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I am an NSF Research Fellow and Assistant Adjunct Professor at UCLA under Benny Sudakov. Before coming to Los Angeles, I was a Ph.D. student in mathematics at UCSD under 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 analogs 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 topology 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 analogs 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 analogs because standard techniques do not always apply.