Alex Eskin

Alex Eskin is the Arthur Holly Compton Distinguished Service Professor of Mathematics at the University of Chicago's Department of Mathematics, within the Physical Sciences Division. His research focuses on dynamical systems, geometric group theory, ergodic theory, and their applications to number theory. Eskin holds a B.S. from UCLA and a Ph.D. from Princeton University (1993), advised by Peter Sarnak.

Key research interests include Teichmüller dynamics, billiards on rational polygons, and the geometry of moduli spaces. He has made seminal contributions to understanding SL(2,R) actions on moduli spaces, Lyapunov exponents, and the classification of invariant measures. His work bridges dynamics, geometry, and number theory, with profound implications for the study of flat surfaces and homogeneous flows.

Eskin has received numerous accolades, including the Breakthrough Prize in Mathematics (2019), Clay Research Award (2007), and membership in the National Academy of Sciences (2015). He has authored over 60 papers, advancing topics like counting closed geodesics in moduli spaces, volumes of strata of abelian differentials, and the rigidity of quasi-isometries in solvable groups.

Notable achievements include proving the 'Magic Wand Theorem' with Mirzakhani and Mohammadi, resolving the classification of orbit closures for SL(2,R) actions, and advancing the understanding of Lyapunov exponents via algebraic geometry. His teaching includes courses like Math 203 (Analysis) at the University of Chicago.