Welcome
A little about my research
Although I am affiliated with the Electrical and Systems Engineering department at Penn, I consider myself neither an engineer nor a mathematician, but something in between. As a mathematician, I work in areas of applied category theory, algebraic combinatorics, and applied algebraic topology. As an engineer, I focus on application areas in multi-agent systems. In particular, I am interested in robotic systems, graph signal processing, and opinion dynamics.
Of paramount importance to my research is a curious operator called the Tarski Laplacian, inspired by the combinatorial Hodge Laplacian (maybe going back to De Rahm but formally introduced in a 1944 German-language journal by Beno Eckmann) which specializes to the (inner-product space) sheaf Laplacian which in turn specializes to the ubiquitous graph Laplacian, known for its central place in spectral graph theory. The Tarski Laplacian acts on assignments of data to a so-called sheaf: an abstract mathematical object that collects data over networks. In particular, the Tarski Laplacian acts on data collected by (order) lattices (e.g. the lattice of subspaces of a vector space, lattice of subsets of a set) called stalks ‘living above’ the nodes of a network.
A little about me
I was born and raised in Bloomington, Indiana. I did my undergrad in Durham, North Carolina. I am now working on my doctorate in Philadelphia, Pennsylvania. I enjoy playing tennis and biking. I enjoy listening and playing jazz and classical music. Above all, I enjoy spending time with my fiancée.