theorems were previously proved by Chang-Wang-Yang when the target manifold is the standard sphere. |
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| PACM Colloquium | |
| Topic: |
Interval analysis and set-membership techniques in estimation |
| Presenter: | Isabelle Braems, MAE, Princeton University |
| Date: | Monday, April 7, 2003, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: | Interval analysis has been developed more than four decades ago to control numerical round-off errors in computers, in a rigorous way. It has then reached many other fields (assisted proof demonstrations, numerical simulation, estimation…) and applications (biology, chemical engineering, economics, computer vision, robotics…) where guaranteed computations are essential. In this talk we shall focus on parameter and state estimation problem. We will emphasize how interval analysis permits to estimate in a guaranteed way a reliable enclosure of all the global minima in optimization problems, or of all the acceptable solutions in the bounded-error context. This talk will first briefly present (or recall) the bases of interval analysis. Several applications -including non-identifiable kinetic parameteridentification, reliable characterization of a thermal set-up, and robot localization- will illustrate the performance of this approach. |
| Algebraic Geometry Seminar | |
| Topic: | TBA |
| Presenter: | Nikos Tziolas, Max Planck Institute |
| Date: | Tuesday, April 8, 2003, Time: 4:30 p.m., Location: Fine Hall 322 |
| Department Colloquium | |
| Topic: | TBA |
| Presenter: | Percy Deift, New York University |
| Date: | Wednesday, April 9, 2003, Time: 4:30 p.m., Location: Fine Hall 314 |
| Geometric Analysis Seminar | |
| Topic: | TBA |
| Presenter: | Yu Yuan, University of Washington |
| Date: | Friday, April 11, 2003, Time: 3:00 p.m., Location: Fine Hall 314 |
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| PACM Colloquium | |
| Topic: | TBA |
| Presenter: | Russel Caflisch, University of California at Los Angeles |
| Date: | Monday, April 14, 2003, Time: 4:00 p.m., Location: Fine Hall 214 |
| Topology Seminar | |
| Topic: | TBA |
| Presenter: | Alejandro Adem, University of Wisconsen |
| Date: | Thursday, April 17, 2003, Time: 4:30 p.m., Location: Fine Hall 314 |
| Geometric Analysis Seminar | |
| Topic: | TBA |
| Presenter: | Aobing Li, Rutgers University |
| Date: | Friday, April 18, 2003, Time: 3:00 p.m., Location: Fine Hall 314 |
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| PACM Colloquium | |
| Topic: | TBA |
| Presenter: | Carlos Castillo-Chavez, Cornell University |
| Date: | Monday, April 21, 2003, Time: 4:00 p.m., Location: Fine Hall 214 |
| Algebraic Geometry Seminar | |
| Topic: | TBA |
| Presenter: | Jason Starr, MIT |
| Date: | Tuesday, April 22, 2003, Time: 4:30 p.m., Location: Fine Hall 322 |
| Department Colloquium | |
| Topic: | TBA |
| Presenter: | Russel Lyons, Indiana University |
| Date: | Wednesday, April 23, 2003, Time: 4:30 p.m., Location: Fine Hall 314 |
| Geometric Analysis Seminar | |
| Topic: | TBA |
| Presenter: | Xiaodong Wang, MIT |
| Date: | Friday, April 25, 2003, Time: 3:00 p.m., Location: Fine Hall 314 |
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| Algebraic Geometry Seminar | |
| Topic: | TBA |
| Presenter: | Tomohide Terasoma, Institute for Advanced Study |
| Date: | Tuesday, April 29, 2003, Time: 4:30 p.m., Location: Fine Hall 322 |
| Department Colloquium | |
| Topic: | TBA |
| Presenter: | S.R.Srinivasa Varadhan, New York University |
| Date: | Wednesday, April 30, 2003, Time: 4:30 p.m., Location: Fine Hall 314 |
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| Algebraic Geometry Seminar | |
| Topic: | TBA |
| Presenter: | B. Guralnick |
| Date: | Tuesday, May 13, 2003, Time: 4:30 p.m., Location: Fine Hall 322 |