The Littlewood conjecture is an open problem in simultaneous Diophantine approximation of two real numbers. Similar problem in a field K of formal series over finite fields is also still open. This positive characteristic version of problem is equivalent to whether there is a certain bounded orbit of diagonal semigroup action on Bruhat-Tits building of PGL(3,K). We describe geometric properties of buildings associated to PGL(3,K), explore the combinatorics of the diagonal action on it and discuss how it helps to investigate the conjecture.
Thu, 10/05/2018 - 10:30 to 11:30