Sage Days 12: San Diego
Titles and abstracts
Simon King (Schiller-Universität Jena): The cohomology of finite p-groups
The cohomology of finite p-groups with coefficients in GF(p) is a subject that links parts of group theory, algebraic topology, and modular representation theory.
The computation of cohomology rings turns out to be very challenging. The first complete cohomology computation for the 267 groups of order 64 by J. F. Carlson took two years with interruptions, mainly due to difficulties in Gröbner basis computations. The computation for the 2328 groups of order 128 seemed to be a long way out of reach.
We achieved a major progress by implementing algorithms of D. J. Green and D. Benson in Sage, based on earlier C-programs of D. J. Green. With our programs, we were able to compute the cohomology of the groups of order 128 in about 10 months CPU time. Also, we computed all but 10 cohomology rings of 3-, 5-, and 7-groups up to order 625.
John Perry: Remarks on Faugère's F5 algorithm
Gröbner bases are an essential part of any serious computer algebra system. This talk considers the important contribution of Faugère's algorithm F5. We discuss the motivation behind its structure, its remarkable efficiency, and ways to mitigate the inefficiencies it introduces. We also discuss the difficulties surrounding a proof of termination.