Cynthia Vinzant
Email: clvinzan (at) ncsu.edu
Office: 3260 SAS Hall
Office hours: Monday, Wednesday 12pm or by appointment
As of 2015, I am an assistant
professor in the math
department at North Carolina State University.
My research involves convex
algebraic geometry and applications of real algebraic geometry and
tropical geometry to convex optimization, in particular semidefinite
programming. In 2011, I completed my Ph.D. thesis, Real Algebraic Geometry in Convex
Optimization, at UC
Berkeley, where my advisor was Bernd Sturmfels. I was an
undergraduate at Oberlin College.
Teaching
During Fall 2016, I am teaching Math
526: Algebraic Geometry.
Recent and upcoming events

Reading seminar on tropical geometry and optimization  NCSU, May and June, 2016

Algebraic vision  AIM, May 26, 2016

International Symposium on Mathematical Theory of Networks and
Systems  Minneapolis, July 1215, 2016

Triangle Lectures in Combinatorics  NCSU, November 19, 2016

Algorithms and Effectivity in Tropical Mathematics and Beyond
Schloss Dagstuhl, Nov. 27  Dec. 2, 2016

Semester on Nonlinear Algebra  ICERM, Fall 2018
Research Group
Writings

Gram spectrahedra
(with Lynn Chua, Daniel
Plaumann, Rainer Sinn),
submitted.

Lowrank sumofsquares representations on varieties of minimal degree
(with Greg Blekherman, Daniel
Plaumann, Rainer Sinn),
submitted.
 Computing complex and real tropical curves using monodromy
(with Daniel Brake and Jonathan Hauenstein),
submitted.

Computing Hermitian determinantal representations of hyperbolic curves
(with Daniel
Plaumann, Rainer Sinn, and
David Speyer),
International Journal of Algebra and Combinatorics, 25(8) (2015)
pp. 1327  1336.
 A small frame and a
certificate of its injectivity. Sampling Theory and Applications
(SampTA) Conference Proceedings. (2015), pp. 197  200.
Supplementary material.

A real stable extension of the Vámos matroid polynomial
(with Sam Burton and Yewon Youm).

What is a spectrahedron?
Notices of the American Mathematical Society 61(5) (2014) pp. 492  494.

An algebraic characterization of
injectivity in phase retrieval
(with Aldo Conca, Dan
Edidin, and Milena
Hering), Applied and Computational Harmonic Analysis 38:2 (2015)
pp. 346356.

Quartic spectrahedra
(with John Christian Ottem,
Kristian Ranestad, and Bernd Sturmfels),
Mathematical Programming, 2(151) Series B, pp. 585612.

Hyperbolic polynomials, interlacers, and sums of squares
(with Mario Kummer and Daniel Plaumann),
Mathematical Programming, 1(153) Series B (2015), pp. 223245.

Determinantal representations of hyperbolic plane curves: An elementary approach
(with Daniel Plaumann),
Journal of Symbolic Computation 57 (2013) pp. 4860.
 The entropic
discriminant (with Raman Sanyal and Bernd Sturmfels),
Advances in Mathematics, 244 (2013) pp. 678707.
 The central curve in
linear programming (with Jesús De
Loera and Bernd
Sturmfels), Foundations of Computational Mathematics 12 (2012)
pp. 509540.
 Computing Linear Matrix Representations of HeltonVinnikov 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. 259277.
Supplementary material.
 Quartic curves and
their bitangents (with Daniel
Plaumann and Bernd
Sturmfels), Journal of Symbolic Computation 46 (2011) pp. 712733. Supplementary material.
 Edges of the BarvinokNovik orbitope,
Discrete & Computational Geometry 46(33) (2011) pp. 479487.
 Real radical initial ideals,
Journal of Algebra, 352(1) (2012), pp. 392407

Lower bounds for optimal alignments of binary sequences, Discrete Applied Math. 157:15 (2009), pp. 33413346.
 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
Undergraduate Research Projects
Past teaching
At NC State, I have previously taught courses on Algebraic
Geometry and Tropical Geometry.
Before coming to NC State, I 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.