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EP/G06170X/1 - Applied derived categories

Research Perspectives grant details from EPSRC portfolio

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Professor RP Thomas EP/G06170X/1 - Applied derived categories

Principal Investigator - Dept of Mathematics, Imperial College London

Other Investigators

Professor A Corti, Co InvestigatorProfessor A Corti

Professor S Donaldson, Co InvestigatorProfessor S Donaldson

Scheme

Programme Grants

Research Areas

Geometry & Topology Geometry & Topology

Mathematical Physics Mathematical Physics

Start Date

01/2010

End Date

12/2015

Value

£1,248,113

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Grant Description

Summary and Description of the grant

Derived categories are abstract algebraic objects that package geometric information. The way they do this is inspired by topology -- a more flexible type of geometry which allows more deformations. As such they endow the original geometry with more flexibility and symmetries. They also filter out a little of the geometric information, so two different geometries might lead to the same derived category. The way in which they do this is very interesting, both in mathematics and physics, where derived categories describe topological D-branes .It has become clear in recent years that derived categories are not quite as abstract, mysterious or fearsome as often thought. Extracting the geometry (and invariants of the geometry) turns out to be quite natural in many situations, and the different geometries that can come from the same derive category give new and important points of view that solve previously intractable problems. Their extra symmetries and flexibility make them more useful in many applications.Derived categories bring a different philosophy to problems, suggesting new approaches to them. We propose to bring this new way of thinking to areas of broad areas of geometry, linking many which have not been touched derived categories before. We hope to solve problems and develop new areas of mathematics, helping to make derived categories into standard mathematical tools used all over the subject.

Structured Data / Microdata


Grant Event Details:
Name: Applied derived categories - EP/G06170X/1
Start Date: 2010-01-01T00:00:00+00:00
End Date: 2015-12-31T00:00:00+00:00

Organization: Imperial College London

Description: Derived categories are abstract algebraic objects that package geometric information. The way they do this is inspired by topology -- a more flexible type of geometry which allows more deformations. As such they endow the original geometry with more flexib ...