About:

This public lecture was part of the Algebra, Geometry and C*-algebras workshop at ICMS.

About the talk:

Infinite sets have always fascinated mathematicians for their paradoxical properties. For example, Galileo noted that there is a one to one correspondence between the natural numbers and all square numbers. Another famous example is the Banach-Tarski paradox, seemingly playing havoc with the notion of volume. In this talk we took a group theorist’s perspective on notions such as paradoxical decompositions, leading us to the study of amenable groups. We gave a survey of these concepts and described a vexatious open question.

About the speaker: 

Brita Nucinkis (she/her) is Professor of Pure Mathematics at Royal Holloway, University of London. She obtained her Ph.D from Queen Mary and Westfield College, University of London, then held a postdoctoral position at the University of Southampton before moving to an Assistant Professorship at the ETH in Zuerich. She returned to Southampton in 2004 before moving to Royal Holloway in 2013. Her area of research focuses on the interplay of group theory, algebraic topology and homological algebra. Her main early contributions are counterexamples to some long-standing conjectures in group cohomology. She had recently become interested in the interplay of group theory and operator algebra, in particular in light of her work on generalisations of Richard Thompson’s group F.