Time: 2019.04.25 16:50 ~ 18:20

place: 404 Math building

Title : Some applications of ergodic methods to number theory

Abstract : There are plenty of applications of ergodic theory to certain problems in number theory from metric number theory to the theory of L-functions. These includes Littlewood's conjecture about simultaneous Diophantine approximation, Linnik's equidistributed property of integral points of 2-dimensional spheres, Margulis' the density of integer values of certain quadratic forms, Szemerédi's theorem concerning arithmetic progressions, and Venkatesh's period bounds and subconvexity. We briefly survey some of basic principles inside the results. After that, we discuss the Kleinbock-Margulis' effective equidistribution of expanding translates of certain orbits in the space of lattices and its positive characteristic analogue, described in a joint work with Seonhee Lim.