DECEMBER 1 - DECEMBER 3, 2004 |
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| Statistical Mechanics Seminar | |
| Topic: | Bose-Einstein condensation of dilute Bose gases in traps |
| Presenter: | Robert Seiringer, Princeton University |
| Date: | Wednesday, December 1, 2004, Time: 2:00 p.m., Location: Jadwin 343 |
| Abstract: | This talk continues the discussion of the Bose gas. We consider low-density gases in traps, as considered in recent experiments. We introduce the Gross-Pitaevskii equation and show that it is asymptotically correct as a description of the ground state of a dilute gas. We will also prove the occurrence of Bose-Einstein condensation. |
| 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 |
| Abstract: | In network models of transport, a particle moves along the edges and through the vertices of some fixed graph. In general, the classical and quantum versions of this problem are very different, the first being formulated in terms of transition probabilities, the second in terms of quantum-mechanical amplitudes. However, in some cases when the latter are random variables drawn from an ensemble, averaging the transport properties over this ensemble leads to an equivalent description in terms of a classical problem. In this talk I will illustrate this with some simple examples, then sketch the elements of the general proof, which uses supersymmetry. |
| Ergodic Theory and Statistical Mechanics Seminar | |
| Topic: | Decay of correlations for the Rauzy-Veech-Zorich map and the central limit theorem for the Teichmueller flow |
| Presenter: | Alexander Bufetov, Princeton University |
| Date: | Thursday, December 2, 2004, Time: 2:00 p.m., Location: Fine Hall 322 |
| Abstract: | Take a unit interval, partition it into several subintervals and rearrange these subintervals according to a given permutation. The resulting map is called an interval exchange transformation. For example, an interval exchange of two intervals is a circle rotation. Take an interval exchange and consider its induced map on a subinterval: the resulting map is again an interval exchange. By choosing the subinterval appropriately, one obtains an exchange of the same number of intervals, and, therefore, a map of the space of interval exchange transformations into itself, called the Rauzy-Veech Zorich induction map (in the case of circle rotations, this construction gives the Gauss map). The induction map preserves an absolutely continuous invariant probability measure (constructed by Veech and Zorich), with respect to which the map is ergodic and its square is exact. The main result of the talk is a stretched exponential bound on the decay of correlations for the Rauzy-Veech Zorich induction map (in the case of the Gauss map, a theorem of Kuzmin). The proof uses the method of Markov approximations of Sinai, Bunimovich-Sinai. A corollary is the Central Limit Theorem for the Teichmueller flow on the moduli space of abelian differentials on a compact Riemann surface. Since the Teichmueller flow can be represented as a special flow over the natural extension of the induction map (in the case of circle rotations, this representation corresponds to coding geodesics on the modular surface by continued fractions), by a Theorem of Melbourne and Torok, the decay of correlations for the induction map implies the Central Limit Theorem for the Teichmueller flow. |
| 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. |
| Group Action and Automorphic Seminar ***NEW *** | |
| Topic: | Actions on Griffiths domains and Kahler groups |
| Presenter: | Bruno Klingler, University of Chicago |
| Date: | Friday, December 3, 2004, Time: 12:30 p.m., Location: PL |
| Abstract: | An important question in algebraic geometry is to understand the structure of fundamental groups of smooth algebraic varieties. I will report on some recent work about the following conjecture by Carlson and Toledo : let M be a smooth projective variety with fundamental group L. Assume L admits an unbounded complex linear representation. Then H^(2}(L, C) is non-zero. |
| SPECIAL Topology Seminar | |
| Topic: | Introduction to Orbifold Cohomology I & II |
| Presenter: | Y. Ruan, University of Wisconsin |
| Date: | Friday, December 3, 2004, Time: 1:30 p.m., Location: Fine Hall 1001 |
| 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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| SPECIAL Topology Seminar | |
| Topic: | Introduction to Orbifold Cohomology I & II |
| Presenter: | Y. Ruan, University of Wisconsin |
| Date: | Monday, December 6, 2004, Time: 1:30 p.m., Location: Fine Hall 1001 |
| SPECIAL Topology Seminar | |
| Topic: | Fat graphs and the cohomology of the bordered mapping class group |
| Presenter: | Veronique Godin, Institute for Advanced Study |
| Date: | Monday, December 6, 2004, Time: 3:00 p.m., Location: Fine Hall 801 |
| 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. |
| Joint Princeton University and Institute for Advanced Study Number Theory Seminar | |
| Topic: | Fixed point formulas and modular forms |
| Presenter: | Georgios Pappas, Institute for Advanced Study |
| Date: | Monday, December 6, 2004, Time: 4:30 p.m., Location: Fine Hall 322 |
| Operations Research and Financial Engineering Seminar - Special Colloquium | |
| Topic: | Overview of the Multi-Armed Bandit Literature with an Emphasis on Risk Aversion |
| Presenter: | Eric Denardo, Yale University and Kenan Trust Visiting Professor for Distinguished Teaching, Princeton University |
| Date: | Tuesday, December 7, 2004, Time: 4:30 p.m., Location: Friend Center, Bowl 004 |
| Abstract: | An introduction to the multi-armed bandit. This talk stresses intuition, includes no proofs, and discusses joint work with Rothblum, Park and Van der Heyden on the case of a risk-averse exponential utility function. |
| 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: | Universal Acyclic groups and the Morse landscape of certain distortion functionals |
| Presenter: | Shmuel Weinberger, University of Chicago |
| Date: | Wednesday, December 8, 2004, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: | In this talk I will try to explain two tools that have been useful in the past few years: the first is the applications of finitely presented acyclic groups that contain all other finitely presented groups and the second is the use of ideas of logic to produce many critical points for certain functionals (pioneered by Nabutovsky). Ideally, I will get to apply both together the study of nonsimply connected hypersurfaces in Euclidean space. |
| 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 |
| Abstract: | We will explain how the Jones polynomial of links appears in symplectic geometry. Seidel and Smith have used Floer homology for two Lagrangians in an affine variety Y to define an invariant of links. Their variety can be identified with an open subset in the Hilbert scheme of points on a Milnor fiber. As a consequence, we describe a set of generators for the Seidel-Smith chain complex which can also be used to compute the Jones polynomial, or as a set of generators for the Heegaard Floer chain complex of the double branched cover. |
| Special Seminar | |
| Topic: | Prime numbers, Riemann, and Langlands |
| Presenter: | Stephen Gelbart, Weizmann Institute and Institute for Advanced Study |
| Date: | Friday, December 10, 2004, Time: 2:30 p.m., Location: Fine Hall 110 |
| Abstract: | We start with some elementary properties of prime numbers, and why they should satisfy the Prime Number Theorem. Next comes the pathbreaking work of Riemann, whose fundamental theory for the zeta-function essentially proves the Prime Number Theory, but leaves open the "Riemann Hypothesis". Finally, we summarize the amazing conjectures of Langlands, stating that all the L-functions of Number Theory are special cases of generalizations of Riemann's zeta-function. |
| 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 |
DECEMBER 13 - 17, 2004 |
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| Joint Analysis Seminar | |
| Topic: | TBA |
| Presenter: | Andrea Malchiodi, SISSA, Italy |
| Date: | Monday, December 13, 2004, Time: 3:00 p.m., Location: Fine Hall 314 |