Our speakers will review well-known theories, present their own works, and point out open problems for the future.
Graduate students are particularly welcome to participate.
In this first talk, the basics of homogenization method through asymptotic expansion and a solvable ODE will be introduced. Extensions to elliptic and evolutionary PDEs will follow along with weak convergence method. We give a polynomial time algorithm for deciding which of these two conditions holds for a given finitely generated matrix group over an algebraic number field. Noting that many computational problems are undecidable for groups with nonabelian free subgroups, we investigate the complexity of problems relating to linear groups with solvable subgroups of finite index. If in addition G has a nilpotent subgroup of finite index, we obtain much stronger results.