Dynamics Seminar 2021-2022

The Dynamics seminar meets in room 901 of Van Vleck Hall on Mondays from 2:30pm - 3:20pm. To sign up for the mailing list send an email from your wisc.edu address to dynamics+join@g-groups.wisc.edu. For more information, contact Caglar Uyanik or Chenxi Wu.

Fall 2021

date	speaker	title	host(s)
Sep. 13	Nate Fisher (UW Madison)	"Boundaries, random walks, and nilpotent groups"	local
Sep. 20	Caglar Uyanik (UW Madison)	"Dynamics on currents and applications to free group automorphisms"	local
Sep. 27	Michelle Chu (UIC)	"TBA"	caglar
Oct. 4	Osama Khalil (Utah)	"Generalized Hecke Operators and Mahler’s Problem in Diophantine Approximation"	caglar
Oct. 11	Theodore Weisman (UT Austin)	"TBA"	zimmer
Oct. 18	Open	TBA
Oct. 25	Open	TBA
Nov. 1	Open	TBA
Nov. 8	Jayadev Athreya (UW Seattle) tbc	TBA	caglar and grace
Nov. 15	Jack Burkart (UW Madison)	TBA	local
Nov. 22	Jonah Gaster (UW Milwaukee)	TBA	caglar
Dec. 6	Matt Clay (Arkansas) tbc	TBA	caglar

Abstracts

Nate Fisher (UW Madison)

Boundaries, random walks, and nilpotent groups

In this talk, we will discuss boundaries and random walks in the Heisenberg group. We will discuss a class of sub-Finsler metrics on the Heisenberg group which arise as the asymptotic cones of word metrics on the integer Heisenberg group and describe new results on the boundaries of these polygonal sub-Finsler metrics. After that, we will explore experimental work to examine the asymptotic behavior of random walks in this group. Parts of this work are joint with Sebastiano Nicolussi Golo.

Caglar Uyanik (UW Madison)

Dynamics on currents and applications to free group automorphisms

Currents are measure theoretic generalizations of conjugacy classes on free groups, and play an important role in various low-dimensional geometry questions. I will talk about the dynamics of certain "generic" elements of Out(F) on the space of currents, and explain how it reflects on the algebraic structure of the group.

Michelle Chu (UIC)

TBA

TBA.

Osama Khalil (Utah)

Generalized Hecke Operators and Mahler’s Problem in Diophantine Approximation

Khintchine's Theorem provides a zero-one law describing the approximability of typical points by rational points. In 1984, Mahler asked whether the same holds for Cantor’s middle thirds set. His question fits into a long studied line of research aiming at showing that Diophantine sets are highly random and are thus disjoint, in a suitable sense, from highly structured sets.

We will discuss the first complete analogue of Khintchine’s theorem for certain self-similar fractal measures, recently obtained in joint work with Manuel Luethi. The key ingredient in the proof is an effective equidistribution theorem for fractal measures on the space of unimodular lattices, generalizing a long history of similar results for smooth measures beginning with Sarnak’s work in the eighties. To prove the latter, we associate to such fractals certain p-adic Markov operators, reminiscent of the classical Hecke operators, and leverage their spectral properties. No background in homogeneous dynamics will be assumed.

Jayadev Athreya (UW Seattle)

TBA

Jonah Gaster (UWM)

TBA

TBA.

Archive of past Dynamics seminars

2020-2021 Dynamics_Seminar_2020-2021