Topic: CMI Mathematics Seminar
Date: Tuesday, April 13, 2021.
Time: 3:30 PM
Algebraic and algorithmic aspects of free-abelian times free groups: rank of subgroups and fixed subgroups of automorphisms
Chennai Mathematical Institute.
This talk is based on the family of groups $\Z^m \times F_n$, namely free-abelian times free groups. These are a special type of right-angled Artin groups (RAAGs). We are going to discuss some algorithmic problems of $\Z^m \times F_n$, a natural extension of free groups and a first step towards further generalisation into another two main directions: semi-direct products and partially commutative groups (PC-groups). The algorithmic problems which we will discuss are ranks of the subgroups, automorphisms and its fixed point subgroups, subgroup intersection problem heading towards a cryptography application. We will use general combinatorics, one dimensional geometry and algebraic techniques to play with the elements of $\Z^m \times F_n$, to explore algebraic aspects and to solve aforementioned algorithmic problems.