Bruhat-Tits theory: a new approach

Abstract: Bruhat-Tits theory associates to a connected reductive group over a nonarchimedean local field (or over a field belonging to a somewhat more general class) an affine building, and various associated structures such as parahoric group schemes, Moy-Prasad filtrations etc. While it has proved to be of central importance in harmonic analysis and representation theory of $p$-adic groups, it has also found significant applications to diverse other areas such as arithmetic groups, fake projective planes etc. In this talk, we describe a new approach to  Bruhat-Tits theory of reductive groups over a discretely valued field $k$ with Henselian valuation ring, which appears to be conceptually simpler, and more geometric, than the original approach of Bruhat and Tits.