Speaker: Xin Zhang（The University of Hong Kong）
Time: 10:00-11:00, Dec 22, 2023
Room: Room 414, Shanghai Institute for Advanced Studies, USTC
It is a discovery of Margulis in 1970s that congruence quotients of SL2(Z) can be used to construct expanders, which are certain sparse but highly connected graphs. The Super Approximation Conjecture of Salehi-Golsefidy and Varju gives a precise prediction on which more general subgroups of SLd(Z) have this property. In this talk, I will survey the history of this conjecture, and describe a recent progress by Tang Jincheng and myself that all Zariski dense subgroups of SL2(Z)×SL2(Z) have this property. This progress relies on the development of a key tool in arithmetic combinatorics conjectured by Salehi-Golsefidy.
