Junior Algebra Seminar (Algebraic Topology and Group Theory)
The Junior Algebra Seminar is a new seminar at Warwick for young researchers in algebra, with a particular focus on algebraic topology, group theory, and associated areas.
In Term 2 the seminar will be held on Mondays 2pm-3pm in B3.02, Zeeman Building, except in weeks 2 and 3.
In Term 3, the seminar will be held on Thursdays 3pm-4pm in MS.05, Zeeman Building, except in week 2.
In general, odd weeks will focus on group theory and related areas, whilst even weeks will focus on algebraic topology and related areas.
The organisers of the seminar are Nathan Lockwood and Dan Roebuck (algebraic topology), and Michael Cavaliere (group theory). Please get in touch with the relevant organisers if you would like to give a talk or suggest a speaker!
This seminar replaces the previous AGATA seminar, which ran in term 3 of the 2022/23 academic year. That seminar focused on algebraic geometry alongside algebraic topology and general algebra; the junior seminar at Warwick focusing on algebraic geometry now is JAWS.
Initially discovered by Gaschutz in the 1950s, before later being extended by Dalla Volta and Lucchini in the 1990s, the theory of crowns in finite groups has a long and rich history, with numerous applications. Central to this theory is the observation that establishing generation results for a particular class of groups, known as crown-based powers, is often sufficient to derive corresponding results for all finite groups. In this talk, we will explore how this framework can be applied to a range of generation problems, highlighting in particular how the structure of a group’s chief factors determines its generation behaviour.
Yorick Fuhrmann (Warwick): Lifting heavy-weight structures on stable infinity-categories
Introduced by Bondarko, weight structures play an important role in the toolbox when studying stable infinity-categories. In this talk I will give an introduction to the subject and then explain how they contribute to the study of a linear version of equivariant spectra, namely modules over the Eilenberg-MacLane spectrum of the constant Mackey functor. Ultimately, we will consider the Picard group of this category.
Josh Bridges (Birmingham) - Small essential 2-subgroups in fusion systems
A (saturated) fusion system on a p-group P contains data about conjugacy within P, the typical case being the system induced by a group on its Sylow p-subgroup. Fusion systems are completely determined by looking at their essential subgroups, which must admit an automorphism of order coprime to p. For p=2, we describe two new methods that address the question: given an essential subgroup E<P of a fusion system on P, what can we say about P? In particular, one method gives us sufficient conditions to deduce that E is normal in P, while the other explores cases where we have strong control over the normaliser tower of E in P.
