# Darstellungstheorietage and Nikolaus Conference 2021

Title: The Modular Isomorphism Problem

Abstract:

The Modular Isomorphism Problem, which had been open for over 50 years, states:

If $$p$$ is a prime, $$G$$ and $$H$$ are finite $$p$$-groups and $$k$$ a field of characteristic $$p$$, does an isomorphism between the group algebras of $$G$$ and $$H$$ over $$k$$ imply an isomorphism of the groups $$G$$ and $$H$$?

The problem has recently been solved by a series of counterexamples, but also various new positive results have been achieved. I will report on these positive results and the methods underlying them.

Joint work with T. Moede, T. Sakurai and M. Stanojkovski.