My research is in finite combinatorics and model theory, a branch of mathematical logic. My advisors were David Marker and Dhruv Mubayi. A general question I am interested in is: how does infinite structure arise as a “limit” of finite structures? Logical zero-one laws provide one way to make this question precise. Much of my research uses tools from extremal combinatorics to prove new logical zero-one laws. Specifically, we have proved new logical zero-one laws for discrete metric spaces and for multigraphs. I have also worked on problems concerning the model theory of homogeneous metric spaces and on problems concerning the role of model theoretic dividing lines in finite graph theory. After I finished my PhD in summer 2016, I accepted a position as a postdoctoral fellow at the University of Maryland.
My area of research is algebraic geometry. That is, zeros of polynomials. I use modern tools and language to study questions that can be traced back to the 19th century. People tend to call this sub discipline of mathematics classical algebraic geometry.
In 2010, I had the great pleasure of becoming a graduate student at UIC and the privilege of working with Izzet Coskun. After grad school I was appointed a postdoctoral fellowship at Harvard and again, had the privilege of working with many great people there, in particular Professors Dawei Chen and Joe Harris.
After seven good years in the US, I am happy to be back in México. I am now an assistant professor at the Nacional University of México in beautiful Oaxaca, where I live with my family.
My research area is in mathematical fluid dynamics, specifically questions regarding regularity for the Euler equations and the Navier-Stokes equations and questions about turbulence. During my graduate studies, I worked on the inviscid dyadic model, blow-up rates for solutions to the three-dimensional Navier-Stokes equations in Sobolev spaces, and the regularity of the three-dimensional Boussinesq equations through techniques such as Littlewood-Paley decomposition. During my postdoc, I began to study problems related to mixing in fluid dynamics. The applications of studying mixing are broad and quite practical, particularly apt for physical problems in heating/cooling and chemical/pharmaceutical production.
I was a PhD student in the MCS group and graduated in May, 2017. I chose theoretical computer science not only because it is beautiful mathematics, using tools from many areas, from combinatorics and graph theory to probability theory to complex analysis, but also because it answers interesting and important questions in fields outside mathematics, most importantly in computer science, but also in philosophy and the social sciences. My research interests are in computational complexity theory, combinatorial optimization, and machine learning. I was fortunate to be advised by Lev Reyzin and György Turán.
I found a very supportive and cooperative environment in the Math Department and more specifically in the MCS group, which made my time at UIC very enjoyable and productive. I collaborated with several professors and graduate students; I wrote one of my papers with four other coauthors! It is also partly due to the help of my advisors and fellow graduate students that I could spend my last three summers doing internships at Amazon and Google. In my final year at UIC, I was supported by the Dean’s Scholar Fellowship, so I could focus on finishing my dissertation. After graduating, I joined Google in New York City.