I am an NSF Research Fellow and postdoc at Rutgers University, where I am mentored by Jeff Kahn. For the 2014-2015 academic year, I was a postdoc at the Institute for Mathematics and its Applications, where I participated in the Discrete Structures: Analysis and Applications program. I spent the first year of my NSF fellowship at UCLA, where I was mentored by Benny Sudakov and the second year at Carnegie Mellon, where I was mentored by Po-Shen Loh.
Before coming to Los Angeles, I was a Ph.D. student in mathematics at UCSD advised by Jacques Verstraete. I was an undergraduate at Caltech and an MMath student in the Combinatorics and Optimization department at University of Waterloo. I've held visiting positions at IPAM and the Renyi Institute thanks to generous funding from NSF-CESRI and Fulbright.
My research lies in the field of extremal combinatorics, specifically extremal set theory questions and their analogues for other discrete structures. Given a finite set X, the general problem in extremal set theory asks how large or small a family of subsets of X can be if it satisfies certain restrictions. Naturally, this type of question appears throughout mathematics, and so extremal set theory can be applied in areas ranging from discrete geometry to theoretical computer science. On the other hand, extremal set theory borrows tools from algebra and probability, and its connections to other branches of mathematics is one of its most beautiful features.
Remarkable analogues of extremal set theory results hold for other objects such as vector spaces, permutations, and subsums of a finite sum. Tantalizingly, while many results about sets should generalize to different settings, not much is known about analogues because standard techniques do not always apply.