Hodge Club

The Hodge Club is the seminar for Hodge Institute graduate students and postdocs. That means we're interested in Algebra, Geometry, Topology, Number Theory, and all possible combinations and derivations of the four. Before the 2016/17 academic year, the Hodge Club was known as the Geometry Club.

We meet every Friday at 16:00, where we take it in turns to present a topic of interest to the rest of the group. We hope to run this as a hybrid seminar, so in particular we will have both an in person and virtual audience. The lecture theatre is not available every week, so some talks will have to be exclusively online. These are noted in the schedule below.

If you are attending in person, we will meet at the ICMS Lecture Theatre (Bayes Centre room 5.10). If you are attending virtually, we will send an email with the Zoom link every week. If you do not receive the weekly emails and would like to be added to the mailing list, please get in touch with one of the organisers.

Talks tend to be fairly informal and provide excellent practice for conference talks in front of a friendly audience. You can find our current schedule and a historical list of talks below.

The Hodge Club for the 2021/22 academic year is organised by Lucas Buzaglo and Hannah Dell.

Current Schedule of talks for 2021/22

1st October Sebastian Schlegel Mejia An interactive stroll towards the E-polynomial of the moduli stack of rank two degree zero Higgs bundles
Abstract: The subject of my talk is the calculation of the E-polynomial of the moduli stack of rank two degree zero Higgs bundles. However, the aim of the talk is not to reach the final calculation nor to give super fancy reasons why you should care about the calculation. Instead, we focus on giving a feeling for the concepts and techniques involved in the calculation. These include (moduli of) Higgs bundles, stacks, motivic measures, and lambda-rings. All kinds of questions and interruptions are strongly encouraged and will be seen as pleasant diversions on our field trip through the land of Higgs bundles and its surroundings.
8th October Augustinas Jacovskis Geometry from derived categories
Abstract: A lot of geometric information about a variety X can be recovered from its derived category D(X). If the variety is Fano, then X can in fact be reconstructed up to isomorphism from D(X). This begs the question of whether less information than D(X) can determine X up to isomorphism. In this talk I’ll discuss some known cases when “less information” means a certain subcategory of D(X) called the Kuznetsov component. Time permitting, I’ll discuss joint work with Zhiyu Liu and Shizhuo Zhang which describes the situation for index 1 Fano threefolds.
15th October Guy Boyde (University of Southampton) Homotopy groups, and how they grow (Online talk)
Abstract: Homotopy groups are an important invariant of topological spaces – loosely, the n-th homotopy group is a picture of the space taken from the point of view of the n-dimensional sphere. Unfortunately, they are incredibly hard to compute – even for a friendly example like the two-dimensional sphere, we do not know all of them. We might therefore like to ask a coarser question. The one I am going to ask in this talk is “what can be said about the behaviour of the homotopy groups as n goes to infinity?” Asking this question reveals lots of interesting structure, and that’s what I’ll aim to tell you about, starting with the basics and including lots of examples.
22nd October Patrick Kinnear An Invertible Sheaf on the Character Stack?
Abstract: It is known that the skein algebra of a surface defines a sheaf of algebras on the coordinate ring of the character variety of the surface, which is in a sense the moduli space of local systems on the surface. It is also known that this sheaf satisfies an invertibility property over an open and dense subset of the character variety. Another way to describe local systems on a surface is via the character stack, and we can ask if there is a stacky version of the above invertibility statement. In this talk we will outline how such a statement can (hopefully!) be obtained from the study of invertible morphisms in the Morita category Alg_3, and will mention recent results characterising invertibility in this category. Along the way we will describe the powerful technology of factorization homology, which connects these two viewpoints.
29th October Speaker TBC Title TBC (Online talk)
Abstract: TBC
5th November Lucien Hennecart Title TBC
Abstract: TBC

Historical schedules

Hodge Club 2020/21
Hodge Club 2019/20
Hodge Club 2018/19
Hodge Club 2017/18
Hodge Club 2016/17
Geometry club 2015/16
Geometry club 2014/15
Geometry club 2013/14
Geometry club 2012/13
You can also visit the old Geometry club website for more historical schedules.