Oberwolfach Lecture 2022: Approximation and Stability of Groups

This year's Oberwolfach Lecture on the occasion of the annual meeting of the Oberwolfach committees was given by Andreas Thom on "Approximation and Stability of Groups". We thank Andreas Thom for his very exciting talk. A summary of the lecture will be published in the Annual Report 2022.

Andreas Thom

Infinite discrete symmetry groups appear in many places in mathematics. A natural circle of questions arises when trying to approximate such groups by finite approximate symmetries. Is this kind of approximation always possible? When does such an approximation come from finite perfect symmetries? We will discuss Gromov’s notion approximability, i.e. that of a sofic group, and various applications. Finally, we will briefly mention the recent break-through result MIP*=RE, that implies a negative answer to Connes’ Embedding Conjecture and has the potential to lead to the construction of a non-approximable group.

Interested readers may view the complete list of Oberwolfach Lectures since 2005.