15.15-16.00: Reception

16.00-16.45: Introductory talk by Stefan Mihajlović: How to get around a 4-manifold?

Abstract: I will introduce manifolds and explain how to build them from building blocks that we call handles. After that, our focus will be on manifolds of dimension 4 - how handles look in this concrete setting, and what moves we can do to change the handle decomposition. Followed by intuitive explanations of 4-dimensional moves, I will try to emphasize diagrammatic 3-dimensional pictures which show how topologists usually work with 4-manifolds hands-on.

17.00-18.00: Main lecture

Abstract: The study of mathematical knots, i.e. the embeddings of a circle in a 3-dimensional space, is a very active area of topology. More than 50 years ago, in 1970, Conway studied the knot 11n34 (http://katlas.org/w/images/d/db/K11n34.gif), now known as the Conway knot. The question of whether the Conway knot bounds a disc when a fourth dimension is allowed has a deep connection with some of the most fundamental open problems in 4-dimensional topology. For several decades this question remained impenetrable, until in 2018 a short and elegant argument of Piccirillo showed that the answer is “no”.

In the talk I will discuss the precise formulation of the question, its importance for 4-dimensional topology, and I will sketch Piccirillo’s proof.