Analysis and probability
Our theme conducts a wide variety of research in modern analysis and probability.
Areas that are well represented at the theme include harmonic analysis, analysis and numerics for stochastic differential equations, dispersive, elliptic, and parabolic partial differential equations (PDEs), geometric measure theory, stochastic PDEs, general relatively, machine learning, limit theorems for stochastic processes, random graphs and processes on them, stochastic networks, interacting-particle system, calculus of variations and spectral theory.
Every student has access to subject specific learning opportunities, broader mathematical training, as well as a range of generic skills training.
Every student can access any of the mathematical & generic skills training activities offered by The Maxwell Institute Training Programme
This theme offers subject specific learning opportunities such as:
- Scottish Mathematical Sciences Training Centre (SMSTC) courses and high level undergraduate courses in analysis and probability
- Working and reading groups: We run regular groups in which students and staff present research papers. This offers a deep dive into cutting edge research topics, whilst providing the speaker with advice and feedback to hone their lecturing skills
The analysis and probability theme has a vibrant research community, enriched by a constant flow of academic visitors from all over the world.
We run weekly Seminars in Analysis and in Probability throughout the academic year, inviting many speakers across a range of topics. If you have a speaker in mind, you can suggest one!
past phd projects
Some examples of past PhD projects offered by supervisors in this theme.
- Certain geometric maximal functions in harmonic analysis.
- Convergence of iterative algorithms for stochastic control and reinforcement learning.
- Random graphs and networks: limits, approximations and applications
- Multiscale stochastic differential equations
- Boundary value problems for parabolic PDEs for operators satisfying Carleson condition
- Low regularity well-posedness of the modified and the generalized Korteweg-de Vries equations