If you are looking for a summary of my research, please read my research statement (pdf) from 2011 (for mathematicians) or the first page of a simpler research statement from 2017 (for scientists). My research interests lie in geometric analysis. Specifically, I study the mean curvature flow and gluing constructions for elliptic and parabolic equation but I am also interested in other geometric evolution equations (Ricci flow, inverse mean curvature flow,...), minimal surfaces, and free boundary problems. In general, I enjoy problems involving geometry and partial differential equations. The picture on the left is a knitted Scherk surface. I created a webpage with the pattern (no seaming!) and a brief intro to the Scherk surface and other minimal surfaces. 
Publications
 (version: November 08, 2016) Shrinking doughnuts via variational methods (with G. Drugan). Submitted to Journal of Geometric Analysis.
 (version: March 08, 2017) Iterated Routh's triangles (with E. Carroll, A. P. Ghosh, and A. Roitershtein). Accepted in the Journal for Geometry and Graphics.
 (version: January 12, 2017) Finite topology selftranslating surfaces for the mean curvature flow (with Juan Davila and Manuel Del Pino). Accepted in Advances in Mathematics (August 2017).
 (version: April 07, 2016) Mean curvature flow of entire graphs evolving away from the heat flow (with G. Drugan). Proceedings of the AMS 145 (2017), pp. 861869.

(version: June 27, 2014) Doubly periodic selftranslating surfaces for the mean curvature flow.
Geometriae Dedicata 174 (2015), 177185.

(version: July 2, 2014) Construction of Complete Embedded SelfSimilar Surfaces under
Mean Curvature Flow. Part III (pdf). Duke Mathematical Journal,
August 2014, Volume 163, number 11, pp 20232056

Complete Embedded SelfTranslating Surfaces under
Mean Curvature Flow (pdf). Journal of Geometric Analysis,
July 2013, Volume 23, Issue 3, pp 13791426
 A longitudinal study on students' development and transfer of the concept of integration (pdf) (with A. Bennett and T. Moore). American Society for Engineering Education Conference Proceedings, June 2629, 2011, Vancouver, British Columbia, Canada.
 Construction of Complete Embedded SelfSimilar Surfaces under Mean Curvature Flow. Part II (pdf). Advances in Differential Equations, volume 15, numbers 56, April/May 2010.
 Translating Tridents (pdf). Comm. in Partial Differential Equations, volume 34, Issue 3 (2009), p 257280.
 Construction of Complete Embedded SelfSimilar Surfaces under Mean Curvature Flow. Part I (pdf). Trans. of the Amer. Math. Soc. 361 (2009), 16831701.
In preparation
 Desingularization of immersed surfaces (with Stephen Kleene).
 A survey of closed selfshrinkers for the mean curvature flow (with G. Drugan and H. Lee)