**Xinwen Zhu**

California Institute of Technology, Pasadena

March 30, 2015

**An introduction to the geometric Satake isomorphism**:
The Satake isomorphism, which describes the spherical Hecke algebra of a p-adic group in terms of the representation ring of its Langlands dual group, is the starting point of the Langlands duality. I will give an introduction to its categorical version, known as the geometric Satake correspondence. Time permitting, I will also discuss its applications.