The local Langlands program aims to understand representations of an algebraic group over a local field in relation to Galois representations of the base field. Thus far, significant progress in this program has been made with geometric approaches. An overarching theme is to construct and study a geometric object whose cohomology is naturally a representation of an appropriate Galois group or an algebraic group. This lecture series aims to provide an introduction to these approaches. It will begin with a brief review of the local class field theory and the local Langlands correspondence for GLn. Then it will introduce several key geometric objects, such as Rapoport-Zink spaces, local Shimura varieties, and the Fargues-Fontaine curve, and discuss how they can be used to realize the local class field theory and the local Langlands correspondence for GLn. 8월 3일(화) 10시-11시 8월 3일(화) 11시20분-12시 20분 8월 5일(목) 10시-11시 8월 5일(목) 11시20분-12시 20분