Dissertation Materials

Dissertation Committee

David Penneys (Advisor)

Micah Chrisman

Thomas Kerler

Oral portion

Date: July 15, 2026

Time: 1:50 PM

Room: MW 154

Zoom Room: Will make available here soon!

Written portion

Title: Functional Analysis in Three-Dimensional Category Theory

Below you can find the most up-to-date draft of the thesis.

Last updated: June 30, 2026

• Thesis



The thesis document is based on the following three projects.



• Gray-categories model algebraic tricategories
• Foundations for operator algebraic tricategories
• The Homotopy 3-Type of Abelian C*-Algebras



We also refer the reader to the following book in progress for background on operator algebras.

• Unitary QUantum Symmetries Lite (UQSL)