Topics in Ricci flow, Riemannian geometry, metric geometry and PDE

Lead Research Organisation: University of Warwick
Department Name: Mathematics

Abstract

The context and potential impact: Geometric analysis is a booming area of mathematics research, with a very large number of spectacular breakthroughs to its name over recent years. It has an unbeaten record of solving problems in other areas of mathematics, such as topology and differential geometry, and this is expected only to accelerate.

Aims and objectives: At the broadest scale, the main aim is to contribute to this great ongoing advance. One area of particular interest is the solution of the Ricci flow on noncompact manifolds in the absence of curvature bounds. As a key ingredient in this programme, Luke is currently investigating a completely new approach to proving integral curvature bounds. This new approach completely avoids the highly technical nature of similar previous results, and offers the hope to prove much stronger results.

Alignment to EPSRC strategy: This is fundamental research with great potential. The general area of research has been repeatedly stressed as requiring support from EPSRC by the two major international reviews of mathematics that EPSRC has commissioned. It offers hope of progress across multiple areas that EPSRC strategy supports, including Geometry, Nonlinear Analysis, Mathematical Analysis, etc.

Publications

10 25 50

Studentship Projects

Project Reference Relationship Related To Start End Student Name
EP/R513374/1 01/10/2018 30/09/2023
2104917 Studentship EP/R513374/1 01/10/2018 31/03/2022 Luke Peachey