Special Colloquium

Speaker: Alex Iosevich (University of Rochester)

Title: Orthogonal bases and tiling: analysis, number theory and combinatorics

Abstract: In 1974 Bent Fuglede conjectured that if a set Omega is a bounded domain in R^d, then the space L^2(Omega) has an orthogonal basis of exponentials if and only if Omega tiles the space R^d by translation. Even though this conjecture was disproved by Terrance Tao in 2004 in dimensions 5 and higher, it is continuing to lead researchers to fascinating connections and ideas that involve a variety of areas of modern mathematics. In this talk we will present a
sampling of these ideas and connections between them, as well as some recent developments in this fascinating field.

Bio: Alex Iosevich got his B.S. in Mathematics at the University of Chicago in 1989 and a Ph.D. in Mathematics at UCLA in 1993 under the direction of Christopher Sogge. After a postdoctoral fellowship at McMaster University, he worked at Wright State University, Georgetown University and the University of Missouri. Iosevich is currently a Professor of Mathematics at the University of Rochester. He has graduated 11 Ph.D. students and in 2015 he became a Fellow of the AMS. Iosevich works in harmonic analysis, geometric combinatorics and additive number theory, with emphasis on connections between those areas.