Alex Eskin is a 2014 Simons Investigator in Mathematics and the Arthur Holly Compton Distinguished Service Professor of Mathematics at the University of Chicago. He obtained his undergraduate degree in mathematics from the University of California, Los Angeles and completed his Ph.D. at Princeton University under the guidance of Professor Peter Sarnak. A large part of his work has centered on mathematical billiards and geometric group theory, for which he received the Clay Research Prize in 2007.
Eskin’s work began with study in the field of number theory, a vast branch of mathematics that is concerned with properties of integers, but his present interests lie in dynamical systems, a change he claims was a natural evolution from his earlier research. “I was studying number theory and then I learned that there are very beautiful results in dynamical systems,” Eskin said. “These are outside the field of number theory, yet can be very powerful in solving number theory problems.”
More recently, Eskin has focused his research on Ratner’s theorems, a group of theorems related to a branch of mathematics concerned with dynamical systems. “At some point, I got obsessed with whether or not there was an analog to Ratner’s theorems. For a while, others tried to make it work, but when they couldn’t, they gave up for fifteen years. Yet it was always in the back of my mind. Fairly recently, there have been a large number of related results in other fields that my current work is based on.” This work has been done in collaboration with Maryam Mirzakhani, a 2013 Simons Investigator in Mathematics.
Eskin said, “For me, the main motivation of my work is not the applications, but rather the interesting beauty of it.”