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
Mini-Workshop: Algebraic, Geometric, and Combinatorial Methods in
Frame Theory - Oberwolfach, Oct. 1-5, 2018
Triangle Lectures in Combinatorics - UNC Chapel Hill, November 10,
AMS Short Course: Sum of Squares: Theory and Applications, JMM
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
Log-concave polynomials, entropy, and a deterministic approximation
algorithm for counting bases of matroids
(with Nima Anari and
Gharan), FOCS 2018.
Generalized eigenvalue methods for Gaussian quadrature rules
Markus Schweighofer), submitted.
Semi-inverted linear spaces and an analogue of the broken circuit complex
(with Georgy Scholten), submitted.
The Chow form of a reciprocal linear space
Kummer), to appear in Michigan Math. Journal.
(with Lynn Chua, Daniel
Plaumann, Rainer Sinn),
Ordered algebraic structures and related topics, Contemp. Math., 697, (2017) pp. 81 - 105.
Low-rank sum-of-squares 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),
Computing Hermitian determinantal representations of hyperbolic curves
Plaumann, Rainer Sinn, and
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.
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)
(with John Christian Ottem,
Kristian Ranestad, and Bernd Sturmfels),
Mathematical Programming, 2(151) Series B, pp. 585-612.
Hyperbolic polynomials, interlacers, and sums of squares
(with Mario Kummer and Daniel Plaumann),
Mathematical Programming, 1(153) Series B (2015), pp. 223-245.
Determinantal representations of hyperbolic plane curves: An elementary approach
(with Daniel Plaumann),
Journal of Symbolic Computation 57 (2013) pp. 48-60.
- The entropic
discriminant (with Raman Sanyal and Bernd Sturmfels),
Advances in Mathematics, 244 (2013) pp. 678-707.
- The central curve in
linear programming (with Jesús De
Loera and Bernd
Sturmfels), Foundations of Computational Mathematics 12 (2012)
- 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) pp. 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
Undergraduate Research Projects
At NC State ...
Spring 2017, Math 437: Applications of
Spring 2017, Reading course on Algorithms in Invariant Theory
Fall 2016, Math 526: Algebraic
Spring 2016, Math 591: Tropical
Fall 2015, Math 526: Algebraic
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.