The Great Western Number Theory Seminar

The GWNT Seminar is a regional number theory seminar for the Southwest of England, bringing together departments from the following institutions: University of Bath, University of Bristol, University of Exeter, University of Oxford and University of Reading. We are funded by a London Mathematical Society Scheme 3 grant, together with contributions from each university.

The next GWNT meeting:

Friday 16th January 2026

University of Bristol

Register here.

Directions: From Temple Meads train station, you can either take the 8/72 buses at the front to the top of Park Street (~20 minutes from the station, buses come frequently), or you can walk (30-45 minutes, largely uphill). See the University's "how to get here" page for more details.

Lecture room: We will be in the Fry Building, Lecture Room 2.04 on the second floor. See the campus map for directions.

Schedule:

•  10:15-11:00am: Arrival and coffee

• 11:00am-12:00pm: Katerina Santicola

• 12:00-12:30pm: Break

• 12:30-1:30pm: Besfort Shala

• 1:30-2.30pm: Lunch

• 2.30-3.30pm: Jordan Docking

• 3.30-4:00pm: Break

• 4:00-5:00pm: Alex Bartel

• ~6pm onwards: Dinner (Zerodegrees)

Speakers:

Alex Bartel (University of Glasgow)

Title: Isospectral manifolds via orders in quaternion algebras

Abstract: I will report on joint work with Aurel Page on a number/representation theoretic approach to the question "Can you hear the shape of a drum". We use quaternion algebras over number fields to construct pairs of manifolds that "sound the same", but differ from each other in subtle ways. I will not assume that you already care about this question.

Jordan Docking (King's College London)

Title: Reduction of Plane Quartic Curves and Cayley Octads

Abstract: In this talk, we'll discuss stable models of plane quartic curves over local fields, and their relationship with Cayley octads, geometric objects coming from the even theta-characteristics of these curves. In particular, we'll consider how degenerations in the Cayley octad produce a classification of such models, as well as how this parallels the cluster picture machinery for hyperelliptic curves. This talk is based on joint work with Ramyond van Bommel, Vladimir Dokchitser, Elisa Lorenzo García, Reynald Lercier and Andreas Pieper.

Katerina Santicola (University of Bath)

Title: Number fields with prescribed ramification featuring the stack BG.

Abstract: The inverse Galois problem has many refinements. In this talk, we focus on the existence of Galois extensions with restricted ramification. The Gras--Munnier formula provides a quick test for whether such extensions exist. We discuss how the Gras--Munnier formula corresponds to a Brauer--Manin obstruction to strong approximation on the classifying stack BG. 

Besfort Shala (University of Bristol)

Title: Mixed character sums

Abstract: I will talk about a distributional result for 'mixed character sums', which are exponential sums with multiplicative coefficients given by values of a Dirichlet character. As a deterministic application, we construct polynomials with coefficients +1 and -1 with large Mahler measure, establishing a new record in Mahler's problem. This is joint work with Jonathan W. Bober and Oleksiy Klurman.

Organisers:

Daniel Loughran (Bath), Julie Tavernier (Bath), Jesse Pajwani (Bristol), Sam Streeter (Bristol), Happy Uppal (Bristol), Henri Johnston (Exeter), James Newton (Oxford), Hanneke Wiersema (Oxford) and Christopher Daw (Reading).