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. You will work, 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 our Algebraic Geometry and Geometry & Topology groups to tackle these questions. These researchers have complementary expertise in algebraic geometry, category theory & non-commutative geometry, and topology. You will work with one or more of them on a specific topic within the broad umbrella of the project. The choice of topic and supervisors will be made in discussion with you, depending on your particular mathematical background and interests. You will have opportunities to discuss mathematics and collaborate with the other PGR students, postdoctoral researchers and staff on the project.
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 your expertise in your research topic, and bring you to the research frontier within it, as well as broader mathematical training including developing your skills in writing and presenting mathematics effectively.