Friday February 02, 2018 2:30 PM  3:30 PM Math Tower P131
 Scott Sutherland, Stony Brook University
On the Lebesgue Measure of the Feigenbaum Julia setIn joint work with Artem Dudko (IMPAN), we show that the Julia set of the quadratic Feigenbaum map has Hausdorff dimension less than two and consequently zero Lebesgue measure, answering a longstanding open question. This is established by a combination of new estimation techniques and a rigorous computerassisted computation.

Friday February 09, 2018 2:30 PM  3:30 PM Math Tower P131
 Dong Chen, Ohio State University
KAMnondegenerate nearly integrable systems with positive metric entropy on arbitrarily small invariant setsIn 1950s Kolmogorov asked the following question, which is closely related to the celebrated KAM theory: Can a nondegenerate nearly integrable Hamiltonian system have a positive KolmogorovSinai entropy (a.k.a. metric entropy)? In this talk we give a positive answer to this question.
In fact, examples with positive metric entropy can be constructed by a C^∞ small Lagrangian perturbation of the geodesic flow on any flat Finsler torus. Moreover positive metric entropy is generated in an arbitrarily small tubular neighborhood of any single trajectory. Similar construction applies to general completely integrable Hamiltonian systems as well. This is a joint work with D. Burago and S. Ivanov.

Friday February 16, 2018 2:30 PM  3:30 PM Math Tower P131
 Kei Irie, Kyoto University
$C^∞$closing lemma for threedimensional Reeb flows
via embedded contact homologyI will explain a proof of $C^∞$closing lemma for threedimensional Reeb flows and Hamiltonian surface maps, using embedded contact homology (ECH). In particular, the key ingredient of the proof is an asymptotic formula for spectral invariants in ECH, which was proved by CristofaroGardiner, Hutchings, and Ramos. If time permits, I will discuss a conjecture which gives a quantitative refinement of this result.

Friday February 23, 2018 2:30 PM  3:30 PM Math Tower P131
 Zhiqiang Li, Stony Brook University
Prime orbit theorems for expanding Thurston mapsAnalogues of the Riemann zeta function were first introduced into geometry by A. Selberg and into dynamics by M. Artin, B. Mazur, and S. Smale. Analytic studies of such dynamical zeta functions yield quantitative information on the distribution of closed geodesics and periodic orbits.
We obtain the first Prime Orbit Theorem, as an analogue of the Prime Number Theorem, in complex dynamics outside of hyperbolic maps, for a class of branched covering maps on the $2$sphere called expanding Thurston maps $f$. More precisely, we show that the number of primitive periodic orbits of $f$, ordered by a weight on each point induced by a nonconstant realvalued Hölder continuous function on $S^2$ satisfying some additional regularity conditions, is asymptotically the same as the wellknown logarithmic integral, with an exponentially small error term. Such a result follows from our quantitative study of the holomorphic extension properties of the associated dynamical zeta functions and dynamical Dirichlet series.
In particular, the above result applies to postcriticallyfinite rational maps whose Julia set is the whole Riemann sphere. Moreover, we prove that the regularity conditions needed here are generic; and for a Lattès map $f$, a continuously differentiable function satisfies such a condition if and only if it is not cohomologous to a constant. This is a joint work with T. Zheng.

Friday March 02, 2018 2:30 PM  3:30 PM Math Tower P131
 Serge Troubetzkoy, Institut de Mathématiques de Marseille
TBATBA

Friday March 09, 2018 2:30 PM  3:30 PM Math Tower P131
 Vadim Kaimanovich, University of Ottawa
TBATBA

Friday March 23, 2018 2:30 PM  3:30 PM Math Tower P131
 Juan RiveraLetelier, University of Rochester
TBATBA

Friday April 13, 2018 2:30 PM  3:30 PM Math Tower P131
 Anand P. Singh, Central University of Rajasthan
TBATBA

Friday April 20, 2018 2:30 PM  3:30 PM Math Tower P131
 Joshua Bowman, Seaver College
TBATBA

Friday April 27, 2018 2:30 PM  3:30 PM Math Tower P131
 Romain Dujardin, Université Pierre et Marie Curie
TBATBA

Friday May 04, 2018 2:30 PM  3:30 PM Math Tower P131
 Leonid Bunimovich, Georgia Tech
TBATBA

