Title: Interactions between number theory and homogeneous dynamics
Speaker: Nimish Shah, OSU
Abstract: Many problems in number theory involve more than one infinite groups of symmetries in a direct or an indirect manner. Typically one of these groups is discrete and the other is a continuous group. The interaction between these two infinite groups is studied via ergodic theory on homogeneous spaces. The ergodic or dynamical properties of this action yield deep insight into the original number theoretic problem.
The goal of this talk is to consider a few example of such number theoretic problems, and show how the dynamical approach has been used in resolving these problems in the recent years.
Note: This is part of the Invitations to Mathematics lecture series given each year in Autumn Semester. Pre-candidacy PhD students can sign up for this lecture series by registering for one or two credit hours of Math 6193 with Professor Henri Moscovici.