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Ph.D. (2013) Texas A&M University
Youngin Kim is performing an independent study on numerical methods for solving polynomial systems Spring 2016.
Billy Broeckelman had an undergraduate research fellowship to study Schubert calculus for three semesters from Fall 2014 to Spring 2015.
Kim Mesewinkel-Risse performed an independent study on Groebner bases and convex polytopes Spring 2015.
Algebraic Geometry and Algebraic Combinatorics
I use highly structured polynomial systems 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 reality theorems. Recent projects have included the development of new square formulations for classical overdetermined problems, allowing them to be studied on computers.
A lifted square formulation for certifiable Schubert calculus (with Sottile), Journal of Symbolic Computation (to appear), 17 pp.
A primal-dual formulation for certifiable computations in Schubert calculus (with Hauenstein and Sottile), Foundations of Computational Mathematics (to appear), 21 pp.
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 no. 1 (2013), 33-58.
The Secant Conjecture in the real Schubert calculus (with Garcia-Puente, Hillar, Martin del Campo, Ruffo, Sottile, and Teitler), Experimental Mathematics, 21 no. 3 (2012), 252-265.