Program Overview

Enumerative Geometry via Triangulated Categories and Bridgeland Stability Conditions

Overview

This project draws together five researchers with a broad range of interests and expertise, including enumerative algebraic geometry, triangulated categories and non-commutative geometry, Bridgeland stability conditions, moduli spaces and their compactifications, Hodge theory, classification of higher-dimensional varieties, and perverse sheaves and stratifications. The project involves working, supervised by members of the team, on one or more of these exciting and active areas of modern geometry.

About this Opportunity

Enumerative geometry – counting geometric objects – has a long and illustrious history going back to the very origins of algebraic geometry. To this day, it remains a source of intriguing and difficult questions which are stimulating innovative mathematics at the intersection of geometry, topology, and algebra. This project brings together researchers from the Algebraic Geometry and Geometry & Topology groups to tackle these questions. The researchers have complementary expertise in algebraic geometry, category theory & non-commutative geometry, and topology.

Who is this For?

• Candidates will have, or be due to obtain, a Master's Degree or equivalent in a relevant subject.
• Exceptional candidates with a First Class Bachelor's Degree in an appropriate field or significant relevant experience will also be considered.

Funding

• This Studentship is funded by XTX Markets and will cover full Home tuition fees.
• It will pay a maintenance grant for 3.5 years.
• The Studentship comes with access to additional funding to fund consumables, conference attendance, etc.
• The Studentship is available to any prospective student wishing to apply, including both home and international students.
• The Studentship will not cover international fees.

Research Areas

The project involves research in the following areas:

• Enumerative algebraic geometry
• Triangulated categories and non-commutative geometry
• Bridgeland stability conditions
• Moduli spaces and their compactifications
• Hodge theory
• Classification of higher-dimensional varieties
• Perverse sheaves and stratifications

Expectations

• The expectation is that the first 1-2 years will be spent on training, and the remainder of the 3.5 years on original research.
• The training will involve both specific aspects to develop expertise in the research topic and broader mathematical training, including developing skills in writing and presenting mathematics effectively.

Admission Criteria

• A Master's Degree or equivalent in a relevant subject is required.
• Exceptional candidates with a First Class Bachelor's Degree in an appropriate field or significant relevant experience may also be considered.

Tuition Fees

• The Studentship will cover full Home tuition fees.
• International fees are not covered by the Studentship.

Maintenance Grant

• A maintenance grant for 3.5 years is provided as part of the Studentship.
• The grant amount is £21,805 p.a. for the specified period.

Additional Funding

• Access to additional funding for consumables, conference attendance, etc., is provided as part of the Studentship.

Inclusivity and Diversity

• The university is committed to working with students to make all reasonable project adaptations, including supporting those with caring responsibilities, disabilities, or other personal circumstances.
• Students with a disability may be entitled to a Disabled Students Allowance on top of their studentship to help cover the costs of any additional support needed.