Index theory for Lie groupoids

The moment when research mathematicians need to pay attention to progress in automated theorem proving is coming closer and closer!

Our project is to use functional analysis, convex analysis and optimization to introduce and analyze various regularization methods with suitable penalty terms, including the sparsity promoting functions and the total variational function. We also seek applications in imaging and industry.

A two dimensional Riemannian manifold is an abstract surface sitting nowhere in particular, but which somehow has the structures imposed on it that a surface gets by sitting in Euclidean space, such as tangent spaces, a metric etc.

The aim of the project is to learn about equivariant stable homotopy theory, and go through as much of the Hill, Hopkins and Ravenel proof as possible.

Lindbladians and related master equations in quantum mechanics

Magnetic equilibrium and particle orbit modelling of the OpenStar Dipole

The LASSO and penalized likelihood methods have become an extremely hot topic in statistics over the past decade, as they offer a computationally efficient method of variable selection particularly in high dimensional situations.

operator theoretic aspects of quantum field theory
computational problems in vector-valued modular forms
tensor categories and functorial conformal field theories

Population genetics deals with the evolution of genomes as a result of the drift of point mutations throughout a population over long timescales.

Investigate representation theorems for lattice operators based on mathematical morphology and develop efficient machine learning methods based on them for applications in signal and image processing.

Study the metastability of Markov processes, in particular interacting particle systems, by analysing the resolvent of the process.

Mimetic and stable numerical methods for nonlinear shallow water equations

Minimal surfaces are surfaces which are critical points of the area functional, are are characterised by the vanishing of their mean curvature.

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