Seminars this week

Abstract

Functors provide the appropriate notion of structure-preserving map between categories, but many applications require a more general notion of relation between categories. I will begin by discussing relations between sets, and bimodules over rings or monoids. I will then explain how profunctors simultaneously generalise relations, bimodules and functors. Finally I will discuss how to compose profunctors by analogy with tensor products of bimodules, so that profunctors are the 1-cells of a bicategory.

Abstract

During the development of multicellular organisms, cells need to make decisions about their fate by integrating information from their neighbours, their surroundings, and their history. I will describe mathematical models of cellular decision making that reveal how cells can adopt different strategies depending on their setting, allowing them to make either rapid coordinated decisions or more measured decisions that provide more scope for the generation of cellular diversity.

Abstract

Dehn surgery is a classical area of low dimensional topology with many beautiful results connecting the subject matter to the description of 3-manifolds, the original Poincare conjecture, and the geometry of knot exteriors. In this talk we will introduce and motivate Dehn surgery with a view to speaking about "exceptional surgeries"; this will naturally bring us to a well known tabulation of 3-manifolds of "small volume". It will be our goal to discuss an unusually simple description of the "exceptional fillings" associated with this tabulation. The presentation will attempt to be intuitive and contain many pictures.

Abstract

In this talk we will recall some basic notions from Dehn surgery and remind ourselves about why we care about "exceptional surgeries" and "exceptional pairs". We then return to a tabulation of 3-manifolds of "small volume" and speak how it is possible to enumerate the set of exceptional slopes, pairs and fillings of "most" manifolds in this tabulation. If time permits we will speak about questions for future consideration.

Arrangements

The seminar is followed by Topology Tea in the common room, with tea and homemade cake.