- 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.
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.
- 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
This Winter, I'm teaching Math 216: Introduction to Differential Equations. In the past, I have taught Math 216, Math 217 and Math 115 at Michigan, as well as Math 1B at Berkeley.
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.