# Calendar

Jun
23
Tue
Karl Hofmann (Technische Universität Darmstadt) @ Lecture held in Elysium
Jun 23 @ 6:00 am – 8:00 am

Title: The group algebra of a compact group and Tannaka duality for compact groups
by Karl Hofmann (Technische Universität Darmstadt) as part of Topological Groups

Lecture held in Elysium.

Abstract
In the 4th edition of the text- and handbook “The Structure of Compact Groups”,
de Gruyter, Berlin-Boston, having appeared June 8, 2020, Sidney A. Morris and
I decided to include, among material not contained in earlier editions, the Tannaka-Hochschild Duality Theorem which says that $the$ $category$ $of$ $compact$ $groups$ $is,dual$
$to$ $the$ $category,of,real,reductive$ $Hopf$ $algebras$. In the lecture I hope to explain
why this theorem was not featured in the preceding 3 editions and why we decided
to present it now. Our somewhat novel access led us into a new theory of real
and complex group algebras for compact groups which I shall discuss. Some Hopf
algebra theory appears inevitable. Recent source: K.H.Hofmann and L.Kramer,
$On$ $Weakly,Complete,Group,Algebras$ $of$ $Compact$ $Groups$, J. of Lie Theory $bold{30}$ (2020), 407-424.

Karl H. Hofmann

Sarah Reitzes (University of Chicago)
Jun 23 @ 10:00 am – 11:00 am

Title: Reduction games, provability, and compactness
by Sarah Reitzes (University of Chicago) as part of Computability theory and applications

Abstract
In this talk, I will discuss joint work with Damir D. Dzhafarov and Denis R. Hirschfeldt. Our work centers on the characterization of problems P and Q such that P is omega-reducible to Q, as well as problems
P and Q such that RCA_0 proves Q implies P, in terms of winning strategies in certain games. These characterizations were originally introduced by Hirschfeldt and Jockusch. I will discuss extensions and generalizations of these characterizations, including
a certain notion of compactness that allows us, for strategies satisfying particular conditions, to bound the number of moves it takes to win. This bound is independent of the instance of the problem P being considered.

Jun
26
Fri
Jack Yoon (PhD candidate): Grätzer-Schmidt theorem in Arithmetical Transfinite Recursion
Jun 26 @ 2:00 pm – 3:00 pm
Jun
29
Mon
Sana Habib (MA candidate): Visualizations of Schottky Groups
Jun 29 @ 2:00 pm – 3:00 pm
Sana Habib’s Masters Presentation
Jun 29 @ 2:00 pm – 3:00 pm
Visualizations of Schottky Groups
Often times, to truly understand a mathematical object it must be viewed from several different perspectives, involving several different foundations. In this thesis, I will present eye-catching visualization techniques for something called Schottky groups, which are similar to general linear groups of degree n over the complex numbers. This is built on an understanding of complex numbers to explore the structure of specific kinds of linear groups. My discussions will include the mathematics needed to imagine such an object, as well as the numerics required to compute such an object. Parts of this will include discussion of programming these objects.

This thesis is an exploration of a particular kind of projective linear group,  Schottky groups, and their variations by understanding them geometrically. The general idea here is how we can study fractal-like sets by looking at images of circles representing group elements. This exploration will lead to the discovery and understanding of Schottky groups.

Furthermore, I do this exploration using first and foremost, a background in complex analysis, and in particular, a deep understanding of Mobius maps. This leads to discovery and understanding of anti-Mobius maps, which will be our main tool in understanding reflections. Additionally, I will use Python3 to program examples and experiments of these ideas. The Python code will provide specific examples. as well as mathematical challenges of its own. These challenges will include creating Mobius and anti-Mobius classes, and using these classes to perform all of these operations.
Jun
30
Tue
Amaury Pouly (CNRS)
Jun 30 @ 4:00 am – 5:00 am

Title: A Survey on Analog Models of Computation
by Amaury Pouly (CNRS) as part of Computability theory and applications

Abstract: TBA

Break (University of Hawaiʻi) @ Lecture held in Elysium
Jun 30 @ 6:00 am – 8:00 am

Title: Topological Groups Seminar One-Week Hiatus
by Break (University of Hawaiʻi) as part of Topological Groups

Lecture held in Elysium.
Abstract: TBA

Jul
7
Tue
Indira Chatterji (Laboratoire J.A. Dieudonné de l’Université de Nice) @ Lecture held in Elysium
Jul 7 @ 6:00 am – 8:00 am

Title: Groups Admitting Proper Actions by Affine Isometries on Lp Spaces
by Indira Chatterji (Laboratoire J.A. Dieudonné de l’Université de Nice) as part of Topological Groups

Lecture held in Elysium.

Abstract
Introduction, known results, and open questions regarding groups admitting a proper action by affine isometries on an $L_p$ space.