Geometry and Topology Seminar: Embedding groups into simple groups

报告人： Xiaolei Wu (Fudan University)
Time & Date: 4:30pm, Mar 28, Friday
地点： Room 1510
Host: 韩肖垄

摘要： simple groups has played an important role in the studying of groups. The Boone-Higman Conjecture says a finitely generated group can be embedded into a finitely presented simple group if and only if it has solvable word problem. The conjecture has now been proved for many classes of groups, including hyperbolic groups, RAAGs and linear groups over the rationals. In this talk, we will first give an overview of the conjecture. Then we discuss a strategy that can be used to embed groups acting faithfully on locally finite trees to finitely presented simple groups. In particular we verify the conjecture for the Baumslag-Solitar groups and free-by-cyclic groups. The talk is based on a joint work with Kai-Uwe Bux and Claudio Llosa Isenrich.

About the speaker: Dr. Xiaolei Wu is an Young Investator at the Shanghai Center for Mathematical Sciences, Fudan University. He obtained his Ph.D in SUNY Binghamton working with F. Thomas Farrell. He was a postdoc at Free University of Berlin, MPI Bonn, Univeristy of Bonn and Bielefeld University. He joined Fudan in 2021. His research interests includes Geometric group theory, manifold topology and Algebraic K-theory.