June 1st (Wednesday) 15:00-17:00 / 510 Morning Center

Speaker: Xin Zhang (University of Illinois Urbana-Champaign)

Title: Counting in Hyperbolic Lattices, with Applications to Sieve and Circle Methods

Abstract: Several seemingly unrelated arithmetic problems boil down to proving a local-global phenomenon for some “thin” group orbit Γv, where v ？ Zd and Γ is a group of d by d matrices. This talk serves as a preliminary talk for my second talk, where I’ll illustrate integral circle packings as an example. In particular, I’ll explain in detail the growth of lattice points of Γ, which is one of the key ingredients.