MARCH 24 - 26, 2004 |
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| Discrete Mathematics Seminar | |
| Topic: | Analysis of random graph processes using differential equations |
| Presenter: | Joel Spencer, Courant Institute, NYU |
| Date: | Wednesday, March 24, 2004, Time: 3:00 p.m., Location: Fine Hall 224 |
| Abstract: | See http://www.math.princeton.edu/~bsudakov/spencer2004.ps |
| Geometry, Representation, and Moduli Seminar | |
| Topic: | Cluster algebras and Poisson geometry |
| Presenter: | Michael Shapiro, Michigan State University |
| Date: | Wednesday, March 24, 2004, Time: 3:00 p.m., Location: Fine Hall 214 |
| Abstract: | In this talk we discuss Poisson properties of cluster algebras introduced by Fomin and Zelevinsky. In particular, we obtain the known Weil-Petersson symplectic structure on Teichmueller space as a result of general cluster algebra construction. |
| Department Colloquium | |
| Topic: | Hypergraph regularity and the multidimensional Szemeredi theorem |
| Presenter: | Timothy Gowers, Cambridge University |
| Date: | Wednesday, March 24, 2004, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: | Szemeredi's regularity lemma is a major tool in graph theory. Recently, it and a companion result have been generalized to hypergraphs, and a consequence of these developments is the first proof of the multidimensional Szemeredi theorem that does not rely on Furstenberg's ergodic-theoretic techniques, and the first to give an explicit (though very weak) bound. |
| Ergodic Theory and Statistical Mechanics Seminar - *** Please note special time and location | |
| Topic: | Instability of totally elliptic points of 4-dimensional symplectic maps |
| Presenter: | Vadim Kaloshin, Institute for Advanced Study |
| Date: | Thursday, March 25, 2004, Time: 4:30 p.m., Location: Fine Hall 801 |
| Abstract: | We shall present recent progress in proving instability of convex totally elliptic points of 4-dimensional symplectic maps or convex periodic totally elliptic periodic trajectories in 2.5 degrees of freedom. The proof are variational and heavily based on Mather diffusion theorem for convex Hamiltonians in 2.5 degrees of freedom. This is a joint work with J. Mather and E. Valdinoci. |
| Topology Seminar | |
| Topic: | Homological Classification of Surface Group Actions on the Plane |
| Presenter: | Danny Calegari, Caltech |
| Date: | Thursday, March 25, 2004, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: | Which 4-manifolds can arise as the total space of a complete foliated R^2 bundle over a surface S? Equivalently, what is the homological classification of actions of a surface group by homeomorphisms on R^2? We concentrate on oriented surfaces and orientation-preserving homeomorphisms, and give a complete homological classification in every degree of smoothness. For surfaces of higher genus, every homological possibility is realized, for any degree of smoothness. Similarly, for surfaces of genus 1, every homological possibility is realized for C^0 actions. But for C^1 or smoother actions, a surprising rigidity phenomenon manifests, and the actions are all homologically trivial. This talk should be of interest to people working in Dynamics, Geometry and Topology, and will be accessible to graduate students. |
| Geometric Analysis Seminar | |
| Topic: | The structure of singularities in mean curvature flow of mean convex sets in 3-dimensions |
| Presenter: | Bruce Kleiner, University of Michigan |
| Date: | Friday, March 26, 2004, Time: 3:00 p.m., Location: Fine Hall 314 |
| Abstract: | I will discuss the formation of singularities in mean curvature flow of surfaces with positive mean curvature. Roughly speaking, the results confirm the naive picture that the only singularities are neck pinches and components which collapse to asymptotically round spheres. This is joint work with Toby Colding. |
| Special Ergodic Theory and Statistical Mechanics Seminar *** Please note special date and time | |
| Topic: | TBA |
| Presenter: | Alex Eskin, University of Chicago |
| Date: | Friday, March 26, 2004, Time: 3:00 p.m., Location: Fine Hall 322 |
MARCH 29 - APRIL 2, 2004 |
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| Joint Princeton University/Institute for Advanced Study Number Theory Seminar | |
| Topic: | On Quantum Unique Ergodicity for Locally Symmetric Spaces |
| Presenter: | Lior Silberman, Princeton University |
| Date: | Monday, March 29, 2004, Time: 4:00 p.m., Location: Fine Hall 322 |
| Abstract: | I shall discuss joint work with Akshay Venkatesh on the quantum unique ergodicity conjecture of Rudnick Sarnak on locally symmetric spaces. In particular, in the case of the (co-compact) lattice associated to an order in a division algebra of degree $3$ over $\mathbb{Q}$, we show that any non-degenerate sequence of Hecke Maass eigenforms becomes equidistributed in the measure-theoretic sense. |
| PACM Colloquium | |
| Topic: | Upper bounds on coarsening rates |
| Presenter: | Robert Kohn, Courant Institute of Mathematics, New York University |
| Date: | Monday, March 29, 2004, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: | I will discuss surface-energy-driven coarsening of two-phase microstructures. Such coarsening is observed in many physical systems; two basic examples are motion by surface diffusion and Mullins-Sekerka (evaporation-condensation) dynamics. Experiments and simulations suggest that solutions are in some sense statistically self-similar. There is, however, virtually nothing known with mathematical rigor. I will briefly introduce this topic, then present recent joint work with Felix Otto (Comm. Math. Phys. 2002). Our main accomplishment is an upper bound on the coarsening rate, consistent with the conjectured self-similar behavior. Our work is also interesting for its viewpoint, which is new and potentially applicable to many other problems. I will close with one such application, to epitaxial growth -- joint work with Xiaodong Yan (Comm. Pure Appl. Math. 2003). |
| Algebraic Geometry Seminar *** Please note special time | |
| Topic: | Hecke tangents and Hitchin discriminants |
| Presenter: | Jun-Muk Hwang, KIAS and Harvard University |
| Date: | Tuesday, March 30, 2004, Time: 3:30 p.m., Location: Fine Hall 322 |
| Abstract: | We will discuss joint-work with S. Ramanan on the moduli of stable bundles over a smooth projective curve. The main result is a duality relation between the variety of tangent vectors of Hecke curves and the discriminant hypersurface of the Hitchin map. One of the applications is a simple proof of the non-abelian Torelli theorem. |
| Mathematical Physics Seminar | |
| Topic: | Ferromagnetism in the Hubbard model --- a constructive approach |
| Presenter: | H. Tasaki, Gakushuin University |
| Date: | Tuesday, March 30, 2004, Time: 4:30 p.m., Location: Jadwin A06 |
| Abstract: | It is believed that strong ferromagnetic order in some solids is generated by a subtle interplay between quantum many-body effects and the spin-independent Coulomb interactions between electrons. I will describe our constructive approach to ferromagnetism in the Hubbard model, which is a standard idealized model for strongly interacting electrons in a solid. I present nonsingular models of itinerant electrons with only spin-independent interactions where the low energy behavior is proved to be that of a ``healthy'' ferromagnetic insulator. I will also discuss some open problems and conjectures regarding metallic ferromagnetism. |
| Joint Institute for Advanced Study/Princeton University Complex Geometry Seminar | |
| Topic: | Variations of Hodge Structure for Calabi-Yau complete intersections in toric varieties |
| Presenter: | John Morgan, Columbia University |
| Date: | Wednesday, March 31, 2004, Time: 2:00 p.m., Location: Fine Hall 322 |
| Discrete Mathematics Seminar | |
| Topic: | [ {A,B,C} , {a,b,c}, A, { A-> a|BC|CB, B-> b|AC|CA, C-> c|AB|BA } ] |
| Presenter: | Doron Zeilberger, Rutgers University |
| Date: | Wednesday, March 31, 2004, Time: 3:00 p.m., Location: Fine Hall 224 |
| Abstract: | See http://www.math.princeton.edu/~bsudakov/doron.html |
| Geometry, Representation, and Moduli Seminar | |
| Topic: | TBA |
| Presenter: | C. C. Liu, Harvard University |
| Date: | Wednesday, March 31, 2004, Time: 3:00 p.m., Location: Fine Hall 214 |
| Department Colloquium | |
| Topic: | TBA |
| Presenter: | Maciej Zworski, University of California, Berkeley |
| Date: | Wednesday, March 31, 2004, Time: 4:30 p.m., Location: Fine Hall 314 |
| Ergodic Theory and Statistical Mechanics Seminar | |
| Topic: | Dense random regular graphs: Methods and challenges |
| Presenter: | Benjamin Sudakov, Princeton University |
| Date: | Thursday, April 1, 2004, Time: 2:00 p.m., Location: Fine Hall 322 |
| Abstract: | Properties of random $d$-regular graphs were studied extensively starting with late 70's. But until very recently almost all the results were obtained for graphs whose degree $d$ is relatively small compared to the number of vertices $n$. In this talk we survey various results for dense random regular graphs which were obtained in the last few yeas. We will focus on the new approaches which were used and discuss some interesting questions which are still open. |
| Joint Analysis Seminar | |
| Topic: | Control theory and high energy eigenfunctions |
| Presenter: | Maciej Zworski, University of California, Berkeley |
| Date: | Thursday, April 1, 2004, Time: 3:30 p.m., Location: Fine Hall 214 |
| Topology Seminar | |
| Topic: | TBA |
| Presenter: | Jacob Rasmussen, Princeton University |
| Date: | Thursday, April 1, 2004, Time: 4:30 p.m., Location: Fine Hall 314 |
| Geometric Analysis Seminar *** Please note special time and location | |
| Topic: | Ricci flows on 3-manifolds with positive scalar curvature |
| Presenter: | Zhongmin Qian, Northwestern University |
| Date: | Friday, April 2, 2004, Time: 1:30 p.m., Location: Fine Hall 322 |
| Geometric Analysis Seminar | |
| Topic: | Scattering theory on symmetric spaces for N-body Hamiltonians |
| Presenter: | Andras Vasy, MIT |
| Date: | Friday, April 2, 2004, Time: 3:00 p.m., Location: Fine Hall 314 |
APRIL 5- APRIL 9, 2004 |
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| Joint Princeton University/Institute for Advanced Study Number Theory Seminar | |
| Topic: | Symplectic Kloosterman sums |
| Presenter: | Arpad Toth, Eotvos University, Budapest |
| Date: | Monday, April 5, 2004, Time: 4:00 p.m., Location: Fine Hall 322 |
| Abstract: | Symplectic Kloosterman sums arise in the Petersson formula for Siegel modular forms of higher genus. We present estimates for these sums, and show how these estimates lead to improved bounds on the Fourier coefficients of Siegel modular forms of genus 2. |
| PACM Colloquium | |
| Topic: | Efficient high-order methods for acoustic and electromagnetic scattering simulations |
| Presenter: | Fernando Reitich, University of Minnesota |
| Date: | Monday, April 5, 2004, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: | In this talk we will present a variety of techniques for the solution of electromagnetic and acoustic scattering problems that are aimed at overcoming the limitations of state-of-the-art scattering solvers. We will begin with a brief review of the techniques most commonly used for the numerical simulation of scattering experiments, highlighting their advantages and shortcomings. In addition to providing a context for the presentation, the review will motivate the continued need for algorithms that can tackle these problems efficiently without sacrificing accuracy and error-controllability. In this connection, we shall first discuss some theoretical considerations that lead to a class of efficient, high-order perturbative methods that are particularly well-suited for rough-surface scattering (e.g. ocean surfaces, diffraction gratings, etc). We shall further explain how these algorithms can be used to resolve the scattering off multi-scale surfaces, leading to consideration of high-frequency problems. With regard to the latter, we shall next present the main ideas behind our recent design of a technique for the solution of the integral-equation formulation of the scattering problem in the high-frequency regime. As we will show, our scheme can deliver error-controllable answers without the need to discretize on the scale of the wavelength of radiation, and it therefore holds significant promise for applicability in a variety configurations (e.g. military vehicles illuminated with centimeter, or even millimeter, waves). Finally, as we shall explain, our high-frequency strategy possesses the additional property that it continuously reduces to a full discretization of the integral equations as the frequency is decreased to a moderate regime. In this regard, and if time permits, we will also present an innovative technique for the efficient solution of the (singular) integral-equations pertaining to volumetric scattering up to these moderate frequencies, that can exhibit arbitrarily large, tunable orders of convergence. |
| Algebraic Geometry Seminar | |
| Topic: | Varieties with ample cotangent bundle |
| Presenter: | Olivier Debarre, Universit. Louis Pasteur, Strasbourg |
| Date: | Tuesday, April 6, 2004, Time: 4:30 p.m., Location: Fine Hall 322 |
| Abstract: | Among various hyperbolicity properties for compact complex varieties, ampleness of the cotangent bundle is one of the strongest. Varieties with ample cotangent bundles defined over a number field should provide an interesting testing ground for a conjecture of Lang: they are expected to have only finitely many rational points. Although these varieties are expected to be reasonably abundant, few examples are known. I will discuss various constructions and prove in particular that a general complete intersection of dimension at most n/2 in an abelian variety of dimension n has ample cotangent bundle. I will also discuss the possibility that an analogous result might hold for complete intersections in the projective space. |
| Discrete Mathematics Seminar | |
| Topic: | TBA |
| Presenter: | Michael Krivelevich, Tel Aviv University |
| Date: | Wednesday, April 7, 2004, Time: 3:00 p.m., Location: Fine Hall 224 |
| Joint Analysis Seminar | |
| Topic: | Integrability, geometry, and singularities of the solutions of a dispersive wave equation |
| Presenter: | Adrian Constantin, Brown University and the University of Lund |
| Date: | Thursday, April 8, 2004, Time: 3:30 p.m., Location: Fine Hall 214 |
| Abstract: | A recently derived nonlinear partial differential equation models the unidirectional propagation of waves on shallow water and in elastic rods. The uniquely rich structure of the equation is the object of our presentation. The equation is a completely integrable infinite-dimensional Hamiltonian system. It can also be viewed in terms of the geodesic flow on the diffeomorphism group of the circle. Moreover, it possesses waves of permanent form (traveling solitary waves) and waves that "break," meaning that the solution remains bounded but its slope becomes unbounded in finite time. However, its solitary waves are stable and they interact like solitons. There is an associated isospectral problem that governs the soliton behavior. |
| Ergodic Theory and Statistical Mechanics Seminar - *** Please note special time and location | |
| Topic: | Bounded geodesics and slowly recurrent billiard trajectories |
| Presenter: | Dmitry Kleinbock, Brandeis University |
| Date: | Thursday, April 8, 2004, Time: 4:30 p.m., Location: Fine Hall 601 |
| Abstract: | This is a joint work with Barak Weiss. In the moduli space of quadratic differentials on a Riemann surface we construct points with bounded Teichmuller geodesic trajectories. An application to billiards in rational polygons provides a construction of rational billiard analogue of badly approximable numbers. |
| Topology Seminar | |
| Topic: | TBA |
| Presenter: | Cameron Gordon, University of Texas, Austin |
| Date: | Thursday, April 8, 2004, Time: 4:30 p.m., Location: Fine Hall 314 |
APRIL 12- APRIL 16, 2004 |
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| Joint Princeton University/Institute for Advanced Study Number Theory Seminar | |
| Topic: | TBA |
| Presenter: | Zhengyu Mao, Rutgers University - Newark |
| Date: | Monday, April 12, 2004, Time: 4:00 p.m., Location: Fine Hall 322 |
| PACM Colloquium | |
| Topic: | Inequalities of Quantum Information Theory |
| Presenter: | Nicholas J. Pippenger, Computer Science, Princeton University |
| Date: | Monday, April 12, 2004, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstact: | The recent upsurge of interest in quantum communication and quantum computation has led to a renewed interest in quantum information theory. Specifically, many results concerning quantum communication and quantum computation involve the quantum entropy, a measure of quantum information, introduced by von Neumann in 1927, that generalizes the classical entropy introduced by Shannon in 1948. (The classical entropy is the special case of quantum entropy in which all density matrices are diagonal.) Even for classical information, a complete characterization of the inequalities satisfied by the entropy is available only when the number of variables is at most three, or when the allocation of entropy is symmetric (though some tantalizing results due to Z. Zhang and R. W. Yeung hint at the complexity of the general case. In this talk we shall discuss the extent to which this theory can be extended to the quantum case. |
| Algebraic Geometry Seminar | |
| Topic: | TBA |
| Presenter: | Ravi Vakil, Stanford University |
| Date: | Tuesday, April 13, 2004, Time: 4:30 p.m., Location: Fine Hall 322 |
| Discrete Mathematics Seminar | |
| Topic: | TBA |
| Presenter: | Van Vu , University of California, San Diego |
| Date: | Wednesday, April 14, 2004, Time: 3:00 p.m., Location: Fine Hall 224 |
| Geometry, Representation, and Moduli Seminar | |
| Topic: | TBA |
| Presenter: | Alexander Braverman, Brown University |
| Date: | Wednesday, April 14, 2004, Time: 3:00 p.m., Location: Fine Hall 214 |
| Ergodic Theory and Statistical Mechanics Seminar | |
| Topic: | Modulational stability of cellular flows |
| Presenter: | Alexei Novikov, Penn State University. |
| Date: | Thursday, April 15, 2004, Time: 2:00 p.m., Location: Fine Hall 322 |
| Abstract: | We investigate stability of the initial modulational perturbations of stationary solutions to the two-dimensional Navier-Stokes equations with a time-independent periodic rapidly oscillating forcing. The stationary solutions are cellular flows and they are determined by the stream function $\phi = \sin x_1/\epsilon \sin x_2/\epsilon + \delta\cos x_1/\epsilon \cos x_2/\epsilon$, $0 \leq \delta \leq 1$. The perturbations satisfy the modulation equation. For small Reynolds number we determine the stability for the fully nonlinear modulation equation. For any Reynolds number we determine the stability of the linearized modulation equation. |
| Ergodic Theory and Statistical Mechanics Seminar - *** Please note special time and location | |
| Topic: | Linear and sub-linear behavior of random walks in random environments on a strip |
| Presenter: | Ilya Goldsheid, Queen Mary, University of London |
| Date: | Thursday, April 15, 2004, Time: 4:30 p.m., Location: Fine Hall 601 |
| Abstract: | The remarkable fact that a transitive random walks in random environment does not necessarily grow linearly but may also exhibit sub linear behavior has been known since 1975 (Solomon; Kesten-Kozlov-Spitser). These results were proved for the case of the simplest random walk in dimension one. The attempts to establish similar results for other cases had a limited success. I shall discuss necessary and sufficient conditions leading to a relatively full description of this sort of behavior for a wide range of one- and quasi one-dimensional models. |
| Bill Browder Birthday Topology Seminar Doubleheader - Note special times | |
| Topic: | Representations and K-Theory of the Braid Group |
| Presenter: | Alejandro Adem, University of Wisconsin |
| Date: | Thursday, April 15, 2004, Time: 3:00 p.m., Location: Fine Hall 314 |
| Topic: | Enlargeability and Index Theory |
| Presenter: | Bernhard Hanke, Universitat Muenchen |
| Date: | Thursday, April 15, 2004, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstact: | Let M be a smooth, compact enlargeable spin manifold. Independently of the Baum-Connes conjecture, we prove nonvanishing of a universal index obstruction associated witn M. This implies the result by Gromov and Lawson that M does not admit a metric of positive scalar curvature. As an application of our methods we show that the map --> B\pi_1(M) classifying the universal cover of M sends the fundamental homology class of M to a non trivial class in H_*(B\pi_1(M); Q. This answers a question of D. Burghelea (1983). |
APRIL 19 - APRIL 23, 2004 |
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| Joint Princeton University/Institute for Advanced Study Number Theory Seminar | |
| Topic: | TBA |
| Presenter: | Harald Helfgott, Yale University |
| Date: | Monday, April 19, 2004, Time: 4:00 p.m., Location: Fine Hall 322 |
| Algebraic Geometry Seminar | |
| Topic: | TBA |
| Presenter: | Mikhail Kapranov, Yale University |
| Date: | Tuesday, April 20, 2004, Time: 4:30 p.m., Location: Fine Hall 322 |
APRIL 26 - APRIL 30, 2004 |
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| Joint Princeton University/Institute for Advanced Study Number Theory Seminar | |
| Topic: | TBA |
| Presenter: | Ben Brubaker, Stanford University |
| Date: | Monday, April 26, 2004, Time: 4:00 p.m., Location: Fine Hall 322 |
| PACM Colloquium | |
| Topic: | PlanetLab: Introducing Disruptive Technology into the Internet |
| Presenter: | Larry Peterson, Computer Science, Princeton University |
| Date: | Monday, April 26, 2004, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: | A new class of geographically distributed network services is emerging, and the most effective way to design, evaluate, and deploy these services is by using an overlay-based testbed. Unlike conventional network testbeds, however, we advocate an approach that supports both researchers that want to develop new services, and clients that want to use them. This dual use, in turn, suggests four design principles that are not widely supported in existing testbeds: services should be able to run continuously and access a slice of the overlay's resources, control over resources should be distributed, overlay management services should be unbundled and run in their own slices, and APIs should be designed to promote application development. This talk describes this high-level vision, and reports the status and plan for the realization of the vision in PlanetLab. |
| Algebraic Geometry Seminar | |
| Topic: | TBA |
| Presenter: | Jaroslaw Wisniewski, Purdue University and Warsaw |
| Date: | Tuesday, April 27, 2004, Time: 4:30 p.m., Location: Fine Hall 322 |
MAY 3 - MAY 7, 2004 |
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| Algebraic Geometry Seminar | |
| Topic: | The Enriques conjecture; or, How canonical is the canonical bundle? |
| Presenter: | Joe Harris, Harvard University |
| Date: | Tuesday, May 4, 2004, Time: 4:30 p.m., Location: Fine Hall 322 |
| Abstract: | The question we're dealing with is this: Is there any way of associating to each smooth curve C of genus g ---or at least to each C in an open subset of moduli---a line bundle on C, other than by taking powers of the canonical bundle? (The answer, by the way, is no: the canonical bundle is truly canonical.) This question was posed almost a century ago; a bogus proof was given by Franchetta in the '40s (as a result of which the statement is usually called Franchetta's conjecture, and a correct proof was given in the '80s by Harer and Mestrano, based on a topological argument of Harer's. In fact, the statement is immediately implied by a stronger conjecture made by Enriques decades earlier. Enriques claimed (or suggested; it's not always clear) an analogous statement for the Severi variety, namely that the only ways of choosing a line bundle on a general plane curve C of degree d and genus g are combinations of the canonical bundle K_C and the hyperplane bundle O_C(1). In this talk I'll discuss a little of the history of the Enriques conjecture, and variants of it; but the main purpose of the talk will be to give a proof of the conjecture that Deepee Khosla and I found recently. |
| Geometry, Representation, and Moduli Seminar | |
| Topic: | TBA |
| Presenter: | Alexander Braverman, Brown University |
| Date: | Wednesday, May 5, 2004, Time: 3:00 p.m., Location: Fine Hall 214 |
MAY 10 - MAY 14, 2004 |
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| Joint Princeton University/Institute for Advanced Study Number Theory Seminar | |
| Topic: | TBA |
| Presenter: | David J. Burns, King's College, London |
| Date: | Monday, May 10, 2004, Time: 4:00 p.m., Location: Fine Hall 322 |
MAY 17 - MAY 21, 2004 |
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| Geometry, Representation, and Moduli Seminar | |
| Topic: | TBA |
| Presenter: | R. Thomas, Imperial College |
| Date: | Wednesday, May 19, 2004, Time: 3:00 p.m., Location: Fine Hall 214 |