Seminar of Algebra

Bruhat-Tits building, as a non-archimedean analogue of the real/complex symmetric space, plays an important role in the study of group schemes, representation theory and number theory. In this talk, we will briefly sketch what is the Bruhat-Tits building of a reductive group over a non-archimedean local field, with an emphasis on the case where the related group is GL(n). After that we will give two interesting applications. One concerns Moy-Prasad filtration and depth of irreducible smooth representations, the other concerns a construction of an infinite family of Ramanujan graphs. This is a general expository talk.