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Details of Grant 

EPSRC Reference: EP/J008451/1
Title: Homological algebra of Feynman graphs
Principal Investigator: Lazarev, Professor A
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department: Mathematics and Statistics
Organisation: Lancaster University
Scheme: Standard Research
Starts: 29 October 2012 Ends: 28 October 2015 Value (£): 209,509
EPSRC Research Topic Classifications:
Algebra & Geometry Mathematical Physics
EPSRC Industrial Sector Classifications:
No relevance to Underpinning Sectors
Related Grants:
EP/J00877X/1
Panel History:
Panel DatePanel NameOutcome
30 Jan 2012 Mathematics Prioritisation Panel Meeting January 2012 Announced
Summary on Grant Application Form
The area of the proposed research is at the junction of several branches of pure mathematics and mathematical physics. It follows the pattern of applying the physical intuition and ideas to solving mathematical problems which has been a characteristic feature of many groundbreaking developments in algebra in geometry in the last two decades.

The project has two closely related themes. One purports to link two deep algebraic constructions which have been extensively studied in their own right. The first is the calculation of the Chevalley-Eilenberg cohomology of infinite matrices with values in an algebra and the second is the calculation of the Chevalley-Eilenberg cohomology of the infinite-dimensional algebra of noncommutative hamiltonians. One conjectural application is the construction of an algebraic version of chain level Gromov-Witten invariants.

The second theme derives its motivation from the general problem of quantizing field theories defined classically, i.e. in terms of an action functional. More precisely, a classical field theory is modelled as a certain algebraic structure, called L-infinity algebra which is determined by a certain polynomial or power series function, and one studies other algebraic structures derived by integrating this function. The application will include topological theories of Chern-Simons type and Poisson sigma-models.
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Organisation Website: http://www.lancs.ac.uk