Group Representations and Applications

Recently, motivated by potential applications in algebraic geometry, string theory, mirror symmetry, and quantum cohomology, linear groups containing elements of bounded deviation have been studied intensively. Also in order to generalize Taylor-Wiles method for proving the automorphy of Galois representations, adequate subgroups are defined, which are of great interest in proving Serre’s modularity conjecture of higher dimension. I will talk about some new progress on related problems including Huppert’s conjecture.