Tonbridge School is looking to recruit a number of Graduate Teachers to start at the school in September 2025. Details about the role, the school, and the market-leading package can be found in the attached job advert.
We are hosting an in-person event on Monday 27th January at Vincents Club from 19:00-21:00 for anyone interested in chatting to current staff about the role.
Registration for this year's conference for women and non-binary people in Maths is now open - sign up here
This year's event will take place on Saturday 1st March 2025 from 10 am - 4:30 pm and more details can be found in the link.
Fri, 02 May 2025
12:00 -
13:00
Quillen Room
Arithmetic of Hyperelliptic Curves in Residue Characteristic 2
Tim Gehrunger
(ETH Zurich)
Abstract
The stable reduction of a hyperelliptic curve encodes many of its arithmetic invariants, such as the curve's conductor, minimal discriminant and Galois representation.
In the case of odd residue characteristic, these models may be classified via their cluster pictures, which provides an explicit way to compute the invariants.
In the talk, we will explain recent progress towards a similar result in residue characteristic 2. In particular, we use marked models of the projective line to classify all genus 2 curves in residue characteristic 2.
Fri, 24 Jan 2025
12:00 -
13:00
Common Room
Junior Algebra Social
Abstract
The Junior Algebra and Representation Theory Seminar will kick-off the start of Hilary Term with a social event in the common room. Come to catch up with your fellow students and maybe play a board game or two. Afterwards we'll have lunch together.
Elephant trunk wrinkles: a mathematical model of function and form
Liu, Y
Goriely, A
Mihai, A
Nonlinearity
volume 38
(06 Feb 2025)
Thu, 13 Mar 2025
17:00
17:00
L3
Non-expanding polynomials
Tingxiang Zou
(University of Bonn)
Abstract
Let F(x,y) be a polynomial over the complex numbers. The Elekes-Ronyai theorem says that if F(x,y) is not essentially addition or multiplication, then F(x,y) exhibits expansion: for any finite subset A, B of complex numbers of size n, the size of F(A,B)={F(a,b):a in A, b in B} will be much larger than n. In fact, it is proved that |F(A,B)|>Cn^{4/3} for some constant C. In this talk, I will present a recent joint work with Martin Bays, which is an asymmetric and higher dimensional version of the Elekes-Rónyai theorem, where A and B can be taken to be of different sizes and y a tuple. This result is achieved via a generalisation of the Elekes-Szabó theorem.
Thu, 06 Mar 2025
17:00 -
18:00
L3
Orthogonal types to the value group and descent
Mariana Vicaria
(University of Münster)
Abstract
First, I will present a simplified proof of descent for stably dominated types in ACVF. I will also state a more general version of descent for stably dominated types in any theory, dropping the hypothesis of the existence of invariant extensions. This first part is joint work with Pierre Simon.
In the second part, motivated by the study of the space of definable types orthogonal to the value group in a henselian valued field and their cohomology; I will present a theorem that states that over an algebraically closed base of imaginary elements, a global invariant type is residually dominated (essentially controlled by the residue field) if and only if it is orthogonal to the value group , if and only if its reduct in ACVF is stably dominated. This is joint work with Pablo Cubides and Silvain Rideau- Kikuchi. The result extend to some valued fields with operators.
Thu, 27 Feb 2025
17:00 -
18:00
L3
Representation Type, Decidability and Pseudofinite-dimensional Modules over Finite-dimensional Algebras
Lorna Gregory
(University of East Anglia)
Abstract
The representation type of a finite-dimensional k-algebra is an algebraic measure of how hard it is to classify its finite-dimensional indecomposable modules.
Intuitively, a finite-dimensional k-algebra is of tame representation type if we can classify its finite-dimensional modules and wild representation type if its module category contains a copy of the category of finite-dimensional modules of all other finite-dimensional k-algebras. An archetypical (although not finite-dimensional) tame algebra is k[x]. The structure theorem for finitely generated modules over a PID describes its finite-dimensional modules. Drozd’s famous dichotomy theorem states that all finite-dimensional algebras are either wild or tame.
The tame/wild dividing line is not seen by standard model theoretic invariants or even the more specialised invariants coming from Model Theory of Modules. A long-standing conjecture of Mike Prest claims that a finite-dimensional algebra has decidable theory of modules if and only if it is of tame representation type. More recently, I conjectured that a finite-dimensional algebra has decidable theory of (pseudo)finite dimensional modules if and only if it is of tame representation type. This talk will focus on recent work providing evidence for the second conjecture.
Intuitively, a finite-dimensional k-algebra is of tame representation type if we can classify its finite-dimensional modules and wild representation type if its module category contains a copy of the category of finite-dimensional modules of all other finite-dimensional k-algebras. An archetypical (although not finite-dimensional) tame algebra is k[x]. The structure theorem for finitely generated modules over a PID describes its finite-dimensional modules. Drozd’s famous dichotomy theorem states that all finite-dimensional algebras are either wild or tame.
The tame/wild dividing line is not seen by standard model theoretic invariants or even the more specialised invariants coming from Model Theory of Modules. A long-standing conjecture of Mike Prest claims that a finite-dimensional algebra has decidable theory of modules if and only if it is of tame representation type. More recently, I conjectured that a finite-dimensional algebra has decidable theory of (pseudo)finite dimensional modules if and only if it is of tame representation type. This talk will focus on recent work providing evidence for the second conjecture.