PhD student in Mathematics

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 solevillar.github.io.

- 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]

- A polynomial-time relaxation of the Gromov-Hausdorff distance.
- With A. S. Bandeira, A. J. Blumberg and R. Ward. (submitted)

- 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)

- 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).

- Differential equations
- From numbers to chaos
- Differential calculus
- Integral calculus
- Functions of a complex variable
- Introduction to mathematics

- Introduction to topology
- Programming (Python)
- Programming (Haskell)
- Linear algebra
- Mathematics for life sciences

- Complex analysis (teaching assistant)
- Linear algebra (lecturer)