Below is the tentative schedule of speakers for this semester. Titles and abstracts will be updated each week.
January 23 – Canceled
January 30 – Organizational Meeting
February 6
Speaker: Billy Duckworth
Title: Introduction to Equivariant Analysis
This is talk is a practice run for the material in my prelim. We will be discussing how certain Borel equivariant factors of probability preserving group actions can be used to describe classic ergodic theoretic properties. The connection to classical analysis will be explored at a high level and in the process the name of the project justified. The focus will be on the philosophy of 'equivariant analysis' and on my own original results, although previous work will be touched on.
February 13
Speaker: Billy Duckworth
Title: Cheap Condensed Math
"Condensed math" is a project of Peter Scholze and Dustin Clausen to reinvent topology in a way that plays better with algebra. The central idea is to replace each space, X, with the functor C(-,X) on the category of compact Hausdorff spaces. That approach runs into enough set theoretic issues to justify this talk happening on a Friday the 13th, but I will be presenting a way to make a "cheap" version of condensed math. We will use a little descriptive set theory to reduce the domain of our functors to a single object category in case we only care about condensed Polish spaces!
February 20
Speaker: Khiem Nguyen
Title: Ultraproducts in Functional Analysis 2
In this talk, we will be looking at metric ultraproducts of commutative unital C*-algebras, describing the spectrum, and showing that a metric ultraproduct of separable C*-algebras does not need to be separable. We will also be investigating conditions when the ultracoproduct of compact Hausdorff spaces is a Parovičenko space.
February 27
Speaker: Khiem Nguyen
Title: Ultraproducts in Functional Analysis 3
In this talk, we will introduce the notion of a nonstandard hull and show that ultracoproducts of βN is not a Stonean space for any free ultrafilter on the naturals.
March 6
Speaker: Billy Duckworth
Title: A Dynamical Perspective on the Peter-Weyl Theorem
The Peter-Weyl theorem is foundational in understanding the structure of compact groups. It gives a decomposition of any unitary action into a direct sum of finite dimensional pieces which has many important implications. We will take a tour through the ideas of this monumental result drawing comparisons to their analogues in ergodic theory.
March 13
Speaker: Chase Giles
Title:
March 20 – Spring Break
March 27
Speaker: Dante Sorrentino
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April 3
Speaker:
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April 10
Speaker: Joe Groszkiewicz
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April 17
Speaker: Kean Fallon
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April 24
Speaker: Kean Fallon
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May 1
Speaker: Kean Fallon
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May 8
Speaker:
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