# The GEARS seminar

The Glasgow Edinburgh Algebra Research Student seminar

The Glasgow Edinburgh Algebra Research Student seminar is an informal meeting between algebra (loosely interpreted!) PhD students and postdocs from Edinburgh, Heriot-Watt, and Glasgow universities. We meet roughly five times per year and give participants the opportunity to either speak about their research, or present an important paper in their area. These meetings normally take place in the late afternoon/evening and the location alternates between Glasgow and Edinburgh.

The GEARS seminar is currently organised by Shivang Jindal (Edinburgh), Marina Purri (Glasgow), and Stefanie Zbinden (Heriot–Watt). For previous organisers, please see the relevant tabs.

We are grateful for the financial support from: the Glasgow Mathematical Journal Learning and Research Support Fund, the Edinburgh Researcher Development Fund, the Heriot-Watt Small Project Grant Scheme, and the EPSRC Programme Grant "Enhancing Representation Theory, Noncommutative Algebra And Geometry Through Moduli, Stability And Deformations."

## Upcoming Meetings

January GEARS Meeting

Date: 25th January 2024

Time: 15:00–17:30

Location: Room G.09 at Lister Learning & Teaching Centre. The address is: 5 Roxburgh Pl, Edinburgh EH8 9SU (This is only two blocks from the Bayes centre.)

Speakers: Samuel Lewis (Glasgow), Yan Yau Cheng (Edinburgh)

Registration: Please fill in this short form by Friday 19th January. We hope to see you there!

Here are the abstracts:

### Yan Yau Cheng - Arithmetic Chern Simons Theory

Mazur first observed in the 60s a deep analogy between the embedding of a knot in a 3-manifold and primes in a number field. Using ideas from this analogy, Minhyong Kim and his collaborators developed the study of arithmetic field theories. This talk will be an introduction to Arithmetic Field Theories, in particular focusing on Arithmetic Chern-Simons Theory.

### Sam Lewis- Classifying hyperbolic intersection arrangements

Choose your favourite connected graph Δ and shade a subset J of its vertices. The intersection arrangement associated to the data (Δ, J) is a collection of hyperplanes in dimension |Jc|, first defined by Iyama and Weymss. This construction involves taking the classical Coxeter arrangement of Δ and then setting all variables indexed by J to be zero. It turns out that for many choices of J the chambers (connected components) of the intersection arrangement admit a nice combinatorial description, and there exists a wall-crossing rule to pass between them. I will start by making all of this more precise, before discussing work in progress to classify intersection arrangements of “hyperbolic” graphs. If time permits I will also talk about some of the geometric motivations for intersection arrangements and their applications to contracted preprojective algebras.

Our most recent meetings: Dec 2023 (Edinburgh) and September 2023 (Glasgow)