|
|
||
| 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). | |
|
|
||
| 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. | |
| Analysis Seminar | ||
| Topic: | TBA | |
| Presenter: | Elon Lindenstrauss, Stanford University | |
| Date: | Monday, March 24, 2003, Time: 4:00 p.m., Location: Fine Hall 314 | |
| 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. | |
| Algebraic Geometry Seminar | ||
| Topic: | An Introduction to the Geometry of Hessenberg varieties | |
| Presenter: | Julianna Tymoczko, Princeton University | |
| Date: | Tuesday, March 25, 2003, Time: 4:30 p.m., Location: Fine Hall 322 | |
| Abstract: | Hessenberg varieties form a family of subvarieties of the flag variety. Significant examples include the Springer fiber (whose cohomology gives the irreducible Weyl group representations) and the Peterson variety (which can be stratified so that the open stratum's coordinate ring gives the quantum cohomology of the flag variety). I will discuss Hessenberg varieties, some important special cases, and give some description of their geometric structure. | |
| Discrete Mathematics Seminar | ||
| Topic: | Learning a hidden matching with application to whole-genome sequencing | |
| Presenter: | Benny Sudakov, Princeton University and the Institute for Advanced Study | |
| Date: | Wednesday, March 26, 2003, Time: 2:15 p.m., Location: Fine Hall 224 | |
| Abstract: | Click here to see abstract | |
| 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. | |
| Cohomology of Groups *** Please note NEW SEMINAR | ||
| Topic: | Finite dimensional G-spaces | |
| Presenter: | William Browder, Princeton University | |
| Date: | Thursday, March 27, 2003, Time: 3:00 p.m., Location: Fine Hall 801 | |
| Abstract: |
Borel in 1957 gave a construction which turned an arbitraryG-space into a free G-space, by multiplying by a free contractible G-space. When can one determine if a given free space X is the end product of such a construction (up to some kind of homotopy)? If G is a finite p-group and if X has the p homology type of a finite complex, and a condition on fundamental group, then X is the mod p type of a finite G-space. This relies on the Smith theorem for homotopy fixed points proved by Lannes-Zarati and by Dwyer-Wilkerson. This was inspired by and generalizes work of Grodal and Smith in the case where X is a sphere. |
|
| 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.
|
|
| 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 | |
|
|
||
| Analysis Seminar | ||
| Topic: | Quasi-Periodic Solutions for Non-Linear Random Schrodinger Equation | |
| Presenter: | Wei-Min Wang, Institute for Advanced Study | |
| Date: | Monday, March 31, 2003, Time: 4:00 p.m., Location: Fine Hall 314 | |
| Abstract: | I start the talk by giving an overview of the problem and related issues. I then sketch the construction of time quasi-periodic solutions for discrete non-linear Schrodinger equation, using a Newton scheme and Lyapunov- Schmidt P and Q decompositions. The main new dificulty is the concurrence of small divisors from the original linear equation and that from the non-linearity. This is joint work with J. Bourgain. | |
| 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 | |
| Analysis Seminar *** Please note special date | ||
| Topic: | Linability and spaceability of some nonlinear sets in Function Spaces | |
| Presenter: | Vladimir Gurariy, Kent State University | |
| Date: | Tuesday, April 1, 2003, Time: 4:00 p.m., Location: Fine Hall 314 | |
| Abstract: | The set M in Vector space X is said to be n-linable ( linable ) in X if M contains a linear manifold Y such that dimY=n ( corr. dimY=infinity ),(if X is Topological vector space and Y is closed infinitedimensional then M is said to be spaceable). In last years were discovered surprisingly many " very nonlinear " sets in Function Spaces, which are linable or even spaceable. For example, the set of nowhere differentiable functions on [0,1] is spaceable in C[0,1]( V.P.Fonf,V.I.Gurariy, M.I.Kadec, 1991). We present some new results in this direction, including following result of author together with Per Enflo: " The set of functions in C with infinitely many zeroes on [0,1] is spaceable any infinitedimensional subspace X of C". In particular this gives positive answer on old question on existence such nontrivial function in X. | |
| 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 | |
| Geometric Analysis Seminar *** Please note special date and location | ||
| Topic: | Regularity of biharmonic maps into Riemannian manifolds | |
| Presenter: | Changyou Wang, University of Kentucky | |
| Date: | Wednesday, April 2, 2003, Time: 3:00 p.m., Location: Fine Hall 322 | |
| 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. | |
| 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 | |
|
|
||
| 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: | A Bernstein problem for special Lagrangian equations | |
| Presenter: | Yu Yuan, University of Washington | |
| Date: | Friday, April 11, 2003, Time: 3:00 p.m., Location: Fine Hall 314 | |
| Abstract: | In this talk, we derive a Bernstein type result for the special Lagrangian equation, namely, any global convex solution must be quadratic. In terms of minimal surfaces, the result says that any global minimal Lagrangian graph with convex potential must be a hyper-plane. | |
|
|
||
| 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 | |
|
|
||
| Analysis Seminar | ||
| Topic: | From Hilbert's variational principle to Einstein's equations as a well posed initial value problem | |
| Presenter: | James York, Cornell University | |
| Date: | Monday, April 21, 2003, Time: 4:00 p.m., Location: Fine Hall 314 | |
| 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: | Stationary Determinantal Processes (Fermionic Lattice Gases) | |
| Presenter: | Russell Lyons, Indiana University | |
| Date: | Wednesday, April 23, 2003, Time: 4:30 p.m., Location: Fine Hall 314 | |
| Abstract | Eigenvalues of random matrices arise in various areas of physics and mathematics. The most-studied such probability measures have a determinantal form. Several people have studied other specific determinantal processes, as well as a general theory. We shall discuss the general theory of stationary random fields on integer lattices that are defined via minors of multi-dimensional Toeplitz matrices. Explicit examples include combinatorial models, finitely dependent processes, and renewal processes in one dimension. Among the interesting properties of these processes, we focus mainly on whether they have a phase transition analogous to that which occurs in statistical mechanics. We describe necessary and sufficient conditions for the existence of such a phase transition and give several examples to illustrate the theorem. This is joint work with Jeff Steif. | |
| Joint Institute for Advanced Study /Princeton University/ Rutgers University Number Theory Seminar | ||
| Topic: | Are motivic L-functions rational? | |
| Presenter: | M. Larson, Indiana | |
| Date: | Thursday, April 24, 2003, Time: 4:15 p.m., Location: Fine Hall 322 | |
| Geometric Analysis Seminar | ||
| Topic: | TBA | |
| Presenter: | Xiaodong Wang, MIT | |
| Date: | Friday, April 25, 2003, Time: 3:00 p.m., Location: Fine Hall 314 | |
|
|
||
| PACM Colloquium | ||
| Topic: | On the time evolution and steady states for inelastic Boltzmann equations | |
| Presenter: | Irene Gamba, University of Texas | |
| Date: | Monday, April 28, 2003, Time: 4:00 p.m., Location: Fine Hall 214 | |
| 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 | |
|
|
||
| Department Colloquium | ||
| Topic: | The lost proof of Loewner's theorem | |
| Presenter: | Barry Simon, Caltech | |
| Date: | Wednesday, May 7, 2003, Time: 4:30 p.m., Location: Fine Hall 314 | |
| Abstract | A real-valued function, F, on an interval (a,b) is called matrix monotone if F(A) < F(B) whenever A and B are finite matrices of the same order with eigenvalues in (a,b) and A < B. In 1934, Loewner proved the remarkable theorem that F is matrix monotone if and only if F is real analytic with continuations to the upper and lower half planes so that Im F > 0 in the upper half plane. This deep theorem has evoked enormous interest over the years and a number of alternate proofs. There is a lovely 1954 proof that seems to have been "lost" in that the proof is not mentioned in various books and review article presentations of the subject, and I have found no references to the proof since 1960. The proof uses continued fractions. I'll provide background on the subject and then discuss the lost proof and a variant of that proof which I've found, which avoids the need for estimates, and proves a stronger theorem. | |
|
|
||
| Algebraic Geometry Seminar | ||
| Topic: | TBA | |
| Presenter: | B. Guralnick | |
| Date: | Tuesday, May 13, 2003, Time: 4:30 p.m., Location: Fine Hall 322 | |