Abstract

The chosen theme for this summer school is at the cross between Algebraic Geometry and Representation Theory. The aim of the summer school is to gather young researchers arising from a quite wide mathematical area in order to build knowledge in two complementary fundamental theories. The first one is Bruhat-Tits theory which deals with the Euclidean buildings and integral models of reductive algebraic groups defined over a local field, the second one is the theory of Affine Grassmannians which are geometric objects arising from Representation Theory. The applications to the Langlands program (in particular the geometric one) will appear along the way. In short, the summer school will gather 80 people during two weeks. Priority will be given to graduate students and to doctors who defended their Phd after 2015. Five lectures of 6 hours will be given by internationally recognized experts. Two lectures will be about Bruhat-Tits theory, two lectures will present the theory of Affine Grassmannians from the representation theory viewpoint and an advanced lecture will focus on the geometric Langlands program. ​Furthermore there will be a daily question session where the public may ask the lecturers. Finally there will be two talks each day, one explicitely related to the lectures and one research talk.