PhD Studentship: Microlocal Analysis and its Applications in Quantum Resonances, Partial Differential Equations with Analytic or Gevrey Regularity, and Several Complex Variables

Overview

The School of Mathematics at the University of Birmingham offers a PhD studentship in microlocal analysis and its applications to quantum resonances, partial differential equations with analytic or Gevrey regularity, and several complex variables. Microlocal analysis explores the classical and quantum correspondence in PDEs, for example through symbol quantisation in the theory of pseudodifferential operators, which links classical observables with quantum operators. It also provides the tools to define, compute and analyse resonances, which describe the oscillation and decay of waves in systems where energy can escape to infinity.

Analytic and Gevrey regularity in the study of PDEs has drawn growing attention. The project aims to develop microlocal analysis techniques in analytic and Gevrey settings. The analytic setting often gives exponentially accurate approximation or control, while Gevrey regularity goes beyond the smooth theory to give quantitative remainder estimates and keeps tools such as cutoffs and partitions of unity that are unavailable in the analytic setting. The techniques are expected to be applied to geometry, quantum mechanics and other areas of mathematical physics. The project is supervised by Dr Haoren Xiong.

What you get

Funding is available through the School of Mathematics for a suitably strong candidate. The scholarship covers tuition fees, training support and a stipend at standard rates for 3 to 3.5 years.

How to apply

Candidates are encouraged to make an informal enquiry with the supervisor.

Key dates

The closing date is 22 October 2026.