- Email: vinzant (at) umich.edu
- Office: 1846 East Hall
- Office Phone: (734) 936-4824
- Research Statement
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.
A real stable extension of the Vámos matroid polynomial
(with Sam Burton and Yewon Youm), in preparation. Based on a Summer 2013 REU project.
An algebraic characterization of
injectivity in phase retrieval
(with Aldo Conca, Dan
Edidin, and Milena
(with John Christian Ottem,
Kristian Ranestad, and Bernd Sturmfels),
submitted to the special issue of Mathematical Programming, Series B on "Polynomial Optimization".
Hyperbolic polynomials, interlacers, and sums of squares
(with Mario Kummer and Daniel Plaumann),
to appear in the special issue of Mathematical Programming, Series B on "Lifts of Convex Sets in Optimization".
Determinantal representations of hyperbolic plane curves: An elementary approach
(with Daniel Plaumann),
Journal of Symbolic Computation 57 (2013) 48-60.
- The entropic
discriminant (with Raman Sanyal and Bernd Sturmfels),
Advances in Mathematics, 244 (2013) 678-707.
- 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 semester (Fall 2013) I am not teaching any courses. In the past, I have taught Math Math 216 (Differential Equations), Math 217 (Linear Algebra) and Math 115 (Calc. I) at Michigan, as well as Math 1B (Calc. II) at Berkeley.
I'm also a former staff member (2006, 2007) of the Hampshire College Summer Studies in
Mathematics, a summer program for mathematically inclined high school students.