In this colloquium style talk, I will first give a quick introduction to etale cohomology and Tate conjecture. Then I will explain my joint work with Yichao Tian and Xinwen Zhu on constructing cycles on the special fibers of Shimura varieties. The talk should be accessible to students who are reasonably familiar with the language of algebraic geometry.

肖梁教授先任教于北大北京国际数学中心。他于2009年从麻省理工毕业、曾在芝加哥大学、加州大学欧文分校和康涅狄格大学任教。肖梁在数论和算术代数几何方向兴趣广泛，包括志村簇的几何，以及p进朗兰兹纲领的研究。