Lucius T. Schoenbaum 

Categorical Logic, Topos Theory, and related subjects.
My advisor is Daniel Sage. Here is a research statement.
Papers
"On the Syntax of Logic and Set Theory." Review of Symbolic Logic, 3, September 2010 arXiv:1003.4102"Towards Visual Type Theory as Mathematical Tool and Mathematical User Interface." Proceedings of 2016 Conference on Intelligent Computer Mathematics (CICM 2016) Bialystok, Poland. link arXiv:1608.03026
"Monads and Generalized Categories." 2016. draft
"A Generalization of the CurryHoward Correspondence." 2016. arXiv:1612.02816
"Ideal Toposes: First Report." in progress.
"Introduction to Generalized Categories." 2016. arXiv:1612.02885
Other Work
"Towards Theory and Applications of Generalized Categories in Areas of Type Theory and Categorical Logic." PhD thesis, in progress."Philosophy, Mathematics, and Proof Theory." Master's thesis. link