2021/22
Organisers: Samuel Lewis and Simone Castellan
23rd August 2022
Johannes Schmitt (Kaiserslautern)
Symplectic resolutions and symplectic reflection algebras
25th May 2022
Local Galois theory and ramification
Ahead of Beth Romano: Epipelagic representations in the local Langlands correspondence
18th May 2022
Franco Rota
Normal forms of (commutative) functions
Ahead of Michael Wemyss: Local normal forms of noncommutative functions
4th May 2022
Rebecca Bellovin
Modular forms and Galois representations
Ahead of Jaclyn Lang: A modular construction of unramified p-extensions of Q(N¹ᐟᵖ)
27th April 2022
James Rowe
Motivating tt-geometry
Ahead of Charalampos Verasdanis: Stratification of tensor triangulated categories
20th April 2022
Pavel Safronov (Edinburgh)
Introduction to noncommutative algebraic geometry
Ahead of Pavel Safronov: Euler structures and noncommutative volume forms
30th March 2022
GAPS variety hour III
Short talks by:
Lewis Dean (juggling patterns via the affine symmetric group)
Isambard Goodbody (topological equivalence of rings)
Charalampos Verasdanis (direct and inverse images of unions and intersections)
Tudur Lewis (mapping class groups)
Ross Paterson (integral representations)
Jay Mackenzie (1-dimensional flows)
Vitalijs Brejevs (twisted Alexander polynomials)
23rd March 2022
Alex Bartel
Some arithmetic of elliptic curves
Ahead of Barinder Banwait: Explicit isogenies of prime degree over number fields
16th March 2022
Lucas Buzaglo (Edinburgh)
Loop algebras and their central extensions
Ahead of Susan Sierra: Ideals in enveloping algebras of loop and affine Lie algebras
9th March 2022
Charalampos Verasdanis
Classification of thick subcategories of triangulated categories
2nd March 2022
Adam Morgan
Elliptic curves, congruent number problem, and the parity conjecture
23rd February 2022
David Murphy
Grassmannian cluster algebras and the twist automorphism
Ahead of Matthew Pressland: Grassmannian twists categorified
16th February 2022
Cameron Wilson
Asymptotic notation, counting primes, and 100% Goldbach
Ahead of Efthymios Sofos: Schinzel's hypothesis and applications to rational points
9th February 2022
Rational points and Lie algebras
Ahead of Jef Laga: Arithmetic statistics via graded Lie algebras
2nd February 2022
Robin Ammon
The absolute Galois group of Q, p-adic Galois representations, and modular forms
Ahead of Rebecca Bellovin: p-adic variation of Galois representations and modular forms
26th January 2022
David Murphy
An introduction to friezes and cluster algebras
19th January 2022
Samuel Lewis and Simone Castellan
Quiver moduli spaces and noncommutative Poisson structures
Ahead of Maxime Fairon: Noncommutative Poisson geometry of Boalch's multiplicative quiver varieties
15th December 2021
GAPS variety hour II
Short talks by:
Charlotte Bartram (moduli spaces)
Isambard Goodbody (Brown representability)
Ross Paterson (rational right triangles with integral area)
Simone Castellan (Heisenberg vertex algebra)
Brian McKonzi (rings of invariants and Artin components)
8th December 2021
Rhys Davies
Rational Cherednik algebras with examples for the symmetric groups
Ahead of Niall Hird: The centre of the restricted rational Cherednik algebra
1st December 2021
Robin Ammon
Arithmetic statistics, number fields and Galois extensions, and elliptic curves
Ahead of Ross Paterson: Average ranks of elliptic curves after p-extension
24th November 2021
Arithmetic statistics, class groups, and negative Pell
Ahead of Carlo Pagano: Statistics of integral points on conics and related problems
17th November 2021
Simone Castellan
Weyl algebras and the Harish-Chandra module
Ahead of Toby Stafford: Invariant holonomic systems for symmetric spaces
10th November 2021
Adam Morgan
Sums of two squares, conics, and coordinates of points on elliptic curves
Ahead of Simon Leo Rydin Myerson: Conic fibrations over elliptic curves and the elliptic sieve
3rd November 2021
GAPS variety hour I
Short talks by:
Samuel Lewis (preprojective algebras)
Vitalijs Brejevs (rational ball problem)
Lisa Lotkeva (singularity knots)
Charlotte Bartram (blowups and resolutions)
Simone Castellan (vertex algebras)
Isambard Goodbody (simplicial objects)
David Murphy (differential graded algebras)
Charalampos Verasdanis (tensor triangulated categories)
Rhys Davies (representation theory of the symmetric group)
27th October 2021
Samuel Lewis
The McKay correspondence
20th October 2021
(Hyper)elliptic curvers, p-adic numbers, and the Hasse principle
Ahead of Adam Morgan: The 2-parity conjecture for Jacobians of hyperelliptic curves
13th October 2021
Vitalijs Brejevs
Monoidal categories and Hopf algebras
Ahead of Andrew Baker: Numerical polynomials, Kummer congruences and Massey products
6th October 2021
Samuel Lewis
Weighted projective space and quotient singularities
Ahead of Franco Rota: Explicit exceptional collections for Johnson-Kollar stacks
29th September 2021
Simone Castellan
Lie algebras and (Poisson) vertex algebras