Moore-Sloan Research Fellow

60 5th Ave, New York, NY 1011

Office 621

soledad.villar at nyu edu

I am Moore-Sloan Research Fellow at the Center for Data Science at New York University. I also have a Collaboration Scientist appointment at the Algorithms and Geometry Simons Collaboration.
Before this I was a Research Fellow at a semester-long optimization program at the Simons Institute, UC Berkeley.
On May 2017 I finished my PhD in Mathematics at the University of Texas at Austin, I was very fortunate to have Rachel Ward as my advisor.
My research is in mathematical data science and optimization. I am also interested in number theory. (Here is my CV.)

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

Optimization and learning techniques for clustering problems Statistical Physics and Machine Learning back together. Cargese, August 2018.

- 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]

- SqueezeFit: Label-aware dimensionality reduction by semidefinite programming.
- With C. McWhirter and D. G. Mixon.
- Fair redistricting is hard.
- With R. Kueng and D. G. Mixon.
- SUNLayer: stable denoising with generative networks.
- With D. G. Mixon.
- Monte Carlo approximation certificates for k-means clustering.
- With D. G. Mixon.
- A polynomial-time relaxation of the Gromov-Hausdorff distance.
- With A. S. Bandeira, A. J. Blumberg and R. Ward. [code]

- A note on learning algorithms for quadratic assignment with graph neural networks.
- With A. Nowak, A. S. Bandeira and J. Bruna (on IEEE Data Science Workshop, 2018). [code]
- Projected power iteration for network alignment.
- With E. Onaran (on SPIE 2017).
- Manifold optimization for k-means clustering.
- With T. Carson, D. G. Mixon and R. Ward (on SampTA 2017). [code]
- 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)