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"What is now proved was once only imagined." Left: A rendition of a Calabi–Yau threefold, a six-dimensional space used in certain models of string theory. My research is in geometric analysis, an exciting area at the intersection of differential geometry and partial differential equations, which has many applications to physics as well as to other areas of math, including algebraic geometry and low-dimensional topology. My interests include geometric variational problems, such as existence and regularity of harmonic maps and minimal submanifolds, as well as complex geometry. While I was an undergraduate, I was researching matroids, which generalize the notion of linear independence in a vector space, affine independence in an affine space, and independence of edge sets in a graph. Here is a list of my publications and preprints:
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