Graham ELLIS - Computational group theory, cohomology of groups and topological methods 2 ; Graham ELLIS - Computational group theory, cohomology of groups and topological methods 2: Summer School 2022 - Cohomology, Geometry and Explicit Number Theory

The lecture series will give an introduction to the computer algebra system GAP, focussing on calculations involving cohomology. We will describe the mathematics underlying the algorithms, and how to use them within GAP. Alexander Hulpke's lectures will being with some general computational group theory (mainly focussing on permutation and matrix groups) and then move on to the cohomology used for the construction of perfect groups. Bettina Eick's lectures will again begin with some general computational group theory (mainly focussing on polycyclic groups) and then move on to the computation of cohomology for polycyclic groups with a view towards the classification of Almost-Bieberbach-Groups and SmallGroups. Graham Ellis's lectures will begin with some general computational topology (mainly focussing on 3-manifolds) and then move on to computations in group cohomology with a view to calculations on congruence subgroups of SL(2,Z) and Bianchi groups.