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On the Modular Isomorphism Problem
We cordially invite you to a series of two lectures by Leo Margolis (Universidad Autónoma de Madrid), an outstanding specialist in algebra, in particular in problems related to group rings. He is, among others, the co-author of the first ever counterexample to the famous Zassenhaus Conjecture regarding unity in group rings, which, despite the efforts of many researchers, remained unresolved for over 40 years.
The lecture entitled On the Modular Isomorphism Problem will take place:
- on Thursday, June 12 at 14:15 in room 3220 (first part)
- on Friday, June 13 at 14:15 in room 3240 (second part)
Abstract: Say we are given only the R-algebra structure of a group ring RG of a finite group G over a commutative ring R. Can we then find the isomorphism type of G as a group? This so-called Isomorphism Problem has obvious negative answers, considering e.g. abelian groups over the complex numbers, but more specific formulations have led to many deep results and beautiful mathematics. The last classical open formulation was the so-called Modular Isomorphism Problem: does the isomorphism type of FG as a ring determine the isomorphism type of G as a group, if G is a p-group and F a field of characteristic p?
In these lectures, after introducing the history of the problem, I will present the first negative answers to the problem and their generalizations. Also positive results and the methods underlying them will be presented. We also explain how the methods used here allow, at least on a conceptual level, also an interpretation in terms of algebraic geometry.
1. Leo Margolis website https://margollo.<wbr></wbr>github.io/
2. On Zassenhaus conjecture https://<wbr></wbr>encyclopediaofmath.org/wiki/<wbr></wbr>Zassenhaus_conjecture
2025-06-06
