Adam Lelkes Heading link
My research focuses on interactions between model theory and external and additive combinatorics. I received my Ph.D. at the University of Illinois at Chicago under the supervision of Dave Marker and Dhruv Mubayi. I finished my PhD in summer 2016, and after postdoctoral positions at the University of Maryland and the University of Chicago, I am now an assistant professor at the Ohio State University.
I completed my Ph.D in January of 2021 thanks to the support of my advisor Nathan Jones, along with the rest of the Number Theory group. While at UIC, I had the privilege of working with many talented professors and enjoyed the strong sense of community among the other graduate students. Although my primary area of research focused on the algebraic structure of elliptic curves, I also completed a Masters in Mathematical Computer Science.
My path to receiving my Ph.D was unconventional. With the support of my advisor, during my final years as a graduate student, I moved to San Francisco to work as a Data Scientist/Software Engineering at a startup while continuing to write my dissertation. This allowed me to get a headstart on my career. Now I work at Google where I focus on making search faster.
My area of research is broadly in the analysis of partial differential equations, but more specifically in the study of collective behavior. Models of collective behavior seek to represent a diverse range of phenomena; flocks of birds (ODEs), opinion dynamics (Game Theory), fluid dynamics and quantum synchronization (PDEs); the applications are endless. I seek to establish well-posedness of such models, as well as to analyze important properties such as long term dynamics of the systems. In my time at UIC I was fortunate to be advised by Roman Shvydkoy, and to learn an incredible amount of mathematics from the entire analysis and PDEs group there. After completing my PhD in Summer 2021, I accepted a postdoctoral position at the Gran Sasso Science Institute in L’Aquila, Italy, where I am continuing my research on models of collective behavior, while learning as much as I can about the cuisine of Italy.
I began my math PhD journey in pure mathematics and later pivoted to mathematical computer science after gaining exposure to computer science topics in internships and taking interesting MCS graduate courses. One of the benefits of the MSCS department is that you can explore courses from pure math, applied math, mathematical computer science (MCS), and statistics, with the freedom to choose any of these routes as your PhD focus. I have a variety of research interests in MCS, including network science, data science, machine learning, and deep learning. Eventually, my research focused on learning theory, developing probably approximately correct (PAC) algorithms to train classifiers with noisy labeled data obtained in crowdsourcing and collaborative settings.