My current research is in trisections of smooth 4manifolds. Trisections are a 4dimensional analog of Heegaard splittings of 3manifolds. A trisection of a smooth, closed 4manifold is a decomposition three 4dimensional 1handlebodies whose pairwise intersections are 3dimensional handlebodies and triple intersection is a surface.
There are many analogies between the theories of trisections and Heegaard splittings. For example, every smooth closed 4manifold admits a trisection which is unique up to the appropriate notion of stabilization. There are also trisection diagrams where is a closed, genus surface and each of are tuples of nonseparating, simple, closed curves in such that each triple is a Heegaard diagram for
Publications and Preprints:

The Relative L–invariant of a Compact 4manifold with Boundary, with Gabriel Islambouli, Maggie Miller, and Maggy Tomova. arXiv:1908.05371, 2019. Submitted.

Trisections of 4manifolds via Lefschetz fibrations, with Burak Ozbagci. Mathematical Research Letters 26(2): 383420, 2019.
 On Dividing a Rectangle, with Robert Dumitru*, Quinn Perian*, Alexander Nealey*, Mohammed Mannan*, Eddie Beck, David Gay, Dipen Mehta*, Anish Pandya*, Ejay Cho*, 2018. (This paper was the result of a research group of Camp Euclid 2016. (*) indicates high school coauthor.)
 Trisecting 4manifolds with Boundary, with David T. Gay and Juanita Pinzón Caicedo. Proceedings of the National Academy of Sciences Oct 2018, 115 (43) 1086110868
 Trisecting Smooth 4dimensional Cobordisms, arXiv:1703.05846, 2017
 Diagrams for Relative Trisections, with David T. Gay and Juanita Pinzón Caicedo, Pacific Journal of Mathematics 294 (2):275305, 2018
 Relative Trisections of Smooth 4manifolds with Boundary, Ph.D. Thesis, The University of Georgia, 2016