Gromov–Witten theory is a robust framework for the enumeration of holomorphic curves on complex manifolds (equivalently, parametrised curves on algebraic varieties). Over the past three decades it has developed into a vast subject, with many striking results and rich connections to areas as diverse as geometric representation theory and theoretical physics.
In the last few years, the subject's centre of gravity has shifted towards logarithmic Gromov-Witten theory, a new approach revolving around moduli spaces of “logarithmic stable maps”. This has expanded the scope of the subject to include a large class of open and degenerate spaces. Crucially it has also introduced novel techniques, coming from logarithmic and tropical geometry. These techniques have a distinctive combinatorial flavour, and their full potential is only starting to be appreciated.
A new line of enquiry has recently opened up in logarithmic Gromov-Witten theory: to study the topology of moduli spaces of logarithmic stable maps. This is a fresh direction, with many unanswered questions and the potential for very rapid growth. It also promises to provide new approaches to classical problems in the field. This PhD project will push forward this line of enquiry, focusing on one item from the following list, to be chosen according to the student’s particular strengths:
The work will require a fusion of abstract algebraic geometry with concrete tropical combinatorics, and the student will gain proficiency in both these areas.
The studentship is funded by Queen Mary and will cover home tuition fees, and provide an annual tax-free maintenance allowance for 3.5 years at the UKRI rate (£19,668 in 2022/23).
For international students interested in applying, please note that this studentship only covers home tuition fees and students will need to cover the difference in fees between the home and overseas basic rate. Tuition fee rates for 2023-24 are to be confirmed. Details on current (2022-23) tuition fee rates can be found at: https://www.qmul.ac.uk/postgraduate/research/funding_phd/tuition-fees/
How to apply
Entry requirements
Fees and funding