School of Mathematics & Physics, University of Lincoln
On Wednesday the 26th of May 2021, Leo Margolis (Vrije Universiteit Brussel) will be giving a seminar on his research at 4pm. The details of his talk are as follows:
Title: On the Modular Isomorphism Problem
Abstract: The Isomorphism Problem for group rings asks for which groups G and H the group rings of these groups over a given commutative ring R are isomorphic as rings. Less formally speaking, it asks how much the linear representations of G over R know about the structure of the group G. Several concrete formulations of the problem were studied, but the only classical formulation which remains open today and was explicitly formulated by R. Brauer is the Modular Isomorphism Problem: Does the group ring of a finite p-group G over a field of characteristic p determine G up to isomorphism?
Though in contrast to other cases the Modular Isomorphism Problem in its strongest form studies a finite object, allows algorithmic approaches and many ideas have been developed, progress has been slow and for any fundamental classes of p-groups the problem remains open. I will review some history of the general Isomorphism Problem, present techniques used in the study of the modular version and give some recent results.
This is joint work with Tobias Moede and Mima Stanojkovski.