Cynthia Vinzant
Email: clvinzan (at) ncsu.edu
Office: 3260 SAS Hall
Office hours: Tuesday 11:30am12:30pm, Wednesday 1:302:30pm 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 Spring 2017, I am teaching Math
437: Applications of Algebra.
I am also running a reading course on Algorithms in Invariant Theory.
Recent and upcoming events

Workshop on the Interface of Statistics and Optimization,
SAMSI, Feb. 810, 2017

Real Algebraic Geometry With a View Toward Moment Problems and Optimization,
Oberwolfach, March 511, 2017

SIAM Optimization, Minisymposium on Polynomial optimization and
sumsofsquares, Vancouver,
May 2225, 2017

Workshop on Computational Algebraic Geometry, FOCM, Barcelona,
July 1012, 2017

ILAS, Minisymposium on Linear Algebra and Positivity with
Applications to Data Science, Iowa State U.,
July 2428, 2017

SIAM conference on Applied Algebraic Geometry, Atlanta,
July 31  Aug. 4, 2017

Bridging Continuous and Discrete Optimization 
Simons Institute, Fall 2017

Geometric and Topological Combinatorics  MSRI, Fall 2017

Nonlinear Algebra  ICERM, Fall 2018
Research Group
Writings

The Chow form of a reciprocal linear space
(with Mario
Kummer), submitted.

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.