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DECEMBER 2006 |
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| Sato-Tate Seminar |
| Topic: |
Arithmetic geometry of the Dwork family, Part II |
| Presenter: |
Nicholas Katz, Princeton University |
| Date: |
Wednesday, December 6, 2006, Time: 1:30 p.m., Location: Fine 314 |
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| Discrete Mathematics Seminar |
| Topic: |
See abstract |
| Presenter: |
Blair D. Sullivan, Princeton University |
| Date: |
Wednesday, December 6, 2006, Time: 2:15 p.m., Location: Fine 224 |
| Abstract: |
See http://www.math.princeton.edu/~bsudakov/blair2006-fall.pdf |
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| Geometry, Representation Theory, and Moduli Seminar |
| Topic: |
A quantum cohomology theory of singularity |
| Presenter: |
Yongbin Ruan, University of Michigan |
| Date: |
Wednesday, December 6, 2006, Time: 3:00 p.m., Location: Fine 214 |
| Abstract: |
By solving the moduli problem of Witten equation (topic of another talk in IAS), we construct a quantum cohomology theory of singularity. This theory is computationally friendly and is conjectured to have many beautiful properties. We will first present a solution to Witten's conjectures in ADE-case. Then, we will discuss mirror symmetry and its role as a phase of Calabi-Yau geometry. |
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| Department Colloquium |
| Topic: |
Blow ups of complex solutions of 3D-Navier-Stokes system and Renormalization Group Method. |
| Presenter: |
Yakov Sinai, Princeton University |
| Date: |
Wednesday, December 6, 2006, Time: 4:30 p.m., Location: Fine 314 |
| Abstract: |
In this talk I shall explain the following result of Dong Li and mine:there exists an open set in the space of 10-parameter families of initial conditions such that for each family from this set there are values of parameters such that the corresponding solution develops blow up in finite time. |
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| Ergodic Theory and Statistical Mechanics Seminar |
| Topic: |
Concentration Inequalities for Dependent Random Variables via the Martingale Method |
| Presenter: |
Leonid Kontorovich, School of Computer Science, Carniegie Mellon |
| Date: |
Thursday, December 7, 2006, Time: 2:00 p.m., Location: Fine 401 |
| Abstract: |
We use the martingale method to establish concentration inequalities for a class of dependent random sequences on a countable state space, with the constants in the inequalities expressed in terms of certain mixing coefficients. Along the way, we obtain bounds on certain martingale differences associated with the random sequences, which may be of independent interest. As an application of our result, we also derive a concentration inequality for inhomogeneous Markov chains, and establish an extremal property associated with their martingale difference bounds. This work complements certain concentration inequalities obtained by Marton and Samson, while also providing a different proof of some known results. Paper written with Kavita Ramanan. http://arxiv.org/abs/math.PR/0609835 |
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| Institute for Advanced Study and Princeton University Number Theory Seminar |
| Topic: |
Periods and relative trace formulas for GL(2) in the local setting |
| Presenter: |
Brooke Feigon, IAS |
| Date: |
Thursday, December 7, 2006, Time: 4:30 p.m., Location: Fine Hall 214 |
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| Topology Seminar |
| Topic: |
On the contact class in Heegaard Floer homology |
| Presenter: |
William H. Kazez, University of Georgia |
| Date: |
Thursday, December 7, 2006, Time: 4:30 p.m., Location: Fine 314 |
| Abstract: |
In joint work with Ko Honda and Gordana Matic, we present an alternate description of the Ozsv\'ath-Szab\'o contact class in Heegaard Floer homology. Using this description, we prove that if a contact structure $(M,\xi)$ has an adapted open book decomposition whose page $S$ is a once-punctured torus, then the monodromy is right-veering if and only if the contact structure is tight. |
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| Differential Geometry and Geometric Analysis Seminar |
| Topic: |
BiLipschitz embedding in Banach spaces |
| Presenter: |
Bruce Kleiner, Yale University |
| Date: |
Friday, December 8, 2006, Time: 3:00 p.m., Location: Fine 314 |
| Abstract |
Motivated by a conjecture from computer science, I will discuss biLipschitz embeddings X ---> V where X is a metric space and V is a Banach space. The focus will be on the case when X is a metric measure space satisfying a Poincare inequality. Of particular interest is the case when the target Banach space is L^1, in which case there is a new link between embedding questions and the structure of sets of finite perimeter in X. By exploiting recent work on geometric measure theory in the Heisenberg group, we show that the Heisenberg group cannot be biLipschitz embedded in L^1, confirming a conjecture of Assaf Naor. This is joint work with Jeff Cheeger. |
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| Analysis Seminar |
| Topic: |
Pseudo-relativistic nonlinear Schrodinger equations |
| Presenter: |
Enno Lenzman, MIT |
| Date: |
Monday, December 11, 2006, Time: 4:00 p.m., Location: Fine 110 |
| Abstract: |
This talk deals with a novel class of dispersive PDEs called pseudo-relativisitic nonlinear Schrodinger equations. These equations have recently found a significant application as effective descriptions for the dynamical evolution of self-gravitating, relativistic matter. Based on this physical motivation, I will present results that aim at understanding the qualitative behavior of solutions for these model equations. Here great emphasis is put on the pseudo-relativistic Hartree equation whose focusing nonlinearity is of critical strength in the sense that large initial data can lead to singularity formation resulting in finite-time blow-up of the solution. Such a breakdown indicates a ``gravitational collapse'' of the physical system (a boson star) modeled by this equation, and it substantiates the intuitive picture of collapsing stellar matter that exceeds a critical total mass. If time permits, I will also discuss very recent work on pseudo-relativistic Hartree-Fock equations} which provide an effective model for the dynamical evolution of fermion stars (such as white dwarfs). Part of the material covered in my talk is joint work with J. Frohlich (ETH Zurich) and L. Jonsson (KTH Stockholm). |
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| Algebraic Geometry Seminar |
| Topic: |
Approximation for rationally connected varieties over function fields of curves |
| Presenter: |
Brendan Hassett, Rice University |
| Date: |
Tuesday, December 12, 2006, Time: 4:30 p.m., Location: Fine 322 |
| Abstract: |
Let B be a smooth complex curve and X a variety smooth and proper over F=C(B). Graber/Harris/Starr have shown that if X is geometrically rationally connected then X(F) is nonempty. Building on work of Koll'ar/Miyaoka/Mori and others, we prove that X satisfies weak approximation at places of good reduction. There are partial results at places of bad reduction, e.g., for Del Pezzo surfaces and hypersurfaces of low degree. We also discuss new density results for integral points of log Fano pairs (X,D) over B. (joint with Yuri Tschinkel) |
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| Discrete Mathematics Seminar |
| Topic: |
Karp-Sipser on random graphs with fixed degree sequence |
| Presenter: |
Tom Bohman, Carnegie Mellon University |
| Date: |
Wednesday, December 13, 2006, Time: 2:15 p.m., Location: Fine 224 |
| Abstract: |
See http://www.math.princeton.edu/~bsudakov/bohman2006-fall.pdf |
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| Geometry, Representation Theory, and Moduli Seminar |
| Topic: |
TBA |
| Presenter: |
M. Aganagic, Berkeley |
| Date: |
Wednesday, December 13, 2006, Time: 3:00 p.m., Location: Fine 214 |
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| Department Colloquium |
| Topic: |
Trees, elliptic operators, and K-theory for group C*-algebra |
| Presenter: |
Paul Baum, Penn State University |
| Date: |
Wednesday, December 13, 2006, Time: 4:30 p.m., Location: Fine 314 |
| Abstract: |
Let G be a locally compact Hausdorff second countable topological group. Examples are Lie groups, discrete groups, p-adic groups and adelic groups. The regular representation of G gives rise to a C* algebra known as the reduced C* algebra of G. Twenty five years ago P.Baum and A.Connes conjectured an answer to the problem of calculating the K-theory of this C* algebra. When true, this conjecture has corollaries in various branches of mathematics. Among these corollaries are the Novikov conjecture (topology) and the stable Gromov-Lawson-Rosenberg conjecture (differential geometry). In essence, the conjecture asserts that every element in the K-theory of the reduced C* algebra of G is the index of some G-equivariant elliptic operator, and that the only relations on these indices are the "obvious" index preserving relations. This is made precise by using the universal example for proper actions of G. In low dimensions this universal example is a tree. Due to the work of a number of mathematicians, the conjecture is now known to be true for certain classes of groups (e.g. connected Lie groups, discrete hyperbolic groups, discrete a-t-menable groups, algebraic p-adic groups, algebraic adelic groups). The search for a counter-example (to a somewhat generalized version of the conjecture) has led to some intriguing questions involving the expander graphs of Lubotzky-Sarnak and a random group (which probably exists) of Gromov. The talk is intended for a general mathematical audience. The basic definitions (C* algebra, K-theory etc) will be carefully stated in the talk. |
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| Ergodic Theory and Statistical Mechanics Seminar |
| Topic: |
Finiteness results for Veech groups |
| Presenter: |
Barak Weiss, Ben Gurion University |
| Date: |
Thursday, December 14, 2006, Time: 2:00 p.m., Location: Fine 401 |
| Abstract: |
Veech groups are stabilizers of flat surfaces which arise in the study of billiards on rational polygons and Teichmuller theory. These are discrete subgroups of SL(2,R) which could be lattices but might not be (they are sometimes infinitely generated!), and are the topic of lots of recent research. I will describe work with John Smillie in which we characterize the Veech groups which are lattices from 3 points of view: the dynamics of the straight flow on the flat surface (Veech dichotomy and its variants); the dynamics of the associated flows on the moduli space of flat surfaces; the geometry of the flat surface. We also provide new restrictions in case the groups are not lattices. |
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| Topology Seminar |
| Topic: |
TBA |
| Presenter: |
Saul Schleimer, Rutgers University |
| Date: |
Thursday, December 14, 2006, Time: 4:30 p.m., Location: Fine 314 |
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| Mathematical Physics Seminar *** Please note special date and time |
| Topic: |
Entangled photons from biexciton decay in a quantum dot |
| Presenter: |
Y. Avron, Technion, Israel |
| Date: |
Friday, December 15, 2006, Time: 2:30 p.m., Location: Jadwin 343 |
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