Analysis and Geometry Seminar

Link to Previous Semesters


Fall 2021

Tuesdays, 11:00 am
Ladd 114







9 November 2021



2 November 2021



26 October 2021



19 October 2021

Frankie Chan:  Profinite Rigidity and Fuchsian Groups (Part 2)


12 October 2021

Frankie Chan: Profinite Rigidity and Fuchsian Groups

Abstract:
Inspired by a result from Bridson--Conder--Reid, my work produces an effective construction for distinguishing the collection of finite quotients of a triangle group with that of a non-isomorphic Fuchsian lattice. With an aim of balancing motivation and technical details, I will begin with some background and exposition on profinite groups and surface theory. This is joint work with Ryan Spitler (Rice University).



5 October 2021

Doğan Çömez: Ergodic Theorems in Fully Symmetric Banach Spaces (Part 2)
 


28 September 2021

Doğan Çömez: Ergodic Theorems in Fully Symmetric Banach Spaces

Abstract: Fully symmetric Banach spaces are large function spaces that include classical Banach spaces. Some well-known examples of spaces of this kind are Orlicz Spaces, Lorentz Spaces and Marcinkiewicz Spaces. Although these spaces are studied extensively in the functional analysis literature, investigation of convergence of ergodic averages in such spaces is fairly recent. In this talk, first we will provide a brief review of symmetric Banach spaces, then we will give necessary and sufficient conditions for almost uniform convergence of ergodic averages. These, in turn, will be utilized in extending several ergodic theorems to the setting of fully symmetric Banach spaces.


21 September 2021

Morgan O'Brien:  A noncommutative return times theorem  (Part 3)


14 September 2021

Morgan O'Brien: A noncommutative return times theorem  (Part 2)
 



7 September 2021

Morgan O'Brien: A noncommutative return times theorem   

Abstract: Weighted and subsequential ergodic theorems are frequent subjects of study in ergodic theory. An important version of these types of results are the Wiener-Wintner type ergodic theorems, which allow for averages of operators weighted by a collection of sequences to be considered simultaneously. In classical ergodic theory, these types of results are known for numerous classes of weights, while the noncommutative setting thus far has required all sequences to be bounded. In these talks, we will discuss a version of the Banach principle that has been specialized for proving such theorems for various types of weights in the von Neumann algebra setting. Using this, we will prove some Wiener-Wintner type ergodic theorems for some broad classes of Hartman sequences.