The goal of this lecture series is to study the recent work of Liang Xiao and Xinwen Zhu on cycles of Shimura varieties via geometric Satake. We shall introduce affine Grassmannians and affine Deligne-Lusztig varieties and discuss in detail the geometry of affine Grassmannians and affine Deligne-Lusztig varieties.  

 

References

[1] Zhu, Xinwen, An introduction to affine Grassmannians and the geometric Satake equivalence. Geometry of moduli spaces and representation theory, 59–154, PCMI Amer. Math. Soc., Providence, RI, 2017.

 

[2] X. Zhu, Affine Grassmannians and the geometric Satake in mixed characteristic, Ann. Math. 185 (2017), 403-492.

[3] L. Xiao, X. Zhu, Cycles on Shimura varieties via geometric Satake, arXiv:1707.05700, 146 pp.