Talk, Topos Institute, Oxford, Oxford, UK
David Lynch’s neo-noir classic Mulholland Drive challenges our sense of continuity, identity, and causality. In this talk, I use its fragmented narrative structure as a metaphorical guide to construct an algebraic quantum field theory using a double functor between free globularly generated double categories.
Talk, University of Florida, Gainesville, Gainesville, Florida
With Andrew Krenz and Quan Long. Presented a construction of a relative monad that allows classical control and information processing of quantum systems. Recording of my part of this talk.
Talk, Adjoint School 2025, Virtual
Presentation done as a part of the 2025 Adjoint School with my peer based on R. Atkey’s “What is a Categorical Model for Arrows?”.
Talk, Joint Mathematics Meeting 2025, Seattle, Washington, USA
Several open problems have been asked and are being solved on the nature of dagger structures that can be defined on Fusion Categories, and many results have been shown for Hermitian (positive dagger) Fusion Categories. However, Non-Hermitian Fusion Categories do exist, the most prominent example of them being the Yang-Lee Category. Using properties of Fusion Categories, previous results that has been found about Fusion Categories with a Hermitian Dagger Structure, and properties that arise from the existence of a Ribbon Structure and the ability to define a braiding, we now shift our focus on investigating Ribbon Fusion Categories that have a Non-Hermitian Dagger structure on them. Utilizing the rich and complicated structure of these categories, we discuss the outline of proofs of theorems on the Muger center, braiding, and spherical structure of such a fusion category, and discuss a potential construction of a TQFT using these results. slides
Talk, Graduates Reminisce Online On Topology (GROOT) Summer Seminar, Virtual
Talk Abstract: Several open problems have been asked and are being solved on the nature of dagger structures that can be defined on Fusion Categories. Using previous work that has been done investigating the Hermitian Dagger case, we now shift our focus to dealing with Fusion Categories that have a Non-Hermitian Dagger structure on them. What can we do with these categories? Do they yield any interesting properties? We discuss the outline of proofs of theorems on the Müger center, braiding, and spherical structure of such a fusion category, and discuss a potential construction of a TQFT, and what it could mean for us.
Talk, Ross Mathematics Program, Columbus, Ohio, USA
An introductory lecture series on Fusion Categories, taught to high schoolers in the 2024 Ross Mathematics Program. notes
Talk, California Institute of Technology (Caltech), Los Angeles, CA, USA
Based on So Okada’s “Quintic periods and stability conditions via homological mirror symmetry”. Part of my final presentation for Ma148b (Topics in Mathematical Physics). notes
Talk, Ross Mathematics Program, Columbus, Ohio, USA
An introduction to category theory through set theory, at a time when I was very fascinated by the potential of using category theory as a logical language for math. slides