I was employed by Professor Allen Knutson and Professor Tara Holm (DMS-1711317) in the Spring of 2024 as a research assistant working on some problems in toric geometry. I have some notes about moment maps and equivariant cohomology in toric geometry which you can find here.
I did a reading course about algebraic groups with Professor Daniel Halpern-Leistner in the Fall of 2023. The notes from the course became an expository paper which you can find here.
I participated in the CAAR-REU at the University of Maryland in the Summer of 2022. During that time, I thought about classical projective geometry. Coxeter has a wonderful book where he shows how to construct a conic in the plane through 5 points using just a ruler. Note that 5 points determines the conic (there are six monomials of degree 2 in 3 variables, and 5 points would impose 5 linear equations on the coefficients and also scaling the coefficients gives the same conic). Nowadays people think about these problems with the modern techniques of enumerative geometry. At the REU, we worried about computational aspects of particular configurations of points in projective geometry. In particular we wanted numerical solutions, but I was pleased to find that one can construct the desired “bisector” using just a ruler. You can find the REU paper here.