About the Lectureship:
The LMS Hardy Lectureship is named after G.H. Hardy, former President of the Society and De Morgan Medallist. Originally awarded to a distinguished overseas mathematician in odd-numbered years.
The LMS Hardy Lecturer visits the UK for a period of about two weeks, and gives the Hardy Lecture at a Society meeting, normally held in London in July. The LMS Hardy Lecturer also gives at least six other lectures, on different topics, at other venues in the UK; the schedule is decided by the LMS Society, Lectures and Meetings Committee in consultation with the LMS Hardy Lecturer, and is designed to allow as many UK mathematicians as possible to benefit from the LMS Hardy Lecturer's presence 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.
For the full list of events, please click here: https://www.lms.ac.uk/events/lectures/hardy-lectureship
Programme:
The Cardiff University School of Mathematics is excited to be hosting Professor Emily Riehl (Johns Hopkins University) during her UK tour as the named LMS Hardy Lecturer 2025. The day will begin in the morning with an introductory talk aimed for students. There will then be two colloquial style talks in the afternoon: the first by Prof. Grigory A. Garkusha and the second by Prof. Emily Riehl. Participants are invited to attend both the morning and the afternoon, or if they wish just the afternoon; please make this specification on the registration form at the bottom of the page.
| 10:15 |
Welcome for morning attendees |
| 10:30 |
Overview of category theory (a lecture for students) |
| 11:30 |
LUNCH |
| 13:15 |
Welcome for afternoon attendees |
| 13:30 |
Grigory A. Garkusha (Swansea University) Title: Motives, categories and stable homotopy types Abstract: Algebraic geometry studies algebraic varieties which are of principal importance. They are relatively easy to understand since they are just defined by polynomial equations. Homotopy theory is a considerably newer area of mathematics, being an important branch of algebraic topology. It studies objects which are preserved under operations such as bending and stretching. Both areas appear naturally in quite a lot of subjects in theoretical physics, coding theory and computer sciences. Motivic homotopy theory is a blend of algebraic geometry and homotopy theory. Its primary object is to study algebraic varieties from a homotopy theoretic viewpoint. Besides quite spectacular applications such as the solution of the Milnor conjecture by Voevodsky and the Bloch-Kato conjecture by Rost and Voevodsky in algebraic geometry, motivic homotopy theory leads to explicit computations of various stable homotopy types in algebraic topology and algebraic K-theory by means of “motives and transfers”. These computations also lead to a variety of categories of motives which recover, in particular, classical stable homotopy theory of spaces. The resulting interplay of algebraic geometry, homotopy theory and enriched category theory provides a fascinating glimpse of the unity of mathematics. |
| 14:30 |
BREAK |
| 15:00 |
Hardy Lectureship Talk, Prof. Emily Riehl (Johns Hopkins University) Title: Homotopy types as homotopy types Abstract: Classically, a "homotopy type" records the information in a topological space that is captured by its homotopy groups. The classical homotopy category of spaces is defined as a quotient of the ordinary category of topological spaces. Quillen famously proved that the homotopy category can also be understood as a quotient of the (better behaved) category of simplicial sets, with Kan complexes encoding homotopy types. Voevodsky extended this result to show that homotopy type theory (i.e., Martin-Löf’s dependent type theory plus the univalence axiom) can be modelled by the category of simplicial sets, again with the Kan complexes encoding homotopy types, now thought of more synthetically the primitive objects in this formal system. In this talk, I’ll highlight some constructions and proofs that are standard in homotopy type theory but less familiar in classical homotopy theory, focussing in particular on the principle of "path induction." |
|
16:15 |
Reception |
Please note that speakers and timings are subject to change.
Accessibility:
This event is taking place in Lecture Theatre 3.38, which is located on the third floor of Abacws Building. There is step free access from the main entrance facing Senghennydd Road and from the main entrance facing Cathays Train Station to Lecture Theatre 3.38.
For further details, please visit the AccessAble page: https://www.accessable.co.uk/cardiff-university/cathays-park-campus/access-guides/abacws-building-computer-science-and-informatics-mathematics
Registration:
Click here to register for the event: https://research-sites.cardiff.ac.uk/gapt/events-hardy-lectureship-2025/
For any questions regarding the event, please contact Simon Wood (woodsi@cardiff.ac.uk)
Travel/Caring Grants to attend the Hardy Lectures:
Travel/Caring grants of up to £50 to support attending the Hardy Lectures, which are at universities on the Hardy Lecture Tour, were available to mathematicians who are based at neighbouring universities to those universities and would require financial support.
For future Hardy Lecture Tours, if you require support, please complete the application form as soon as you can and at least 3 working days before the Hardy Lecture you wish to attend. Please note that there are limited funds available and so grants may be awarded on a first-come, first-served basis.
If you have any queries, please email lmsmeetings@lms.ac.uk