This summer school focuses on exciting recent developments at the intersection of geometric group theory and algebraic topology. The full force of the tools and ideas in the interplay between these two subjects have yet to be exploited. The aim of this school is to expose young researchers to the results and questions arising from the interactions between these two fields, giving them competitive tools to explore high level research problems. There will be three mini-courses on the following topics:
• Miklòs Abert – On the growth of homology and torsion homology
• Clara Löh – Covering spaces by amenable subsets
Amenable groups are “small” in the sense of large-scale geometry. In analogy with the Lusternik–Schnirelmann category, one can ask how many amenable subsets are needed to cover a topological space. A cohomological lower bound can be obtained via bounded cohomology. This lower bound can be established in several ways. We will explore the approach via classifying spaces of families of subgroups. Moreover, we will discuss related results and problems in geometric group theory and geometric topology.
• Conchita Martìnez-Pérez – (Co)homological and homotopical finiteness and Sigma invariants of groups
The objective of this mini-course is to provide an introduction to modern aspects of the theory of (co)homological and homotopical finiteness conditions in groups. These conditions can be seen as higher dimensional versions of finite generation or finite presentability and are ubiquitous in modern geometric group theory. We will also give an introduction to the beautiful theory of Sigma invariants, which provides a tool to understand (co)homological and homotopical finiteness conditions of certain normal subgroups of a group.
And research talks by:
• Natalia Castellana
• Indira Chatterji
• Alessandra Iozzi
• Karen Vogtmann
The afternoons will consist of discussion sessions, research talks to bring the content of the lecture series to current mathematics, as well as impromptu lectures on topics of the participants choosing. There will also be the opportunity for participants to give short talks on their research. Alongside the mathematical content, the female leaders in the field will also be invited to talk about their careers, and there will be a career panel as well as social and networking events.
Due to limitations on space and funding available, we will only be able to accept between 30-35 participants.
Registration for the Summer School will close on January 20th.
We gratefully acknowledge financial support from SwissMAP, the European Mathematical Society, and the University of Geneva.
