Cynthia Vinzant

Email: vinzant (at) umich.edu

Office: 1846 East Hall

Office Phone: (734) 936-4824

Office Hours: Monday 1-3pm, Friday 2-3pm

I'm an RTG assistant professor 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

The entropic discriminant (with Raman Sanyal and Bernd Sturmfels), submitted to Advances in Mathematics.
The central curve in linear programming (with Jesús De Loera and Bernd Sturmfels), submitted to Foundations of Computational Mathematics
Computing Linear Matrix Representations of Helton-Vinnikov Curves, with Daniel Plaumann and Bernd Sturmfels), to appear in the volume in honor of Bill Helton, Mathematical Methods in Systems, Optimization and Control, eds. Harry Dym, Mauricio de Oliveira, Mihai Putinar, "Operator Theory: Advances and Applications". 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

The central curve in linear programming - UW Madison, 1/27/11
The convex hull of a parametrized curve - SIAM, Pittsburgh, 7/15/10
Faces of the Barvinok-Novik Orbitope - Banff, 2/18/10
Degree stability of SOS modulo an ideal - UC Davis, 5/21/09
Parametric sequence alignment - SFSU, 9/19/08

Unbounded Representation

UREP is a graduate student group at UC Berkeley focused on promoting diversity within the department. One of the projects UREP sponsors is a speaker series called Career Talks on the different career paths available after graduate school. I helped organize this along with (at various times) Trevor Potter, Anne Shiu, Betsy Stovall and Harold Williams. Suggestions for speakers are always welcome.

Teaching

This Winter, I'm teaching Math 217: Linear Algebra. The course material for students is posted on CTools. In Fall 2011, I taught Math 115.

In Fall 2007 and Spring 2008, I was a GSI for 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.