Cynthia Vinzant
Email: clvinzan (at) ncsu.edu
Office: 3260 SAS Hall
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, Spring 2018
Math/CSC 416: Introduction to Combinatorics
Math 526: Algebraic Geometry
Recent and upcoming events

Summer School on Hyperbolic Polynomials, Sums of Squares and
Optimization  Georgia Tech, June 25  29, 2018

MiniWorkshop: Algebraic, Geometric, and Combinatorial Methods in
Frame Theory  Oberwolfach, Oct. 15, 2018

Triangle Lectures in Combinatorics  UNC Chapel Hill, November 10,
2018

AMS Short Course: Sum of Squares: Theory and Applications, JMM
Baltimore,
Jan. 14  15, 2019

Geometry of Real Polynomials, Convexity and Optimization  Banff,
May 27 31, 2019

Nonlinear Algebra  ICERM, Fall 2018

Geometry of Polynomials  Simons Institute, Spring 2019
Research Group
Writings

Logconcave polynomials, entropy, and a deterministic approximation
algorithm for counting bases of matroids
(with Nima Anari and
Shayan Oveis
Gharan), FOCS 2018.

Generalized eigenvalue methods for Gaussian quadrature rules
(with Greg
Blekherman,
Mario Kummer,
Cordian
Riener, and
Markus Schweighofer), submitted.

Semiinverted linear spaces and an analogue of the broken circuit complex
(with Georgy Scholten), submitted.

The Chow form of a reciprocal linear space
(with Mario
Kummer), to appear in Michigan Math. Journal.

Gram spectrahedra
(with Lynn Chua, Daniel
Plaumann, Rainer Sinn),
Ordered algebraic structures and related topics, Contemp. Math., 697, (2017) pp. 81  105.

Lowrank sumofsquares representations on varieties of minimal degree
(with Greg Blekherman, Daniel
Plaumann, Rainer Sinn),
to appear in International Mathematics Research Notices.
 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 ...
Spring 2017, Math 437: Applications of
Algebra
Spring 2017, Reading course on Algorithms in Invariant Theory
Fall 2016, Math 526: Algebraic
Geometry
Spring 2016, Math 591: Tropical
Geometry
Fall 2015, Math 526: Algebraic
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.