LMS Hardy Lectureship 2025 - Emily Riehl in Manchester

Title: Contractibility as uniqueness

Abstract: What does it mean for something to exist uniquely? Classically, to say that a set A has a unique element means that there is an element x of A and any other element y of A equals x. When this assertion is applied to a space A, instead of a mere set, and interpreted in a continuous fashion, it encodes the statement that the space A is contractible, i.e., that A is continuously deformable to a point. This talk will explore this notion of contractibility as uniqueness and its role in generalizing from ordinary categories to infinite-dimensional categories.

The LMS Hardy Lectureship is named after G.H. Hardy, former President of the Society and De Morgan Medallist. The LMS Hardy Lecturer visits the UK for a period of about two weeks, gives the Hardy Lecture at a Society meeting,  and gives at least six other lectures at other venues in the UK.

The University of Manchester is proud to host this year's Hardy Lecturer as part of their tour in the UK.

The 2025 Hardy Lecturer is Emily Riehl. Professor Riehl has established herself as a leading expert in higher category theory and has also developed an interest in connections with computer science such as homotopy type theory. She is an accomplished and enthusiastic expositor of mathematics at a variety of levels aimed at mathematicians as well as popular writing with articles in Scientific American and New Scientist. She also plays a leading role in broader engagement of mathematicians and other scientists from marginalized and discriminated against groups.