Seminars
In the academic year 2025-26, Semester 2, the Algebra and Combinatorics Seminar will run on Thursdays of Weeks 3, 5, 7, 9 and 12, at 1-2pm. The venue is Maths Lecture Theatre C.
Our Semester 1 programme is as follows.
Week 3 (Thursday 12th February) – Jeff Hicks (St Andrews)
Title: Topology in (non)-commutative algebra
Abstract: The polynomial ring in k-variables is one of the best understood rings. One of the fundamental results in the area is Hilbert’s Syzygy theorem (1890), which in the modern formulation states that a finitely generated module over this ring admits a free resolution of length at most k. In the 1990s Bayer and Sturmfels observed that many of these free resolutions had “underlying structure” given by a topological space. From this intuition, they introduced a framework (cellular resolutions) that provided a method for constructing new resolutions of a module from the data of a topological space. Unsurprisingly, many properties of these modules were encoded in the topology of the associated space.
If you, for some reason, think of the polynomial ring as the monoid ring of ℕk, then you might ask if there is a similar story for non-commutative monoids. A partial answer — which predates Bayer and Sturmfels — is in the foundational work of Eilenberg and Mac Lane (~1950) on classifying spaces and group cohomology. In this talk, I will mostly give an exposition of Bayer-Sturmfels’ work and its relationship to Eilenberg-Mac Lane spaces. Time permitting , I will discuss some work in progress with Lauren Cranton Heller, Mahrud Sayrafi, and Jay Yang on the general case monoid rings and applications.
Week 5 (Thursday 26th February) – Joseph Edwards/Struan McCartney (St Andrews)
Title: TBC
Abstract: TBC
Week 7 (Thursday 19th March) – Callum Barber/Yayi Zhu (St Andrews)
Title: TBC
Abstract: TBC
Week 9 (Thursday 2nd April) – Dorte Behrens/Pierre Zhou (St Andrews)
Title: TBC
Abstract: TBC
Week 12 (Thursday 23rd April) – Theodor Thorbjornsen/Joseph Ward
(St Andrews)
Title: TBC
Abstract: TBC