李京艳 , 普拉文·库马尔 , 吴杰

Pedro Henrique Amorim Alves

2026年08月27日 15:00 至 16:00

A3-4-301

Zoom 242 742 6089 (BIMSA)

The study of congruence subgroups has been central to recent developments in the integral homology of $SL_2(A)$. In this talk, I will present a technique that enables you to calculate the abelianization of subgroups whose commutator is a congruence subgroup. From this, we obtain an exact sequence that provides information about $H_2(SL_2(\mathcal{O}_{K,S}))$. We have also conjectured a connection between this homology group and values of the Dedekind zeta function, through a homological version of the Birch-Tate formula. This work was conducted in collaboration with Isadora V. Picinini, Bruno R. Ramos, and Thiago Veríssimo.

Pedro Henrique Amorim Alves is a master’s student at the Universidade de São Paulo, under the supervision of Professor Behrooz Mirzaii. He holds a bachelor’s degree in mathematics from the Universidade Federal de Mato Grosso do Sul. His current project focuses on the congruence subgroup problem in Algebraic K-theory and the homology of linear groups. He is also interested in the connections between Algebraic Geometry and K-theory through Chow Groups and Motivic Cohomology. He is visiting BIMSA with a support from the "ICMRA Visiting Scholars Program".