Soledad Villar
University of Texas at Austin
2515 Speedway
RLM 10.126
mvillar at math utexas edu

I am a PhD student in Mathematics at the University of Texas at Austin. My research is in mathematical data science and optimization. I am also interested in number theory. (Here is my CV.) I am very fortunate to have Rachel Ward as my advisor.

I am also a programmer. I write about my projects in my Blog. Below is my favorite so far (Clustering the MNIST data set using semidefinite programming).

Check out my blog at

Mathematical data science

I am interested in computational and mathematical aspects of extracting information from data. In particular I have studied and implemented optimization algorithms for machine learning related problems.


Journal papers (accepted)
Clustering subgaussian mixtures by semidefinite programming.
With D. G. Mixon and R. Ward. (accepted in Information and Inference) [code]
Probably certifiably correct k-means clustering.
With T. Iguchi, D. G. Mixon and J. Peterson. (accepted in Mathematical Programming) [code]
Journal papers (under revision)
A polynomial-time relaxation of the Gromov-Hausdorff distance.
With A. S. Bandeira, A. J. Blumberg and R. Ward. (submitted)
Conference papers
Relax, no need to round: integrality of clustering formulations.
With P. Awasthi, A. S. Bandeira, M. Charikar, R. Krishnaswamy and R. Ward. (on ITCS 2015)
On the tightness of an SDP relaxation of kmeans clustering.
With T. Iguchi, D. G. Mixon and J. Peterson. (preprint)

Number theory

I am also interested in number theory. I am very grateful to Gonzalo Tornaria, my advisor and mentor as an undergraduate and master student in Universidad de la Republica, Uruguay, who spent a lot of his time and energy teaching me math.
Gross formula on heights and special values of L-series.
My master thesis on modular forms and quaternion algebras (in Spanish).
Pell curves cryptography and generalizations.
My undergraduate thesis (in Spanish).

University of Texas at Austin (2012-present)

I have worked as a Teaching Assistant (leading discussion sessions, holding office hours and grading) for the following courses.
  • Differential equations
  • From numbers to chaos
  • Differential calculus
  • Integral calculus
  • Functions of a complex variable
  • Introduction to mathematics

Universidad de la Rep├║blica, Uruguay (2008-2012)

College of Engineering (2012)
I worked as an Instructor (holding lectures and grading) for Calculus 1.
College of Natural Sciences (2008-2012)
I worked as a Teaching Assistant (leading discussion sessions and grading) in the following courses.
  • Introduction to topology
  • Programming (Python)
  • Programming (Haskell)
  • Linear algebra
  • Mathematics for life sciences

Universidad Cat├│lica del Uruguay (2010-2011)

I worked as a teaching assistant and lecturer in the following courses.
  • Complex analysis (teaching assistant)
  • Linear algebra (lecturer)

Math Olympiads

I started doing math for fun thanks to the Uruguay Math Olympiads. After I graduated from high school I joined the organization as a volunteer. I worked as a trainer and a jury for the National Math Olympiads. I have conducted workshops and seminars for high school students and teachers in which I taught tools on problem solving.