Wednesday February 07, 2018 2:30 PM  3:30 PM Math Tower P131
 DyiShing Ou, Stony Brook University
Nonexistence of wandering domains for infinitely renormalizable : I
Hénon mapsThe plan of the lectures is to prove the theorem: A strongly dissipative infinitely renormalizable Hénonlike map with stationary combinatorics does not have a wandering domain.
I will focus on the case of the perioddoubling combinatorics. After the proof, I will say a few words about extending the proof to other stationary combinatorics.
The plan of the first talk is to cover the topics:
1. unimodal renormalization,
2. Hénon renormalization,
3. dynamics of an infinite perioddoubling renormalizable Hénon map.
We will begin to prove the theorem in the following talk.

Wednesday February 14, 2018 2:30 PM  3:30 PM Math Tower P131
 DyiShing Ou, Stony Brook University
Nonexistence of wandering domains for infinitely renormalizable Henon maps: part IIIn this talk, we will prove the nonexistence of wandering domains for a strongly dissipative infinitely (perioddoubling) renormalizable Henonlike map. I will classify the domain into two regions: the good region and the bad region. In the good region, the classical results from unimodal maps can be applied to Henonlike maps. In particular, if a wandering domain exists, the horizontal size of the elements in a rescaled orbit of the wandering domain (called the closest approach) expands at a definite rate. However, in the bad region, the Henonlike map behaves differently from a unimodal map and the property break down. I will show that the bad behavior can occur at most finitely many times in the rescaled orbit to conclude the theorem.
After proving the theorem, I will give some remarks on my recent work of extending the proof to other stationary combinatorics.

Wednesday February 21, 2018 2:30 PM  3:30 PM Math Tower P131
 Babak Modami, Stony Brook University
Minimal nonuniquely ergodic foliations on surfaces: IMeasured foliations (laminations) on surfaces are wellknown examples of dynamical systems in low dimension. The first return maps of measured foliations are interval exchange transformations which have been studied extensively. Measured foliations also determine the trajectories of Teichmüller and WeilPetersson geodesics in the Teichmüller space.
In this minicourse, I outline my joint work with Brock, Leininger and Rafi about construction of minimal nonuniquely ergodic laminations.
This work was inspired by a construction of Gabai and the earlier work of LenzhenLeiningerRafi where laminations are realized as the limits of sequences of curves on surfaces. An advantage of our method is explicit estimates for intersection numbers of the curves in sequences and the associated subsurface coefficients. These estimates are crucial to control the behavior of geodesics and determine their limit sets in the Thurston compactification of Teichmüller space (which won't be discussed in the minicourse).

Wednesday February 28, 2018 2:30 PM  3:30 PM Math Tower P131
 Babak Modami, Stony Brook University
Minimal nonuniquely ergodic foliations on surfaces: IIMeasured foliations (laminations) on surfaces are wellknown examples of dynamical systems in low dimension. The first return maps of measured foliations are interval exchange transformations which have been studied extensively. Measured foliations also determine the trajectories of Teichmüller and WeilPetersson geodesics in the Teichmüller space.
In this minicourse, I outline my joint work with Brock, Leininger and Rafi about construction of minimal nonuniquely ergodic laminations. This work was inspired by a construction of Gabai and the earlier work of LenzhenLeiningerRafi where laminations are realized as the limits of sequences of curves on surfaces. An advantage of our method is explicit estimates for intersection numbers of the curves in sequences and the associated subsurface coefficients. These estimates are crucial to control the behavior of geodesics and determine their limit sets in the Thurston compactification of Teichmüller space (which won't be discussed in the minicourse).

Wednesday March 14, 2018 2:30 PM  3:30 PM Math Tower P131
 Rostislav Grigorchuk, Texas A&M University
TBATBA

Wednesday March 28, 2018 2:30 PM  3:30 PM Math Tower P131
 Sabya Mukherjee, Stony Brook University
TBATBA

Wednesday April 04, 2018 2:30 PM  3:30 PM Math Tower P131
 Sabya Mukherjee, Stony Brook University
TBATBA

Wednesday April 18, 2018 2:30 PM  3:30 PM Math Tower P131
 Dror Varolin, Stony Brook University
TBATBA

Wednesday April 25, 2018 2:30 PM  3:30 PM Math Tower P131
 Dror Varolin, Stony Brook University
TBATBA

