Visiting Assistant Professor
BMath, University of Waterloo, 2011
M.A.St., University of Cambridge, 2012
Ph.D., University of California - Berkeley, 2017
Algebra and Algebraic Geometry, Discrete Math, Operations Research, and Probability
My research centers around total positivity, which is the study of spaces and their positive parts. For example, a square matrix is called totally positive if all of its square submatrices have a positive determinant. Such matrices can be parametrized using networks, and all their eigenvalues are real and positive. I study the positive parts of matrix spaces and their generalizations, such as algebraic groups and flag varieties, and explore their connections with areas such as combinatorics, representation theory, topology, and theoretical physics.
- (with Pavel Galashin and Thomas Lam) Regularity theorem for totally nonnegative flag varieties. J. Amer. Math. Soc. 35 (2022), no. 2, 513–579.
- Moment curves and cyclic symmetry for positive Grassmannians. Bull. Lond. Math. Soc. 51 (2019), no. 5, 900–916. arXiv:1805.06004
- (with Lauren K. Williams) The m=1 amplituhedron and cyclic hyperplane arrangements. Int. Math. Res. Not. IMRN (2019), no. 5, 1401–1462. arXiv:1608.08288
Office: 108 Hayes-Healy Bldg.
255 Hurley Bldg
Notre Dame, IN 46556-4618