| Department Colloquium | |
| Topic: | Gromov-Witten theory for target curves |
| Presenter: | Rahul Pandharipande, Princeton University |
| Date: | Wednesday, February 26, 2003, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: | Gromov-Witten theory concerns integrals over the moduli space of maps from Riemann surfaces to target varieties X. I will present a complete description of the theory for 1-dimensional targets with connections to representation theory and integrable hierarchies. The talk represents joint work with A. Okounkov. |
| Ergodic Theory and Statistical Analysis Seminar | |
| Topic: | On Newhouse phenomenon |
| Presenter: | Vadim Kaloshin, Institute for Advanced Study |
| Date: | Thursday, February 27, 2003, Time: 2:00 p.m., Location: Fine Hall 214 |
| Abstract | Consider the space of $C^r$ diffeomorphisms (smooth invertible selfmaps) of a compact surface $M$ (e.g. $S^2$ or $T^2$) Diff$^r(M)$ with $r\geq 2$. A sink of $f:M \to M$ is a periodic point $x \in M$ which attract all points from its neighbourhood (as in your kitchen). Points attracted to $x$ called basin of attraction of $x$. In 60-th Thom conjectured that a generic diffeomorphism can not have infinitely many coexisting sinks. Indeed, each sink has an open basin of attraction and infinitely many of those seems too much. In 70-th Newhouse constructed an open set of diffeomophisms $N \subset \textup{Diff}^r(M)$ such that generic diffeomorphism in $N$ does have infinitely many coexisting sinks. It is an amazing phenomenon, called Newhouse phenomenon. It disproves Thom's conjecture and significant obstacle to discribe ergodic properties of surface diffeomorphisms. We shall discuss this phenomenon and show a sufficiently general result that indicates in some sense this phenomenon has "probability zero". This is a particular case of so-called Palis conjecture. |
| Joint Princeton University/IAS/Rutgers University Number Theory Seminar | |
| Topic: | Classical versus quantum fluctuations for the modular surface |
| Presenter: | Peter Sarnak, Princeton University and New York University |
| Date: | Thursday, February 27, 2003, Time: 4:15 p.m., Location: Rutgers 607 Hill Center |
| Topology Seminar | |
| Topic: | Algebraic K-theory of poly-(finite or cyclic) groups |
| Presenter: | Frank Quinn, VPISU and Princeton University |
| Date: | Thursday, February 27, 2003, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: | Controlled algebraic K-theory is used to relate ordinary K-theory and various exotic homology groups. We formulate the "infinite hyperelementary induction conjecture" refining the isomorphism conjecture of Farrell-Jones, and show the conjecture is true for poly-(finite or cyclic) groups. |
| Graduate Student Seminar | |
| Topic: | Null Yang-Mills fields on $S^3\times S^1$. |
| Presenter: | Jonathan Holland, Princeton University |
| Date: | Friday, February 28, 2003, Time: 12:30 p.m., Location: Fine Hall 1201 |
| Abstract: | We present all local solutions of the linear Yang-Mills equations on Lorentzian $S^3\times S^1$ with the prescribed geometrical behavior that they be null and twisting. We explore the intimate connection between such solutions and the CR geometry of some associated twistor spaces, as well as some embedding problems which arise. |
| Geometric Analysis Seminar | |
| Topic: | Singular Perturbation for the first eigenfunction on Riemannian manifolds |
| Presenter: | David Holcman, UC San Francisco |
| Date: | Friday, February 28, 2003, Time: 3:00 p.m., Location: Fine Hall 314 |
| Abstract: | Recently, we developed an approach to study the concentration of the first eigenfunction of a second order postive operator on Riemannian Compact manifolds. The set of limit measures will be described and can be characterized explicitly. In particular in some cases, the first eigenfunction sequence concentrates along manifolds of dimension k. Explicit formula can be given for the restriction of the invariant measure to the invariant manifold, which satisfies some transport equation. In this presentation, some previous results about singular perturbation for PDE with critical exponent and gradient vector field on compact manifolds will be recalled. The rest of the talk concerns the linear case. Joint work with I. Kupka (Paris VI). |
| PACM Colloquium | |
| Topic: | Modeling textures with total variation minimization and oscillating patterns in image processing |
| Presenter: | Luminata Vese, University of California, Los Angeles |
| Date: | Monday, March 3, 2003, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: | This talk is devoted to the decomposition of a given (possibly textured) image $f$ into a sum of two components $u+v$, where $u$ is a function of bounded variation (a cartoon approximation of $f$), while $v$ is an oscillating function, representing texture or noise. To model the oscillatory component $v$, we investigate the use of some spaces defined by duality, instead of the standard $L^2$ norm. These new techniques for image decomposition and texture modeling follow some recent ideas of Y. Meyer. The obtained algorithms are very simple, making use of differential equations and are easily solved in practice. Finally, I will present various numerical results on real textured images, showing the obtained decomposition $u+v$. I will also illustrate how the proposed methods can be used for image restoration, texture discrimination and texture segmentation. This is joint work with S. Osher and A. Sole. |
| Algebraic Geometry Seminar | |
| Topic: | Volume of the Space of Real Cubic Surfaces |
| Presenter: | James Carlson, University of Utah |
| Date: | Tuesday, March 4, 2003, Time: 4:30 p.m., Location: Fine Hall 322 |
| Abstract: |
We show that the moduli space of real cubic surfaces has, in a natural way, the structure of real hyperbolic orbifold of dimension four. We discuss the structure of this space, its fundamental group, and we compute its exact hyperbolic volume. As a result we can, for instance, show that real cubics with twenty-seven real lines comprise less than two percent of the full space. |
| Department Colloquium | |
| Topic: | Proof of the strong perfect graph conjecture |
| Presenter: | Paul Seymour, Princeton University |
| Date: | Wednesday, March 5, 2003, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: |
In 1961, Claude Berge proposed the conjecture that, in every graph with no odd hole or odd antihole, the number of colours needed to properly colour the graph equals the size of the largest complete subgraph. (An "odd hole" means an induced subgraph which is an odd cycle of length >= 5, and an "odd antihole" is the same in the complement graph.) This became one of the most well-known and popular open problems in graph theory. In joint work with Maria Chudnovsky, Neil Robertson and Robin Thomas, we proved the conjecture last summer. Most previous approaches to the conjecture were based on studying properties of a minimal counterexample, but our approach was different. We proved that every graph with no odd hole or antihole either falls into one of five well-understood classes, or admits a useful decomposition; and Berge's conjecture is a consequence. The proof is lengthy (150 pages), and this talk will just be a survey of some of the background and ideas involved. |
| Ergodic Theory and Statistical Analysis Seminar | |
| Topic: | Parabolic Anderson Problems |
| Presenter: | Michael Cranston, University of Rochester |
| Date: | Thursday, March 6, 2003, Time: 2:00 p.m., Location: Fine Hall 214 |
| Abstract: | We consider the almost sure behavior of solutions of the equation\partial u(t,x)/\partial t =\kappa \Delta u(t,x) + dW_x(t) u(t,x) , u(0,x)=u_0(x). This equation arises in a variety of situtions and was the subject of the memoir of Carmona and Molchanov. We consider the cases where x could be in the integer lattice, Z^d, or in R^d. In the integer lattice case we take W_x to be a field of independent Levy processes. We prove existence of lim 1/t log u(t,x)=\lambda(\kappa) a.s. when u_0 is a bounded,nonzero, nonnegative function and give asymptotics for the Lyapunov exponent, \lambda(\kappa), as \kappa goes down to zero. In the case of R^d, we take W_x to be a C^2 correlated field of Brownian motions. Then we show again that lim 1/t log u(t,x)=\lambda(\kappa) a.s. when u_0 is a bounded nonnegative function and give asymptotics for the Lyapunov exponent, \lambda(\kappa), as\kappa goes down to zero. The asymptotic behavior of \lambda(\kappa) is quite different in the two cases. |
| Joint Princeton University/IAS/Rutgers University Number Theory Seminar | |
| Topic: | Combinatorial measure theory related to the Kakeya set conjecture |
| Presenter: | Jean Bourgain, Institute for Advanced Study |
| Date: | Thursday, March 6, 2003, Time: 4:15 p.m., Location: IAS SH-101 |
| Topology Seminar | |
| Topic: | Legendrian knots and cables |
| Presenter: | John Etnyre, University of Pennsylvania |
| Date: | Thursday, March 6, 2003, Time: 4:30 p.m., Location: Fine Hall 314 |
| Geometric Analysis Seminar | |
| Topic: | The differential geometry of ordinary differential equations: relations to the conformal structures of Fefferman |
| Presenter: | George Sparling, University of Pittsburgh |
| Date: | Friday, March 7, 2003, Time: 3:00 p.m., Location: Fine Hall 314 |
| Abstract: | Two strands of thought due primarily to Elie Cartan will be combined with ideas of Charles Fefferman to give new descriptions of the geometry of second and third order ordinary differential equations. Properties of infinite differential ideals associated naturally to ordinary differential equations will be analyzed. This is joint work with Pawel Nurowski of the University of Warsaw. |
| Analysis Seminar | |
| Topic: | The F. and M. Riesz theorem for complex vector fields |
| Presenter: | Shiferaw Berhanu, Temple University |
| Date: | Monday, March 10, 2003, Time: 4:00 p.m., Location: Fine Hall 314 |
| PACM Colloquium | |
| Topic: | TBA |
| Presenter: | Andrea Bertozzi, Duke University |
| Date: | Monday, March 10, 2003, Time: 4:00 p.m., Location: Fine Hall 214 |
| Algebraic Geometry Seminar | |
| Topic: | Odd theta characteristics: embedding M_g and A_g |
| Presenter: | Samuel Grushevsky, Princeton University |
| Date: | Tuesday, March 11,2003 Time: 4:30 p.m., Location: Fine Hall 322 |
| Abstract: | Starting from the classical problem of recovering a plane curve from its bitangents, we discuss, following the work of Caporaso and Sernesi, recovering a canonical curve of genus $g$ in $P^g$ from the hyperplanes tangent to it in $g-1$ points. We then present a generalization of this question to the moduli of abelian varieties, construct an embedding of (some level covers of) $M_g$ and $A_g$ into a Grassmanian, and discuss some applications. This is joint work with Riccardo Salvati Manni. |
| 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. |
| Topology Seminar | |
| Topic: | TBA |
| Presenter: | John Luecke, University of Texas at Austin |
| Date: | Thursday, March 13, Time: 4:30 p.m., Location: Fine Hall 314 |
| 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. |
| SPRING BREAK | |
| PACM Colloquium *** Please note special time | |
| Topic: | TBA |
| Presenter: | Steven Strogatz, Cornell University |
| Date: | Monday, March 24, 2003, Time: 12:30 p.m., Location: Fine Hall 214 |
| 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: | TBA |
| Presenter: | Madhu Sudan, MIT |
| Date: | Wednesday, March 26, 2003, Time: 4:30 p.m., Location: Fine Hall 314 |
| 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: | Fanghua Lin, Courant Institute, New York University |
| Date: | Friday, March 28, 2003, Time: 3:00 p.m., Location: Fine Hall 314 |
| PACM Colloquium | |
| Topic: | TBA |
| Presenter: | Anna-Karin Tornberg, Courant Institute |
| 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 |
| 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: | TBA |
| Presenter: | Changyou Wang, University of Kentucky |
| Date: | Friday, April 4, 2003, Time: 3:00 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 parameter identification, 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 |
| 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 |
| 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 |
| 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 |
| 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 |