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| Discrete Mathematics Seminar | |
| Topic: | Every function is the representation function of an additive basis for integers |
| Presenter: | Melvyn Nathanson, Lehman College (CUNY) |
| Date: | Wednesday, February 19, 2003, Time: 2:15 p.m., Location: Fine Hall 224 |
| Department Colloquium | |
| Topic: | Arnold's Diffusion |
| Presenter: | John Mather, Princeton University |
| Date: | Wednesday, February 19, 2003, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: | For a small perturbation of an integrable convex Hamiltonian system in two and a half or three degrees of freedom, there exist orbits that that wander over most of phase space. In this talk, I will provide a precise statement of this result and provide a very brief indication of the methods of proof. I will also briefly discuss related results. |
| Ergodic Theory and Statistical Analysis Seminar | |
| Topic: | Quasi periodic solutions of non-linear random Schrodinger equation I |
| Presenter: | Wei-Min Wang, Institute for Advanced Study |
| Date: | Thursday, February 20, 2003, Time: 2:00 p.m., Location: Fine Hall 214 |
| Abstract: | We start the construction toward time quasi periodic solutions of discrete non-linear random Schrodinger equation using a Newton scheme. Compared with other more extensively studied non-linear Schrodinger, the main new difficulty is the concurrence of small-divisors from the original linear operator and that from the non-linearity. In this talk, I will give an overview of the problem and emphasize the treatment of the p-equations after each linearization. This is joint work with J. Bourgain. |
| Joint Princeton University/IAS/Rutgers University Non-Linear Analysis Seminar *** Note special date | |
| Topic: | Harnack estimates of Li-Yau-Hamilton type for the Ricci flow |
| Presenter: | Ben Chow, UC San Diego |
| Date: | Thursday, February 20, 2003, Time: 4:00 - 6:00 p.m., Location: Fine Hall 214 |
| Abstract: | We will survey some works on differential Harnack type estimates for the Ricci flow. Starting from the work of Li-Yau on the heat equation, Hamilton's matrix estimate for the Ricci flow, the geometric space-time approach (joint with Sun-Chin Chu), a generalization (joint with Dan Knopf), and its recent extension due to Bing Cheng. |
| Joint Princeton University/IAS/Rutgers University Number Theory Seminar | |
| Topic: | Modular symbols have a normal distribution |
| Presenter: | Yiannis Petridis, CUNY |
| Date: | Thursday, February 20, 2003, Time: 4:15 p.m., Location: Fine Hall 322 |
| Topology Seminar | |
| Topic: | Analogies between number theory and 3-dimensional topology |
| Presenter: | Adam Sikora, Institute for Advanced Study |
| Date: | Thursday, February 20, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: | We will describe some surprising similarities between 3-dimensional topology and number theory observed by B. Mazur, and others. These similarities can be summarized by saying that knots are like prime numbers and 3-manifolds like number fields. We prove results both in topology and in number theory which further extend these analogies. |
| Geometric Analysis Seminar | |
| Topic: | Geometric Paneitz-Branson operator: concentration phenomena and fourth order pde's |
| Presenter: | Frederic Robert, ETH |
| Date: | Friday, February 21, 2003, Time: 3:00 p.m., Location: Fine Hall 314 |
| Analysis Seminar | |
| Topic: | Variations on a theme of Morawetz |
| Presenter: | Jim Colliander, University of Toronto |
| Date: | Monday, February 24, 2003, Time: 4:00 p.m., Location: Fine Hall 314 |
| Abstract: | The identification of monotone-in-time quantities underpins some of the basic insights into the long-time behavior on nonlinear Schrodinger evolutions. For example, in the focusing setting, the variance identity reveals a monotone behavior implying the existence of blow-up solutions. In the defocusing case on R^3,the Morawetz identity of Lin-Strauss provides spacetime norm bounds implying scattering behavior. This talk describes a unified approach to obtaining monotone-in-time quantities for NLS evolutions, generalizing these two classic examples. A scattering result for the R^3 cubic defocusing case will also be discussed. This talk describes joint work with M. Keel, G. Staffilani, H. Takaoka and T. Tao. |
| PACM Colloquium | |
| Topic: |
Numerical experiments on the interaction between the large- and small-scale motion of the Navier-Stokes Equations |
| Presenter: | Heinz Kreiss, University of California, Los Angeles |
| Date: | Monday, February 24, 2003, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: | The problem we want to discuss is motivated by weather prediction. To start a numerical forcast one needs initial data which must be provided by observations. Unfortunately, the observational net is too sparse to determine the small-scale of the initial data. We ask the following question: Using the time history of the large-scale data, can one reconstruct the small-scale of the data? As a model problem, we consider solutions to the unforced incompressible Navier-Stokes equations in a $2\pi$-periodic box. We split the solution into two parts representing the large-scale and small-scale motions. We define the large-scale as the sum of the first $k_c$ Fourier modes in each direction, and the small-scale as the sum of the remaining modes. We attempt to reconstruct the small-scale by incorporating the large-scale solution as known forcing into the equations governing the evolution of the small-scale. We want to find the smallest value of $k_c$ for which the time evolution of the large-scale sets up the dissipative structures so that the small-scale is determined to a significant degree. Existing theory based on energy estimates gives a pessimistic estimate for $k_c$ that is inversely proportional to the smallest length-scale of the flow. At this value of $k_c$ the energy in the small-scale is exponentially small. In contrast, numerical calculations indicate that $k_c$ can often be chosen remarkably small. We attempt to explain why the time evolution of a relatively few number of large-scale modes can be used to reconstruct the small-scale modes in many situations. We also show that similar behavior is found in solutions to Burgers' equation. |
| Special Analysis Seminar *** Please note special time and location | |
| Topic: | Nonlinear Instability for the 2D Euler Equations |
| Presenter: | Susan Friedlander, University of Illinois - Chicago |
| Date: | Tuesday, February 25, 2003, Time: 4:00 p.m., Location: Fine Hall 601 |
| Algebraic Geometry Seminar | |
| Topic: | Cohomology of local systems on M_2 and A_2 |
| Presenter: | Carel Faber, Royal Institute of Stockholm |
| Date: | Tuesday, February 25, 2003, Time: 4:30 p.m., Location: Fine Hall 322 |
| Mathematical Physics Seminar | |
| Topic: | Stochastic Loewner Evolution and Dyson's Circular Ensembles |
| Presenter: | John Cardy, IAS and Oxford University |
| Date: | Tuesday, February 25, 2003, Time: 4:30 p.m., Location: Jadwin A06 |
| Abstract: | SLE is a new approach to decribing the statistics of cluster boundaries in 2d critical systems. We show that the problem of $N$ radial SLEs in the unit disc is equivalent to Dyson's Brownian motion on the boundary of the disc, with a parameter $\beta=4/\kappa$. As a result various equilibrium critical models give realisations of circular ensembles with $\beta$ different from the classical values of $1,2$ and $4$ corresponding to random matrices. |
| 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 (room TBA) |
| 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. |
| 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: | TBA |
| Presenter: | Luminata Vese, University of California, Los Angeles |
| Date: | Monday, March 3, 2003, Time: 4:00 p.m., Location: Fine Hall 214 |
| 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. |
| Joint Princeton University/IAS/Rutgers University Number Theory Seminar | |
| Topic: | TBA |
| 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: | TBA |
| Presenter: | George Sparling, University of Pittsburgh |
| Date: | Friday, March 7, 2003, Time: 3:00 p.m., Location: Fine Hall 314 |
| 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 |
| 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: | TBA |
| Presenter: | Michael Anderson, SUNY at Stony Brook |
| Date: | Friday, March 14, 2003, Time: 3:00 p.m., Location: Fine Hall 314 |
| 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 |
| 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 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 |
| 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 |
| 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 |