Research and Writing

My primary research interest is category theory and higher category theory.  Pursuit of these ideas often leads me to study abstract homotopy theory as well.

More specifically, I am interested in ways of taking traces of higher categories along various axes and in connected algebraic and homotopical models of higher categories.

	Research		Writing
Berger-Joyal Duality and Traces I (arXive:2509.11423)	In this paper my advisor and I extend Clemens Berger's duality between the n-fold wreath product and Joyal's combinatorial n-disks to allow descriptions of duals of other wreath products.	2-Categorical Pasting	The pasting theorem is a foundational result in the theory of 2-categories.  The first formal proof was produced by Power in 1990 where a pasting diagram is encoded as a plane graph with labels. When learning this result, I was curious if a proof could be obtained using Street's computads.
		Stacks as 2-Sheaves	A careful proof that a stack on the category of spaces - viewed as a category fibred in groupoids with conditions on descent data - is a 2-sheaf when interpreted as a pseudo-functor.
		Nets, Filters, and Convergence	My undergraduate thesis is an expository account of the theory of convergence space.  These generalize ordinary topological spaces by making the convergence of filters the primitive notion.