NOVEMBER 17 - 19, 2004 |
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| Statistical Mechanics Seminar | |
| Topic: | Theory of the Bose gas, Part III |
| Presenter: | Eliot Lieb, Princeton University |
| Date: | Wednesday, November 17, 2004, Time: 2:00 p.m., Location: Jadwin 343 |
| Abstract: | Eliot Lieb will give part 3 of the series of lectures on the theory of the Bose gas. The basic theory of the ground state energy of a dilute Bose gas will be derived. (The first lecture on 9/15 was an overview and the second on 9/29 was on the Bogoliubov theory.) |
| Discrete Mathematics Seminar | |
| Topic: | Generalization of Dirac's Theorem |
| Presenter: | Endre Szemeredi, Rutgers University |
| Date: | Wednesday, November 17, 2004, Time: 2:30 p.m., Location: Fine Hall 224 |
| Abstract: | Click here |
| Geometry, Representation Theory, and Moduli Seminar | |
| Topic: | Mirror symmetry for weighted projective planes and their noncommutative deformations |
| Presenter: | Dmitri Orlov, Institute for Advanced Study |
| Date: | Wednesday, November 17, 2004, Time: 3:00 p.m., Location: Fine Hall 214 |
| Abstract: | The derived categories of coherent sheaves of weighted projective spaces and their noncommutative deformations will be described. We explain how the homological mirror symmetry conjecture looks for the weighted projective planes and show that it holds in this case. Moreover, we also show that this mirror correspondence between derived categories can be extended to toric noncommutative deformations of a weighted projective planes where B-branes are concerned, and their mirror counterparts, non-exact deformations of the symplectic structure of the Landau-Ginzburg where A-branes are concerned. |
| Department Colloquium | |
| Topic: | Flows on homogeneous spaces and number theory |
| Presenter: | Elon Lindenstrauss, Princeton University |
| Date: | Wednesday, November 17, 2004, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: | The groundbreaking work of Ratner and Margulis, and the many deep and diverse implications of Ratner's theorem convincingly demonstrate the importance of the study of invariant measures for dynamical systems of algebraic origin, particularly flows on homogeneous spaces. Recently, progress has been made on studying actions of diagonalizable actions on homogeneous and these too have found various applications. I will survey some of these recent results. Part of the work I will be presenting is joint with M. Einsiedler and A. Katok. |
| Joint Analysis Seminar | |
| Topic: | A deterministic control based approach to motion by curvature. |
| Presenter: | Sylvia Serfaty, Courant Institute |
| Date: | Thursday, November 18, 2004, Time: 3:30 p.m., Location: Fine Hall 214 |
| Abstract: | In a joint work with Bob Kohn, we give a new control-type interpretation on the level-set approach to motion by curvature and related interface motion laws. More precisely, we give a family of discrete-time, two-person games whose value functions converge in the continuous-time limit to the solution of the motion-by-curvature PDE. The value function of a deterministic control problem is normally a first-order Hamilton-Jacobi equation, while the level-set formulation of motion by curvature is a second-order parabolic equation. |
| Geometric Analysis Seminar | |
| Topic: | On the Genus-One Gromov-Witten Invariants of Complete Intersection Threefolds |
| Presenter: | Aleksey Zinger, Stanford University |
| Date: | Friday, November 19, 2004, Time: 4:00 p.m., Location: Fine Hall 314 |
| Abstract: | I will describe a formula relating the genus-one Gromov-Witten invariants of a projective complete intersection threefold to the GW-invariants of the ambient projective space. Along with a separate desingularization result, this formula allows one to compute the genus-one GW-invariants of such threefolds. It might be possible to use this formula to verify the genus-one mirror symmetry prediction for curves in Calabi-Yau threefolds |
NOVEMBER 22 - 24, 2004 |
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| Analysis Seminar | |
| Topic: | On the duality of metric entropy |
| Presenter: | Shiri Artstein, Princeton University |
| Date: | Monday, November 22, 2004, Time: 3:00 p.m., Location: Fine Hall 314 |
| Abstract: | A question which goes back to Pietsch in the 70s and is called "the duality of entropy numbers conjecture" asks whether the classical fact that a linear operator between two Banach spaces is compact if and only if its dual is compact is true also in a stronger, quantitative, manner. We will state this conjecture, and prove it in the special and central case when either the domain or the range of the operator is a Hilbert space. In the language of covering numbers (which are defined by N(K, T) = min {N s.t. K can be covered by N translates of T }) we will show that there exist two universal constants c and C such that for any convex body in any dimension n, (1/C) \log N(D,(1/c)K') < \log N(K,D) < C \log N(D,cK'), where D is the euclidean unit ball in dimension n and K' is the polar of K (i.e., K' = {x : sup_{y in K} <x, y> =< 1 }). If time permits we will also describe the generalization of this theorem to the case where either the domain or the range is K-convex (which includes all L_p spaces, and also all uniformly convex or uniformly smooth spaces). The general case remains an open problem. This is joint work with V. Milman, S. Szarek and N. Tomczak-Jaegermann. |
| PACM Seminar | |
| Topic: | Qualitative/Quantitative Analysis of a Class of Biological Networks |
| Presenter: | Eduardo Sontag, Department of Math and BioMaPS Institute for Quantitative Biology, Rutgers University |
| Date: | Monday, November 22, 2004, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: | The analysis of signaling networks constitutes one of the central questions in systems biology: there is an pressing need for powerful mathematical tools to help understand, quantify, and conceptualize their information processing and dynamic properties. Approaches based upon detailed modeling and simulation are hampered by the fact that is virtually impossible to experimentally validate the form of the nonlinearities used in reaction terms, or, even when such forms are known, to accurately estimate coefficients (parameters). In this presentation, we show how some signaling systems may be profitably studied by first decomposing them into several subsystems, each of which is endowed with certain "qualitative" mathematical properties. These properties, in conjunction with a relatively small amount of "quantitative" data, allow the behavior of the entire, reconstituted system, to be deduced from the behavior of its parts. This novel approach emerged originally from our study of possible multi-stability or oscillations in feedback loops in cell signal transduction modeling, but turns out to be of more general applicability. (Most of the work reported in this talk was carried out in collaboration with D. Angeli, and parts of it with J. Ferrell, G. Enciso, and P. de Leenheer.) |
| Joint Princeton University and Institute for Advanced Study Number Theory Seminar | |
| Topic: | New exponential sum estimates |
| Presenter: | Jean Bourgain, Institute for Advanced Study |
| Date: | Monday, November 22, 2004, Time: 4:30 p.m., Location: Fine Hall 322 |
| Algebraic Geometry Seminar | |
| Topic: | Triangulated categories of singularities and D-branes in Landau-Ginzburg models |
| Presenter: | Dmitri Orlov, Institute for Advanced Study |
| Date: | Tuesday, November 23, 2004, Time: 4:30 p.m., Location: Fine Hall 322 |
| Abstract: | The purpose of my talk is to introduce triangulated categories related to singularities of algebraic varieties and to establish a connection of these categories with categories of D-branes in Landau-Ginzburg models. |
| Statistical Mechanics Seminar | |
| Topic: | Linear response far from equilibrium |
| Presenter: | David Ruelle, IHES |
| Date: | Wednesday, November 24, 2004, Time: 2:00 p.m., Location: Jadwin 343 |
| Abstract: | The linear response in nonequilibrium statistical mechanics can be described mathematically as the differentiation of an Sinai-Ruelle-Bowen (SRB) measure with respect to a parameter. For certain types of dynamics (uniformly hyperbolic) one gets a very satisfactory description, with a modified fluctuation-disssipation theorem, and analyticity properties correponding to "causality". For other systems (Henon-like), "causality" seems to break down, and things are less simple. What does this mean? |
| Discrete Mathematics Seminar | |
| Topic: | Erdos-Hajnal sets and semi-group decompositions |
| Presenter: | Joshua Cooper, New York University |
| Date: | Wednesday, November 24, 2004, Time: 2:30 p.m., Location: Fine Hall 224 |
| Abstract: | Click here |
NOVEMBER 29 - DECEMBER 3, 2004 |
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| PACM Seminar | |
| Topic: | Frames and the Fundamental Inequality |
| Presenter: | Jelena Kovacevic, Center for BioImage Informatics, Carnegie Mellon University |
| Date: | Monday, November 29, 2004, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: | In recent years, we have seen an explosion of work on frames, in particular finite frames. We find finite tight frames when the lengths of the frame elements are predetermined. In particular, we derive a ``fundamental inequality" which completely characterizes those sequences which arise as the lengths of a tight frame's elements. Furthermore, using concepts from classical physics, we show that this characterization has an intuitive physical interpretation. At the end of the talk, we also examine some recent applications of frames. |
| Joint Princeton University and Institute for Advanced Study Number Theory Seminar | |
| Topic: | Generic transfer to non-self dual automorphic representations of GL(N) |
| Presenter: | Mahdi Asgari, Institute for Advanced Study |
| Date: | Monday, November 29, 2004, Time: 4:30 p.m., Location: Fine Hall 322 |
| Algebraic Geometry Seminar | |
| Topic: | A higher dimensional analog of the moduli space of pointed stable rational curves |
| Presenter: | Angela Gibney, University of Pennsylvania |
| Date: | Tuesday, November 30, 2004, Time: 4:30 p.m., Location: Fine Hall 322 |
| Abstract: | I'll introduce a smooth projective variety T_{d,n} whose closed points correspond to stable n-pointed rooted trees of projective spaces. When d=1 this variety is isomorphic to $\overline{M}_{0,n+1}$, the fine moduli space of stable n+1 pointed cures of genus zero. I'll describe some facts about the space T_{d,n} as well as some open problems. This talk is about joint work between myself, L. Chen and D. Krashen. |
| Discrete Mathematics Seminar | |
| Topic: | Counting homomorphisms from Q d to Z |
| Presenter: | David Galvin, Institute for Advanced Study |
| Date: | Wednesday, December 1, 2004, Time: 2:30 p.m., Location: Fine Hall 224 |
| Abstract: | Click here |
| Department Colloquium | |
| Topic: | Quantum and Classical Network Model |
| Presenter: | John Cardy, Oxford University and the Institute for Advanced Study |
| Date: | Wednesday, December 1, 2004, Time: 4:30 p.m., Location: Fine Hall 314 |
| Joint Analysis Seminar | |
| Topic: | L^1 estimates for vector fields |
| Presenter: | Jean van Schaftingen, University of Louvain |
| Date: | Thursday, December 2, 2004, Time: 3:30 p.m., Location: Fine Hall 214 |
| Topology Seminar | |
| Topic: | Toroidal orbifolds and group cohomology |
| Presenter: | Alejandro Adem, University of Wisconsin and Princeton University |
| Date: | Thursday, December 2, 2004, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: | Given an orbifold arising from a finite group action on an n-torus, we will describe a method for computing the cohomology of its classifying space. In particular we will obtain complete calculations for certain six-dimensional examples, which have been of interest in math/physics. More generally we will show that this relates to a natural conjecture in group cohomology. This is joint work with J.Pan. |
| Geometric Analysis Seminar | |
| Topic: | Analytic torsion on Calabi-Yau three-folds |
| Presenter: | Hao Fang, Institute for Advanced Study |
| Date: | Friday, December 3, 2004, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: | We study the analytic torsion on Calabi-Yau manifolds and define a holomorphic invariant modifying the so called BCOV torsion. We study the asymptotic behavior of the new invariant near a singular Calabi-Yau variety; especially for Calabi-Yau with only ODP singularity. The result is a current curvature formula for Calabi-Yau three-folds. As an application, we verify a conjecture of Beshadsky-Ceccotti-Ooguri-Vafa. In many examples, we link our invariant to automorphic forms. This is a recent joint work with Z. Lu and K.-I. Yoshikawa. |
DECEMBER 6 - 10, 2004 |
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| PACM Seminar | |
| Topic: | Reduced Scaling Methods for Quantum Electronic Structure |
| Presenter: | Emily Carter, PACM and Mechanical & Aerospace Engineering, Princeton University |
| Date: | Monday, December 6, 2004, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: | The problem of solving the Schroedinger equation in quantum mechanics, in order to describe the behavior of N electrons, is in principle an N! hard problem in an infinite basis. This is due to the need to describe the correlated motion of electrons. Some typical approaches to solving this 3N-dimensional PDE will be introduced, including mean-field and many-body methods. An analysis of their scaling properties will be given. My research group's particular strategies for reducing the prohibitive scaling of these methods while retaining accuracy of the solution will be presented. These schemes are based on simple physical and mathematical principles, for both molecular quantum chemistry and for condensed matter electronic structure. We will end with an outlook of the applied mathematical research challenges that remain for describing large numbers (e.g., thousands) of atoms with quantum mechanics. When these challenges are overcome, we will be able to predict the behavior of complicated molecules and materials with unprecedented fidelity. |
| Discrete Mathematics Seminar | |
| Topic: | Parameters of codes on bipartite graphs |
| Presenter: | Alexander Barg, University of Maryland |
| Date: | Wednesday, December 8, 2004, Time: 2:30 p.m., Location: Fine Hall 224 |
| Abstract: | Click here |
| Department Colloquium | |
| Topic: | TBA |
| Presenter: | Shmuel Weinberger, University of Chicago and New York University |
| Date: | Wednesday, December 8, 2004, Time: 4:30 p.m., Location: Fine Hall 314 |
| Joint Analysis Seminar | |
| Topic: | Prescribing symmetric functions of the eigenvalues of the Ricci tensor |
| Presenter: | Matt Gursky, University of Notre Dame |
| Date: | Thursday, December 9, 2004, Time: 3:30 p.m., Location: Fine Hall 214 |
| Abstract: | In joint work with J. Viaclovsky, we studied the problem of prescribing symmetric functions of the eigenvalues of the Schouten tensor for a conformal metric on a compact manifold (often referred to as the "Sigma-k Yamabe problem"). This is equivalent to solving a fully nonlinear elliptic equation of second order. Assuming the function satisfies certain structural conditions, and the underlying manifold satisfies a natural 'admissibility' condition, we prove a priori estimates for solutions. The proof involves a blow-up analysis and classification of certain global singular solutions. |
| Topology Seminar | |
| Topic: | Symplectic Floer theories, Hilbert Schemes, and the Jones polynomial |
| Presenter: | Ciprian Manolescu, Princeton University |
| Date: | Thursday, December 9, 2004, Time: 4:30 p.m., Location: Fine Hall 314 |
| Joint Columbia University-Courant Institute-Princeton University Differential Geometry Seminar *** Please note special time |
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| Topic: | Ricci curvature for metric-measure spaces |
| Presenter: | John Lott, University of Michigan |
| Date: | Friday, December 10, 2004, Time: 2:30 p.m., Location: Fine Hall 314 |
| Joint Columbia University-Courant Institute-Princeton University Differential Geometry Seminar *** Please note special time |
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| Topic: | The Calabi-Yau conjectures for embedded surfaces |
| Presenter: | William Minicozzi, Johns Hopkins University |
| Date: | Friday, December 10, 2004, Time: 4:00 p.m., Location: Fine Hall 314 |