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Numbers, Periods and QFT

15 - 17 April 2010
 Institute for Particle Physics Phenomenology
 Durham University

Modern computational practice in particle physics has produced an enormous database connecting quantum field theory and particle physics to problems in number theory and algebraic geometry. The appearance of polylogarithms, multiple zeta values and other periods in these computations is testimony to that. On the mathematical side, these numbers and special functions are of interest in their own right. Amongst their most fundamental properties are the relations they satisfy resulting from the fact that they origin from iterated integrals. There is a lot of common algebraic structure to be studied in the mathematical theory of these numbers and in physics amplitudes.

We will start by reviewing the Hopf algebra structure of renormalization and aim to end with a description of the Hodge-theoretic aspects of Feynman amplitudes. The purpose of this workshop is to present latest developments in this field in pedagogical lectures that should be accessible to PhD students in a format that provides ample time for discussion.

The lectures will be given by Dirk Kreimer (Institut des Hautes Etudes Scientifiques, Paris) and Francis Brown (Institut de Mathématiques de Jussieu)

Organisers:  Herbert Gangl, Nigel Glover

Programme (Indico)

 

Thursday, April 15

13.00

Lunch

Collingwood
 

14:25

Welcome

Nigel Glover (IPPP)
 

14:30

Hopf algebras, renormalization and Feynman graphs 

Dirk Kreimer (IHES)
 

15:30

break

 
 

15:45

Hopf algebras, renormalization and Feynman graphs cont.

Dirk Kreimer (IHES)
 

16:45

Discussion

 
 

17:15

Might quantum field theory and number theory help each other?

David Broadhurst (The Open University)
 

19:00

Dinner

 Collingwood

Friday, April 16

9:30

Properties of Feynman graph polynomials

Christian Bogner (Aachen)
 

10:30

break

 
 

11:00

Periods, Feynman integrals and number theory

Francis Brown (IMJ)
 

12.00

Discussion

 
 

13.00

Lunch

 Collingwood
 

14.15

The use of Hochschild cohomology in QFT

Dirk Kreimer (IHES)
 

15:15

break

 
 

15:30

The use of Hochschild cohomology in QFT cont.

Dirk Kreimer (IHES)
 

16:30

Discussion

 
 

19:00

Dinner

 Collingwood
 

Saturday, April 17

9:30

From graph polynomials to limiting mixed Hodge structures

 Dirk Kreimer (IHES)
 

10:30

break


 

10:45

From graph polynomials to limiting mixed Hodge structures cont

Dirk Kreimer (IHES)
 

11:45

Discussion 

 
 

13:00

End

 

 

Participation in the workshop is free of charge, and accommodation on April 15 and April 16 and travel expenses will be covered by the IPPP for UK participants. Please send an email to Linda (l.a.wilkinson@durham.ac.uk) if you would like to participate. Please note that finding accommodation at Durham at this time of the year is not easy, so that arrangements need to be made well in advance for participants wishing to stay overnight.