Lecturer: Cao Yang

Abstract:After the establishment of class field theory, Tate et al. extends its cohomology interpretation (i.e. cohomology of Gm) to finitely Abelian group, torus and Abelian variety, and establishes the arithmetic duality theory. In this short class, I will start with Galois cohomology theory and introduce the arithmetic duality theory of torus and the local-global problem of its application to Norm 1 torus.

Introduction to the Lecturer:Cao Yang is a researcher of University of Science and Technology of China. He was graduated from the Department of Mathematics of Shandong University in 2010 and Université Paris-Saclay (formerly Université Paris sud 11) in 2017. Later, he became a post doctor student at Max-Planck-Gesellschaft, and then became a Humboldt Research Fellow at Universität Hannover. He was employed by University of Science and Technology of China in 2020. His research field is diophantine geometry, that is, research on the solution of diophantine equation by algebraic geometry. His main achievements are as follows: (1) Prove that that descending obstacle is the most subtle in the ascending obstacles of the local-global principle of rational points, and solve the open problem of Professor Poonen of MIT; (2) For a class of algebraic groups and homogeneous space, establish the purity of the local-global principle of whole points, and solve the core condition of open problem of Professor Wittenberg of Université Paris XIII.

Invitee:Zhao Lilu, Professor from School of Mathematics

Time:

9:20-11:30, September 29 (Wednesday)

9:20-11:30, September 30 (Thursday)

Venue:Academic Hall #1032, Block B, Zhixin Building, Central Campus

Hosted by School of Mathematics, Shandong University