Is it possible to define gauge theories on singular spaces? The answer to this question is emphatically yes​, and the prime example of such spaces are two-dimensional orbifolds known as spindles​. First, I will introduce spindles from a symplectic geometry perspective. Then I will discuss the notion of orbi-bundles, which allows one to consistently describe regular gauge fields/spinors on orbifolds.

Dr Jindong Wang will talk about; 'Stabilised Finite Element Methods for General Convection–Diffusion Equations'

This talk presents several stabilised finite element methods for general convection–diffusion equations, with particular emphasis on recent extensions to vector-valued problems arising in magnetohydrodynamics (MHD). Owing to the non-self-adjoint structure of the operator and the potentially large disparity between convective and diffusive scales, standard Galerkin discretisations may exhibit non-physical oscillations. We design a class of upwind-type schemes and exponentially fitted methods for vector-valued problems that mitigate these effects, highlighting both their shared stabilisation mechanisms and the distinctive features that arise in the vector-valued setting. These developments illustrate concrete strategies for the design and analysis of finite element discretisations for general convection–diffusion problems.