My Talks And Seminars

Upcoming Talks

Conference Talks

• Saturating the Welch Bound for Frames over Finite Fields
  Special Session on Symmetric Subspace Configurations at Constructive Functions 2025, Vanderbilt, Nashville Tennessee (May 2025).
  Abstract: This talk concerns frames and equiangular lines over finite fields. We find a necessary and sufficient condition for systems of equiangular lines over finite fields to be equiangular tight frames (ETFs). As is the case over subfields of $\mathbb{C}$, it is necessary for the Welch bound to be saturated, but there is an additional condition required involving sums of triple products. We also prove that similar to the case over $\mathbb{C}$, collections of vectors are similar to a regular simplex essentially when the triple products of their scalar products satisfy a certain property. Finally, we investigate switching equivalence classes of frames and systems of lines focusing on systems of equiangular lines in finite orthogonal geometries with maximal incoherent sets, drawing connections to combinatorial design theory.
  Presentation: Presentation
  
  

Seminar Talks

• Theorems for Free?
  Applied Category Theory Seminar (November 2024). Presentation Coming Soon


• What is Algebra? Why should you care? And what make it so abstract anyways?
  Lightning talk, Greenslopes Graduate Seminar (October 2024). Presentation Notes


• Composition, Categories, and Databases
  Applied Category Theory Seminar (September 2024). Presentation Notes


• Suboject Classifiers and Defining a Topos
  Applied Category Theory Seminar (April 2024). Presentation: Notes


• F-Algebras and Catamorphisms in Scala
  Applied Category Theory Seminar (November 2023). Presentation: Slides


• Maximal Systems of Equiangular Lines in Finite Unitary Geometry
  Greenslopes Graduate Seminar (October 2023)
  Abstract: This talk will explore Unitary Geometries and systems of equiangular lines and how they relate to luxury cars (Mercedes-Benz) as well as quantum computing. We will start by talking about the speaker's limited view of "geometry" which allows them to effortlessly generalize geometry to be a special case of frame theory. We will then discuss some well-known results in frame theory for complex frame and real frames and the more recent generalizations in their finite field analogs. These connect back to the original goal of the talk which is exploring systems of equiangular lines. We will then look at some open problems and connections to quantum computing.


• Simple Types
  Applied Category Theory Seminar (January 2023)


• A Nondeterministic Introduction to Complexity Theory
  Greenslopes Graduate Seminar (December 2022)


• The DisCoCat (Distributional Compositional Categorical) model of meaning
  Applied Category Theory Seminar (October 2022)


• Examples of Functors and Natural Transformations
  Applied Category Theory Seminar (September 2022)

Conferences Attended

• Groups, Nilpotents and Tensors (April 2023)
  Colorado State University, Fort Collins, Colorado
• Recent Progress on Optimal Point Distributions and Related Fields (June 2024)
  ICERM, Providence, Rhode Island Partially Funded By Conference

Seminars Organized

• Greenslopes: Joint Math and Statistics Graduate Seminar
  Previous Organizer, with Joe Geisz, during Fall 2024.