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Ph.D. (2013) Texas A&M University
Billy Broeckelman is studying Schubert calculus with me. Billy is an undergraduate research fellow at UNK (2014-present).
Algebraic Geometry and Combinatorics
I use polynomial systems with a lot of structure to study phenomena in algebraic geometry. This occurs at the interface between pure and computational mathematics. Some of my projects have involved solving billions of related systems to detect real structures. My most recent projects have been to develop new square formulations for classical overdetermined problems, allowing them to be studied on computers.
A primal-dual formulation for certifiable computations in Schubert calculus (with Hauenstein and Sottile), Foundations of Computational Mathematics (to appear).
A congruence modulo four in real Schubert calculus (with Sottile and Zelenko), Crelle's Journal, (online) February 2014 (print - to appear), 24 pp.
Lower bounds in real Schubert calculus (with Hillar and Sottile), Sao Paulo Journal of Mathematical Sciences 7, 1 (2013), 33-58.