Email: vinzant (at) umich.edu

Office: 1846 East Hall

Office Phone: (734) 936-4824

Office Hours: Monday 3-5pm, Friday noon-1pm (Math Lab)

I'm a Hildebrandt assistant professor and NSF postdoc in the math department at University of Michigan, Ann Arbor. My research involves convex algebraic geometry and applications of real algebraic geometry and tropical geometry to convex optimization, in particular semidefinite programming. I recently finished my Ph.D. thesis, Real Algebraic Geometry in Convex Optimization, at UC Berkeley, where my advisor was Bernd Sturmfels.

Writings

• Hyperbolic polynomials, interlacers, and sums of squares (with Mario Kummer and Daniel Plaumann).

• Determinantal representations of hyperbolic plane curves: An elementary approach (with Daniel Plaumann), submitted to the special issue of the Journal of Symbolic Computation on Classical Algebraic Geometry.

• The entropic discriminant (with Raman Sanyal and Bernd Sturmfels), to appear in Advances in Mathematics.

• The central curve in linear programming (with Jesús De Loera and Bernd Sturmfels), Foundations of Computational Mathematics 12 (2012) 509-540.

• Computing Linear Matrix Representations of Helton-Vinnikov Curves, with Daniel Plaumann and Bernd Sturmfels), Mathematical Methods in Systems, Optimization and Control, (eds. Harry Dym, Mauricio de Oliveira, Mihai Putinar), Operator Theory: Advances and Applications, Vol 222, Birkhauser, Basel, 2012, pp. 259-277. Supplementary material.

• Quartic curves and their bitangents (with Daniel Plaumann and Bernd Sturmfels), Journal of Symbolic Computation 46 (2011) 712-733. Supplementary material.

• Edges of the Barvinok-Novik orbitope, Discrete & Computational Geometry 46(33) (2011) pp. 479-487.

• Real radical initial ideals, Journal of Algebra, 352(1) (2012), pp. 392–407

• Lower bounds for optimal alignments of binary sequences, Discrete Applied Math. 157:15 (2009), pp. 3341-3346.

• Mathematical approaches to the pure parsimony problem (with Paul Blain, Courtney Davis, Al Holder, and Jorge Silva), appearing as "Diversity Graphs" in "Clustering Challenges in Biological Networks"

Slides from Talks

• A sums of squares relaxation for hyperbolicity cones - SIAM, Minneapolis, July 2012
• The central curve in linear programming - UW Madison, January 2011
• The convex hull of a parametrized curve - SIAM, Pittsburgh, July 2010
• Faces of the Barvinok-Novik Orbitope - Banff, February 2010
• Degree stability of SOS modulo an ideal - UC Davis, May 2009
• Parametric sequence alignment - SFSU, September 2008

Teaching

I'm a former staff member (2006, 2007) of the Hampshire College Summer Studies in Mathematics, a summer program for mathematically inclined high school students.