5 Minutes with Soledad Villar

Number theory and Uruguay data science? As part of this month’s Women in Data Science at CDS series, we catch up with Moore Sloan Research Fellow, Soledad Villar

Soledad Villar is a Moore-Sloan Research Fellow at NYU’s Center for Data Science, and she holds a Collaborative Scientist appointment at the Algorithms and Geometry Simons Collaboration.

She was formerly a Research Fellow at UC Berkeley’s Simons Institute. She earned a Ph.D. in Mathematics at the University of Texas at Austin, a Master’s in Number Theory and Bachelor’s in Mathematics from Universidad de la Republica in Uruguay, and a Bachelor’s in Computer Science from Universidad Catolica del Uruguay. Her research focuses on optimization, statistics, machine learning, and applied harmonic analysis. She is also interested in number theory.

1. How did you decide to become a Moore-Sloan Research Fellow, and how has the experience been so far?

Being a Moore-Sloan Research Fellow is a unique opportunity for an applied mathematician. The position provides me with the freedom to develop my own research program and the opportunity to collaborate in multidisciplinary research (not to mention that the NYU Courant Institute is just down the road, which has a top math department). My experience has been great so far. I am happy to be part of the Math and Data group organized by Afonso Bandeira, Joan Bruna and Carlos Fernandez-Granda.

Since I joined NYU, I have started working in different problems in addition to my previous line of work. I have been thinking about deep learning from a theoretical point of view and I am exploring some applications of deep learning to social sciences. I am grateful that my job is awesome.

2. Have you encountered differences in the way data science is approached in Uruguay compared to the United States?

I am by no means an authority to talk about data science in Uruguay—but from the industry point of view, most of my knowledge about the state of data science in Uruguay is through my sister, Florencia, who works as a data science consultant in the Uruguayan branch of a large multi-national company.

In her experience, the main differences between data science in Uruguay and US are in terms of scale (the amount of data managed in Uruguay is smaller, given that Uruguay is a country with 3 million people) and broadness (in Uruguay data science is exclusively used for commercial applications, whereas here it has been applied in many fields, including manufacturing and health care).

From the academic point of view, based on my experience as a math student in Uruguay, I found that the mathematics curricula was focused in pure mathematics and did not really offer a perspective on applications. Collaborations between mathematicians and researchers from other fields are very rare. I think that trend is slowly changing and now we can see more collaboration between math and engineering.

3. What initiated your interest in number theory? Does that interest overlap with your focus on optimization?

My interest in number theory started from the math olympiads (which I started participating in when I was twelve years old). In college, I studied math and computer science, and I was initially interested in the computational side of number theory. For instance, how one can use groups arising from number theory objects (like elliptic curves) to do cryptography.?My undergrad and masters advisor, Gonzalo Tornaria, is a number theorist that sometimes works in very intense computational projects, like verifying a famous number theory conjecture up to 10¹² by using sophisticated engineering solutions.

I arrived to optimization from a computational motivation, particularly as an approach to combinatorial problems. I haven’t explored a connection between optimization and number theory yet.

4. What are you currently working on as part of your Moore-Sloan Fellowship, and what do you hope to be working on in the future?

I am currently working on a project with Dustin Mixon (Ohio State) where we analyze some aspects of gerrymandering from a game theoretical point of view and we produce numerical simulations. I am also discussing with Joan Bruna about deep learning for problems in graph and how these techniques can compare to (or can take ideas from) classical optimization approaches.

Another line of work I have explored with Dustin is the use of generative models for classical signal processing inverse problems like image denoising. We’re trying to explain what activation functions allow denoising by local methods using spherical harmonics.

On a more theoretical note, I am also co-organizing a seminar with Afonso Bandeira, Shuyang Ling and Tim Kuninsky where we look at a specific problem on random graphs and explore what type of solutions different algorithms from the literature can provide. In particular there is a type of algorithm arising from a Bayesian approach that can be analyzed using techniques from statistical physics. I am especially interested in understanding the techniques and applying them to other problems related to data science (it has been suggested that they may even have applications to deep learning). I am also working with Efe Onaran at NYU Tandon to apply these techniques to graph matching.

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