NOVEMBER 10 - 12, 2004 |
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| Statistical Mechanics Seminar | |
| Topic: | Bosons in disc-shaped traps |
| Presenter: | Jakob Yngvason, University of Vienna |
| Date: | Wednesday, November 10, 2004, Time: 2:00 p.m., Location: Jadwin 343 |
| Abstract: | Recently it has become possible to produce dilute Bose gases in traps that confine the particle motion strongly in one or two directions so that the system becomes effectively lower dimensional. A rigorous derivation of the low-dimensional behavior from the many-body Hamiltonian of a three-dimensional gas is not a simple problem, however, because the ground state wave function can generally not be approximately factorized in the longitudinal and transverse variables. In the lecture the dimensional reduction from 3D to 2D in thin, disk-shaped traps will be discussed. |
| Discrete Mathematics Seminar | |
| Topic: | Analysis of Boolean functions and (a small sample of) its applications |
| Presenter: | Muli Safra, Tel Aviv University and IAS |
| Date: | Wednesday, November 10, 2004, Time: 2:30 p.m., Location: Fine Hall 224 |
| Abstract: | Click here |
| Geometry, Representation Theory, and Moduli Seminar | |
| Topic: | Amoebas and algebraic dynamic |
| Presenter: | Manfred Einsiedler, Princeton University |
| Date: | Wednesday, November 10, 2004, Time: 3:00 p.m., Location: Fine Hall 214 |
| Abstract: | I will describe how amoebas help to describe the dynamical properties of $\mathbb Z^d$-actions by automorphisms of compact abelian groups, and give concrete examples for that connection. One property, that is best characterized by the amoeba, is expansiveness of subactions. A $\mathbb Z^k$-subaction is expansive if there exists an $\epsilon>0$ such that there are not two points $x\neq y$ that stay $\epsilon$-close forever (for the $\mathbb Z^k$-action). |
| Department Colloquium ***CANCELLED *** | |
| Topic: | The Sharp Form of the Strong Szego Theorem |
| Presenter: | Barry Simon, Caltech |
| Date: | Wednesday, November 10, 2004, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: | This talk will discuss a proof of the Strong Szego theorem on the second term in the asymptotics of Toeplitz determinants. After a brief discussion of the history, I'll discuss the elementary argument that reduces the sharp (optimal) result to the case of analytic symbols. I'll then present a new proof of the theorem in the analytic case. I'll present the necessary background from the theory of orthogonal polynomials on the unit circle along the way. |
| Ergodic Theory and Statistical Mechanics Seminar | |
| Topic: | Random matrices, statistical mechanics and hyperbolic symmetry breaking |
| Presenter: | Thomas Spencer, Institute for Advanced Study |
| Date: | Thursday, November 11, 2004, Time: 2:00 p.m., Location: Fine Hall 322 |
| Abstract: | We explain how fluctuations of a lattice field theory with hyperbolic symmetry SU(1,1) arise naturally from the study of certain random band matrix ensembles. These ensembles are related to GUE but incorporate an additional spatial structure. If the lattice dimension is 3 or more, we prove that this symmetry is broken so that moments of the field are bounded in the infinite volume limit. Implications for the band random matrix ensembles are discussed. The key ingredients of our proof are the use of horospherical coordinates and Brascamp-Lieb inequalities. This is joint work with Martin Zirnbauer. |
| Joint Analysis Seminar | |
| Topic: | Asymptotically simple solutions of the vacuum Einstein equations in even dimensions |
| Presenter: | Michael Anderson, SUNY at Stonybrook |
| Date: | Thursday, November 11, 2004, Time: 3:30 p.m., Location: Fine Hall 214 |
| Abstract: | We will discuss a new construction of space-times in the title with $\Lambda > 0$ or $\Lambda = 0$ based on solving the Cauchy problem for a conformally invariant system of equations formed from the Fefferman-Graham (ambient obstruction) tensor. |
| Topology Seminar | |
| Topic: | Shrinkwrapping and the Taming of Hyperbolic 3-Manifolds |
| Presenter: | David Gabai , Princeton University |
| Date: | Thursday, November 11, 2004, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: | We show that if N is a complete hyperbolic 3-manifold with finitely generated fundamental group, then N is the interior of a compact 3-manifold; thereby obtaining a positive proof of the "Marden Conjecture" also known as the "Tameness Conjecture" (Also proven by Ian Agol). A key ingredient is Shrinkwrapping which is a method for producing surfaces of intrinsic curvature ¾-1. We will discuss some of its many applications to hyperbolic geometry and 3-manifold topology. (This is joint work with Danny Calegari). |
| Joint Columbia University-Courant Institute-Princeton University Differential Geometry Seminar | |
| Topic: | Optimal Metrics, Curvature Functionals, and the Differential Topology of 4-Manifolds |
| Presenter: | Claude LeBrun, Columbia University |
| Date: | Friday, November 12, 2004, Time: 2:00 p.m., Location: Room 101, Warren Weaver Hall, Courant Institute |
| Joint Columbia University-Courant Institute-Princeton University Differential Geometry Seminar | |
| Topic: | Volume Growth and Moduli Spaces of Critical Riemannian Metrics in Dimension Four |
| Presenter: | Jeff Viaclovsky, MIT |
| Date: | Friday, November 12, 2004, Time: 3:30 p.m., Location: Room 101, Warren Weaver Hall, Courant Institute |
NOVEMBER 15 - 19, 2004 |
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| Analysis Seminar | |
| Topic: | A singular energy minimizing free boundary |
| Presenter: | Daniela De Silva, MIT |
| Date: | Monday, November 15, 2004, Time: 3:00 p.m., Location: Fine Hall 314 |
| Abstract: | In this talk, we will exhibit the first example of a singular energy minimizing free boundary. This example occurs is dimension 7, which is conjectured to be the optimal dimension for free boundary regularity. This is analogous to the 8-dimensional Simons cone, in the theory of minimal surfaces. We will highlight the similarities between the two theories, explaining how the proof of the minimality of the Simons cone, was the inspiration for our proof. This is a joint work with David Jerison. |
| Special Topology Seminar | |
| Topic: | Homology operations on free loop spaces and other mapping spaces |
| Presenter: | Craig Westerland, Institute for Advanced Study |
| Date: | Monday, November 15, 2004, Time: 3:00 p.m., Location: Fine Hall 801 |
| PACM Seminar | |
| Topic: | Astrophysical Gas Dynamics |
| Presenter: | Jim Stone, Department of Astrophysical Sciences, Princeton University |
| Date: | Monday, November 15, 2004, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: | Most of the visible matter in the Universe is a plasma, that is a dilute gas of electrons, ions, and neutral particles. In many cases the dynamics of this plasma is described to a good approximation by the equations of compressible hydrodynamics, magneto-hydrodynamics (in the case that magnetic fields are present), or radiation MHD (in the case that photons provide significant energy or momentum transport). Studying multidimensional, time-dependent and/or highly nonlinear processes in astrophysical plasmas usually requires numerical methods, however developing accurate and robust methods for compressible MHD and/or radiation MHD is still an active area of research in applied mathematics. I will describe some problems in astrophysics which motivate the development of such methods, describe recent advance in numerical algorithms for MHD and their implementation on parallel processors, and describe some of what we have learned from application of the methods. |
| Joint Princeton University and Institute for Advanced Study Number Theory Seminar | |
| Topic: | Filtered (phi,N)-modules and p-adic differential equations |
| Presenter: | Laurent Berger, IHES |
| Date: | Monday, November 15, 2004, Time: 4:30 p.m., Location: Fine Hall 322 |
| Abstract: | In this talk, I will give applications of Kedlaya's recent results on p-adic differential equations. In particular, I will give a new proof of Colmez-Fontaine's theorem which describes semistable p-adic representations. |
| Algebraic Geometry Seminar | |
| Topic: | Doing the twist with stable varieties |
| Presenter: | Dan Abramovich, Brown University |
| Date: | Tuesday, November 16, 2004, Time: 4:30 p.m., Location: Fine Hall 322 |
| Discrete Mathematics Seminar | |
| Topic: | TBA |
| Presenter: | Endre Szemeredi, Rutgers University |
| Date: | Wednesday, November 17, 2004, Time: 2:30 p.m., Location: Fine Hall 224 |
| 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: | TBA |
| Presenter: | Elon Lindenstrauss, Princeton University |
| Date: | Wednesday, November 17, 2004, Time: 4:30 p.m., Location: Fine Hall 314 |
| 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 |
| 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.) |
| 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, NYU |
| 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, IAS |
| 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, IAS |
| 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 |
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 NYU |
| Date: | Wednesday, December 8, 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 |