Topic: group theory

Ryan O’Donnell presents simple explicit families of expander graphs whose analysis needs only a small amount of group theory. The lecture explains their expansion properties and shows how these constructions can lead to stronger objects, including super-expanders and non-sofic groups with property (T).

Roman Sauer and Uri Bader join Saar and Shaked to discuss a collaborative proof of a rigidity result involving symmetries and group theory. The conversation explores the mathematical result, how family relationships shaped the collaboration, and the participants’ routes into mathematical research at the Isaac Newton Institute.

Justin Chen introduces groups as collections of actions and explains their relationship to symmetry. The discussion uses accessible examples to show the power of abstraction, then considers the challenges of explaining group theory to non-specialists. Chen also reflects on his experience communicating mathematics and his plans for further study.