Taught the course, Math in Human Society, which surveyed the utility and importance of mathematics in communication, finance, political theory, and other domains.

Social network analysis. We have brought statistical, graph-theoretic, and discrete homological tools to bear on massive real-world social networks, with goals of better understanding and predicting individual connections and aggregate network structure, and of identifying structural properties associated to important real-world behaviors and communities.

For several semesters each i tutored and supervised tutors at the Math Emporium, instructed / guided vector geometry recitations, and instructed full courses in differential calculus, vector geometry, and multivariable calculus. I also founded and organized an undergraduate seminar series in mathematical modeling.

Geometric combinatorics; Schubert calculus. I contributed to the Focused Research Group in Affine Schubert Calculus through my thesis and supplemental projects. My thesis project is to construct an explicit polynomial homology class associated with an affine Schubert variety. The class is that of a matrix variety obtained as the closure of a two-sided orbit whose projection is the affine Schubert variety. This would imbue the polynomial with geometric naturality. The construction uses equivariant cohomology, and degree-one ideal generators are defined and proved using new combinatorics. A well-chosen Gröbner basis for the ideal is expected to yield a combinatorial proof that the polynomial is in fact a k-Schur polynomial, and therefore to provide a geometric expansion of k-Schur functions into Schur functions.

Responsible coffee delivery. We delivered roasts from Strange Coffee Company and raised awareness about farming, trade, and roasting issues.