This talk will describe the basic properties of the de Rham algebra, which is a generalisation of the de Rham algebra over smooth schemes, which was introduced by L. Illusie in his monograph 'Complexe cotangent et déformations'.
The simplicial boundary is another way to study the boundary of CAT(0) cube complexes. I will define this boundary introducing the relevant terminology from CAT(0) cube complexes along the way. There will be many examples and many pictures, hopefully to help understanding but also to improve my (not so great) drawing skills.
Abstract: Ricci solitons are genralizations of Einstein metrics which have become subject of much interest over the last decade. In this talk I will give a basic introduction to these metrics and discuss how to reformulate the Ricci soliton equation as a Hamiltonian system assuming some symmetry conditions. Using this approach we will construct explicit solutions to the soliton equation for manifolds of dimension 5.
Quasimorphisms (QM) of groups to the reals are well studied and are linked to stable commutator length (scl) via Bavard Duality- Theorem. The notion of QM can be generalized to yield maps between groups such that each QM from one group pulls back to a QM in the other.
We will give both a short overview of features of scl and investigate these generalized QMs with large scale properties of the commutator group.