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JANUARY 2010 |
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| Miniconference on Dynamical Systems at Princeton |
| January 14-15, 2010 |
| A09 Jadwin Hall (complex connected to Fine Hall) |
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| Thursday, January 14, 2010 |
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| Topic: |
A Phase transition for a model of Random band matrices |
| Presenter: |
Thomas Spencer |
| Time: |
10:00 a.m. - 10:55 a.m. |
| Abstract: |
Random band matrices are a generalization of Wigner matrices in which matrix elements are concentrated in a band about the diagonal. Spectral properties of these matrices can be expressed in terms of certain statistical mechanics models with hyperbolic symmetry. This talk will discuss a phase transition for a simplified version of one such model in 3D. The model is essentially equivalent to a random walk in a correlated random environment. The transition corresponds to a change in the long time behavior of this walk from localization to diffusion. This is joint work with M. Disertori and M. Zirnbauer. |
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| Topic: |
Zero temperature limits of Gibbs states |
| Presenter: |
Michael Hochman |
| Time: |
11:00 a.m. - 11:55 a.m. |
| Abstract: |
Let f be a Holder potential on the full one-sided shift {0,1}^\mathbb{N}, and let \mu_b denote the Gibbs measure for f at inverse temperature b (existence and uniqueness are classical, as is the smooth dependence on b). It was thought that in this situation the limit of \mu_b as b tends to infinite should exist: although van Enter and Ruszel gave a counterexample over an infinite state space, in the finite state case Bremont proved that convergence does take place when f takes on finitely many values. I will present joint work with Jean-Rene Chazottes in which we construct a counterexample and discuss some of its features. I will also discuss results in the multidimensional case. |
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| Topic: |
Escape rates and variational principles for dynamical systems with holes |
| Presenter: |
Mark Demers |
| Time: |
2:00 p.m. - 2:55 p.m. |
| Abstract: |
We present recent results regarding escape rates and conditionally invariant measures for a periodic Lorentz gas with holes. We then derive a variational principle connecting the escape rate to the pressure on the survivor set, the set of points which never enters the hole. This relation generalizes to a broad class of systems with holes and requires only weak assumptions on the size and boundary of the hole. When the underlying dynamical system is smooth (before the introduction of the hole) the variational principle allows us to determine how the escape rate changes as we vary the size and position of the hole. This is joint work with Paul Wright and Lai-Sang Young. |
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| Topic: |
Progress on Affine Sieves |
| Presenter: |
Alex Kontorovich |
| Time: |
3:00 p.m. - 3:55 p.m. |
| Abstract: |
We will discuss recent progress with Jean Bourgain on the Affine Sieve, which aims to find primes or almost-primes in sets of integers generated by group actions, with applications to prime entries in matrix groups. |
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| Topic: |
The Mobius function, randomness and dynamics |
| Presenter: |
Peter Sarnak |
| Time: |
4:30 p.m. - 5:25 p.m. |
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| Friday, January 15, 2010 |
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| Topic: |
The Full Renormalization Horseshoe for Unicritical Maps, revisited |
| Presenter: |
Mikhail Lyubich |
| Time: |
9:30 a.m. - 10:25 a.m. |
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| Topic: |
Geometry and Topology of Chaotic Transport |
| Presenter: |
John Delos |
| Time: |
11:00 a.m. - 11:55 a.m. |
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| Topic: |
On Arnold diffusion in arbitrary degrees of freedom and an almost dense orbit on energy surface |
| Presenter: |
Vadim Kaloshin |
| Time: |
12:00 p.m. - 12:55 p.m. |
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| Topic: |
Ergodicity of some open systems with particle-disk interactions |
| Presenter: |
Tanya Yarmola |
| Time: |
2:30 p.m. - 2:55 p.m. |
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| Topic: |
Lyapunov exponents, periodic orbits and horseshoes in infinite dimensional systems |
| Presenter: |
Zeng Lian |
| Time: |
3:00 p.m. - 3:25 p.m. |
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| Topic: |
Global wellposedness for a certain class of large initial data for the 3D Navier-Stokes equations |
| Presenter: |
Percy Wong |
| Time: |
3:30 p.m. - 3:55 p.m. |
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| Topic: |
Central Limit Theorem for Random Poisson polygons in an Arbitrary convex set in R^2 |
| Presenter: |
John Pardon |
| Time: |
4:30 p.m. - 4:55 p.m. |
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| Topic: |
Regular or stochastic dynamics in higher degree families of unimodal maps |
| Presenter: |
Trevor Clark |
| Time: |
5:00 p.m. - 5:25 p.m. |
| Abstract: |
About fifteen years ago, Palis conjectured that typical dynamical systems should possess good statistical properties. Through the work of Avila, Lyubich, de Melo and Moreira, this has been proven for unimodal maps with a non-degenerate critical point. I will show how to remove the condition on the critical point in analytic families of unimodal maps; along the way proving that that the hybrid classes in the space of unimodal maps yield a lamination near all but countably many maps in the family. The essential difference in the higher degree case is the presence of non-renormalizable maps without "decay of geometry". The key to their study is the use of a generalized renormalization operator, which has much in common with the usual renormalization operator. |
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| Department Colloquium |
| Topic: |
Some recent convergence results for nonconventional ergodic averages |
| Presenter: |
Timothy Austin, UCLA |
| Date: |
Wednesday, January 20, 2010, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: |
The phenomenon of multiple recurrence in ergodic theory occurs when several of the images of one fixed positive-measure set under some probability-preserving transformations, indexed by the points of some finite configuration in the acting group, all overlap in a set of positive measure. Instances of this were first investigated very generally by Furstenberg, who related them to Szemeredi's Theorem in additive combinatorics and so gave a new proof of that theorem. His analysis focuses on certain `nonconventional' ergodic averages, and these have gone on to attract considerable further interest. In this talk we will discuss some recent progress in their analysis, showing how an extension of an initially-given system of commuting probability-preserving transformations can be used in a proof of the norm convergence of some such averages. |
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| FEBRUARY 2010 |
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| Algebraic Geometry Seminar |
| Topic: |
TBA |
| Presenter: |
Antoine Ducros, University Paris VI |
| Date: |
Tuesday, February 2, 2010, Time: 4:30 p.m., Location: Fine Hall 322 |
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| PACM Colloquium |
| Topic: |
TBA |
| Presenter: |
Konstantin Mischaikow, Mathematics and BioMaPS Institute, Rutgers University |
| Date: |
Monday, February 15, 2010, Time: 4:00 p.m., Location: Fine Hall 214 |
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| MARCH 2010 |
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| Algebraic Geometry Seminar |
| Topic: |
TBA |
| Presenter: |
Aaron Bertram, University of Utah |
| Date: |
Tuesday, March 9, 2010, Time: 4:30 p.m., Location: Fine Hall 322 |
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| Algebraic Geometry Seminar |
| Topic: |
TBA |
| Presenter: |
Sándor Kovács, University of Washington |
| Date: |
Tuesday, March 23, 2010, Time: 4:30 p.m., Location: Fine Hall 322 |
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| Algebraic Geometry Seminar |
| Topic: |
TBA |
| Presenter: |
Maksym Fedorchuk, Columbia University |
| Date: |
Tuesday, March 30, 2010, Time: 4:30 p.m., Location: Fine Hall 322 |
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