EPSRC logo

Details of Grant 

EPSRC Reference: EP/Y009959/1
Title: Curve counting via categorification
Principal Investigator: Koseki, Dr N
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department: Mathematical Sciences
Organisation: University of Liverpool
Scheme: New Investigator Award
Starts: 01 April 2024 Ends: 31 March 2027 Value (£): 411,743
EPSRC Research Topic Classifications:
Algebra & Geometry
EPSRC Industrial Sector Classifications:
No relevance to Underpinning Sectors
Related Grants:
Panel History:
Panel DatePanel NameOutcome
06 Sep 2023 EPSRC Mathematical Sciences Prioritisation Panel September 2023 Announced
Summary on Grant Application Form
Counting curves inside a given space is the most classical problem in geometry. For example, one can ask a question such as 'How many lines pass through two given points in the plane?' Sometimes the set of all curves satisfying certain geometric properties is finite, but other times not. A modern approach to enumerative geometry is to assign numbers, called `virtual invariants' to the spaces parametrising all curves we want to count, whether or not they are finite sets. There are several different virtual invariants, and some of them were introduced by physicists in string theory.

The first aim of this project is to understand how different kind of invariants are related. Another aim is to refine these numerical counts. Namely, I will investigate certain vector spaces and certain categorical structures defined from the spaces parametrising curves, which recover the numerical invariants by taking their dimensions. These refined invariants will distinguish geometries more finely and lead to a deeper understanding of counting invariants in enumerative geometry and string theory.

Key Findings
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
Potential use in non-academic contexts
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
Impacts
Description This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
Summary
Date Materialised
Sectors submitted by the Researcher
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
Project URL:  
Further Information:  
Organisation Website: http://www.liv.ac.uk