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NOVEMBER 2006 |
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| Sato-Tate Seminar |
| Topic: |
Arithmetic geometry of the Dwork family |
| Presenter: |
Nicholas Katz, Princeton University |
| Date: |
Wednesday, November 29, 2006, Time: 1:30 p.m., Location: Fine 314 |
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| Discrete Mathematics Seminar |
| Topic: |
Global connectivity from local conditions |
| Presenter: |
David Galvin, University of Pennsylvania |
| Date: |
Wednesday, November 29, 2006, Time: 2:15 p.m., Location: Fine 224 |
| Abstract: |
See http://www.math.princeton.edu/~bsudakov/galvin2006-fall.pdf |
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| Geometry, Representation Theory, and Moduli Seminar |
| Topic: |
Quantum cohomology of Hilbert scheme of points of A_n resolutions II |
| Presenter: |
Alexei Oblomkov, Princeton University |
| Date: |
Wednesday, November 29, 2006, Time: 3:00 p.m., Location: Fine 214 |
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| Department Colloquium |
| Topic: |
Zeros of L-functions and ranks of Selmer groups |
| Presenter: |
Chris Skinner, Princeton University |
| Date: |
Wednesday, November 29, 2006, Time: 4:30 p.m., Location: Fine 314 |
| Abstract: |
It has long been recognized that certain `special' zeros of L-functions (motivic, automorphic, pick your favorite flavor) have an arithmetic significance. For example, the order of the zero of the Dedekind zeta function of a number field is equal to the rank of the group of units of the integer ring of this field (so the fact that the Riemann zeta function does *not* vanish at s=0 reflects the fact that the units of the integers are a finite group). Similarly, the order of vanishing at s=1 of the L-function of an elliptic curve over the rationals is expected to be the rank of the group of rational points on the curve. In this talk I will describe some recent efforts to provide theoretical evidence for this expectation and its generalizations to other L-functions. |
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| Ergodic Theory and Statistical Mechanics Seminar |
| Topic: |
On stochastic properties of billiards and on tagged particle diffusion in the 1d Rayleigh gas |
| Presenter: |
Peter Balint, Budapest University of Technology and Economics |
| Date: |
Thursday, November 30, 2006, Time: 2:00 p.m., Location: Fine 401 |
| Abstract: |
In this talk I would like to consider stochastic phenomena arising in various classical mechanical systems. The first part of the talk is meant to give an overview on some recent progress related to ergodic and statistical properties of hyperbolic billiards (joint works with Sebastien Gouezel, Pavel Bachurin and Imre Peter Toth). The second part describes some new observations on tagged particle diffusion in the 1d Rayleigh gas (joint result with Balint Toth and Imre Peter Toth). |
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| Institute for Advanced Study and Princeton University Number Theory Seminar |
| Topic: |
Sieve methods for Quantum Unique Ergodicity and general shifted sums |
| Presenter: |
Roman Holowinsky, IAS |
| Date: |
Thursday, November 30, 2006, Time: 4:30 p.m., Location: Fine 214 |
| Abstract: |
In this talk, I shall introduce a sieve method for bounding the average size of shifted convolution summation terms related to the Quantum Unique Ergodicity Conjecture for a fixed Hecke-Maass cusp form. This bound will be uniform in the spectral parameter provided that standard bounds hold for the symmetric square and symmetric fourth power L-functions at the point s=1. We shall see that the sieve method can be applied to a wide variety of shifted sums, including sums with multiple shifts. |
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| Topology Seminar |
| Topic: |
A combinatorial definition of Heegaard-Floor homology for links |
| Presenter: |
Dylan Thurston, Columbia University and Barnard College |
| Date: |
Thursday, November 30, 2006, Time: 4:30 p.m., Location: Fine 314 |
| Abstract: |
We give a completely combinatorial definition and proof of invariance of Heegaard-Floer homology for links in the 3-sphere. The definition is based on a grid-link presentation of the link, also known as an arc presentation. In particular, this yields a simple algorithm for computing the knot genus. If time permits, we will describe how to extract invariants of Legendrian and transverse links in this homology. Parts of this talk are work of Manolescu, Ozsváth, and Sarkar, and parts are joint work with Manolescu, Ozsváth, and Szabó. |
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DECEMBER 2006 |
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| Differential Geometry and Geometric Analysis Seminar |
| Topic: |
TBA |
| Presenter: |
Mario Bonk, University of Michigan |
| Date: |
Friday, December 1, 2006, Time: 3:00 p.m., Location: Fine 314 |
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| PACM Colloquium - Distinguished Lecture Series |
| Topic: |
Genomic Information: Biology and Medicine in the 21st Century |
| Presenter: |
Eric S. Lander, Broad Institute, Massachusetts Institute of Technology |
| Date: |
Friday, December 1, 2006, Time: 8:00 p.m., Location:A02 McDonnell Hall |
| Abstract: |
The Human Genome Project was just an early step in a decades-long scientific program aimed at achieving a systematic and comprehensive view of biology and medicine. This program involves deep collaboration among biologists, chemists, physicians, engineers and -- importantly -- mathematicians and computer scientists. The lecture will describe current projects in genomic medicine, including comparative genomics, human genetics, cancer genetics and chemical biology. Along the way, it will highlight analytical issues that arise from the massive amounts of genomic information that are rapidly becoming available. |
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| Analysis Seminar |
| Topic: |
Global Well-Posedness for the $L2$-critical NLS in higher dimensions |
| Presenter: |
Natasa Pavlovic, Princeton University |
| Date: |
Monday, December 4, 2006, Time: 4:00 p.m., Location: Fine 110 |
| Abstract: |
In this talk we will present a joint work with Daniela De Silva, Gigliola Staffilani and Nikolaos Tzirakis on global well-posedness for the $L^{2}$ critical NLS in ${\mathbb R}^n$ with $n \geq 3$. Inspired by a recent paper of Fang and Grillakis, we combine the method of almost conservation laws with a local in time Morawetz estimate to improve global well-posedness results in higher dimensions. |
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| Algebraic Geometry Seminar |
| Topic: |
TBA |
| Presenter: |
Günter Harder, Max Planck Institut für Mathematik; IAS |
| Date: |
Tuesday, December 5, 2006, Time: 4:30 p.m., Location: Fine 322 |
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| Operations Research and Financial Engineering Seminar |
| Topic: |
Stability of utility-maximization in incomplete markets |
| Presenter: |
Gordan Zitkovic, University of Texas |
| Date: |
Tuesday, December 5, 2006, Time: 4:30 p.m., Location: E-219, E-Quad |
| Abstract: |
The effectiveness of utility-maximization techniques for portfolio management relies on our ability to estimate correctly the parameters of the dynamics of the underlying financial assets. In the setting of complete or incomplete financial markets, we investigate whether small perturbations of the market coefficient processes lead to small changes in the agent's optimal behavior derived from the solution of the related utility-maximization problems. Specifically, we identify the topologies on the parameter process space and the solution space under which utility-maximization is a continuous operation, and we provide a counterexample showing that our results are best possible, in a certain sense. A novel result about the structure of the solution of the utility-maximization problem where prices are modeled by continuous semimartingales is established as an offshoot of the proof of our central theorem. |
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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: |
TBA |
| Presenter: |
Bruce Kleiner, Yale University |
| Date: |
Friday, December 8, 2006, Time: 3:00 p.m., Location: Fine 314 |
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| Analysis Seminar |
| Topic: |
TBA |
| Presenter: |
Enno Lenzman, MIT |
| Date: |
Monday, December 11, 2006, Time: 4:00 p.m., Location: Fine 110 |
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| Algebraic Geometry Seminar |
| Topic: |
TBA |
| Presenter: |
Brendan Hassett, Rice University |
| Date: |
Tuesday, December 12, 2006, Time: 4:30 p.m., Location: Fine 322 |
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| Discrete Mathematics Seminar |
| Topic: |
TBA |
| Presenter: |
Tom Bohman, Carnegie Mellon University |
| Date: |
Wednesday, December 13, 2006, Time: 2:15 p.m., Location: Fine 224 |
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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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