Ideas for projects (for references send me an email or ask me after class):

About the course: this is a topics course in topological groups and dynamics. We will be focusing on techniques and phenomena that go beyond the realm of locally compact groups. In the absence of classical techniques which rely on local compacteness, we will develop various frameworks for analyzing the structure of "large" topological groups, such as: Fraisse theoretic methods; Baire category methods; structured completions and compactifications. As we develop these techniques we will provide a wide range of applications and examples from topology, analysis, and logic. Here are three centerpieces that, among others, will be covered:


Background. This course is intended for graduate and advanced undergraduate students. We will assume that the students have some background in topology and the theory of metric spaces. Some background in logic, functional analysis, and representation theory will be useful but not necessary. Through a broad syllabus I intend to motivate and raise interest about certain topics rather than exclude the "non-specialists" so please do not hesitate to contact me if you have any questions!

Books and notes. I will be posting notes on a weekly basis. That being said, some relevant books are: Su Gao's "Invariant descriptive set theory", Vladimir Pestov's " Dynamics of Infinite-Dimensional Groups: The Ramsey-Dvoretzky-Milman Phenomenon", Greg Hjorth's "Classification and Orbit Equivalence Relations".

Grades. The grades will be based on participation and on a final project. For the project each of you will read some paper(s), present the main ideas in class, and write a short paper on the topic.

Course.
Math 191 Fall 2018
10:30 - 11:55 TR, 289 LINDE

Instructor.
Aristotelis Panagiotopoulos
Office. 102 Kellogg
panagio at caltech.edu
Office hours. Any time (knock door or send an email)

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