ℓ²-Betti numbers of RFRS groups
Abstract
RFRS groups were introduced by Ian Agol in connection with virtual fibering of 3-manifolds. Notably, the class of RFRS groups contains all compact special groups, which are groups with particularly nice cocompact actions on cube complexes. In this talk, I will give an introduction to ℓ²-Betti numbers from an algebraic perspective and discuss what group theoretic properties we can conclude from the (non)vanishing of the ℓ²-Betti numbers of a RFRS group.
Cohomogeneity one Ricci solitons and Hamiltonian formalism
Abstract
There is a considerable body of work, primarily due to A. Dancer and M. Wang, on the analogous procedure for the Einstein equation.
In this talk, I will introduce the abovementioned methods and illustrate with examples their usefulness in finding explicit formulae for Ricci solitons. I will also discuss the classification of superpotentials.
15:30
Factorization algebras in quite a lot of generality
Abstract
The objects of arithmetic geometry are not manifolds. Some concepts from differential geometry admit analogues in arithmetic, but they are not straightforward. Nevertheless, there is a growing sense that the right way to understand certain Langlands phenomena is to study quantum field theories on these objects. What hope is there of making this thought precise? I will propose the beginnings of a mathematical framework via a general theory of factorization algebras. A new feature is a subtle piece of additional structure on our objects – what I call an _isolability structure_ – that is ordinarily left implicit.