Seminar series
Date
Wed, 04 Jun 2025
16:00
16:00
Location
L6
Speaker
Filippo Baroni
Organisation
University of Oxford
Every topologist knows that a mug is a doughnut, but did you know that the Loch Ness monster is a baguette?
This talk is meant as a gentle introduction to the theory of big surfaces and their mapping class groups. This is a topic that has gained significant traction in the last few years, and is undergoing an exciting phase of explosive expansion.
We will start by giving lots of examples of surfaces of infinite type, working our way towards a general classification theorem. We will then introduce big mapping class groups, and outline some of their topological properties that are reminiscent of classical geometric group theory. Finally, following a programme proposed by Calegari in 2009, we will investigate to what extent the classical theory of curve and arc graphs of finite-type surfaces generalises to the infinite-type setting.
The level of prior required knowledge on the topic of big mapping class groups will be the same as that of the speaker one week before the talk — that is, none.