Numbers, Periods and QFT

Europe/London
OC218 (Durham, IPPP)

OC218

Durham, IPPP

Description
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.
    • 14:25 14:30
      Welcome 5m
    • 14:30 15:30
      Hopf algebras, renormalization and Feynman graphs 1h
      Speaker: Dirk Kreimer
    • 15:30 15:45
      break 15m
    • 15:45 16:45
      Hopf algebras, renormalization and Feynman graphs - continued 1h
      Speaker: Dirk Kreimer
    • 16:45 17:15
      Discussion 30m
    • 17:15 17:55
      Might quantum field theory and number theory help each other? 40m
      Speaker: David Broadhurst, The Open University
    • 09:30 10:15
      Properties of Feynman graph polynomials 45m
      Speaker: Christian Bogner (Aachen)
      Slides
    • 10:30 11:00
      coffee 30m
    • 11:00 12:00
      Periods, Feynman integrals and number theory 1h
      Speaker: Francis Brown (Jussieu)
      Slides
    • 12:00 12:30
      Discussion 30m
    • 13:00 14:00
      lunch 1h
    • 14:30 15:30
      The use of Hochschild cohomology in QFT 1h
      Speaker: Dirk Kreimer
    • 15:30 15:45
      break 15m
    • 15:45 16:45
      The use of Hochschild cohomology in QFT - continued 1h
      Speaker: Dirk Kreimer
    • 16:45 17:15
      Discussion 30m
    • 09:45 10:45
      From graph polynomials to limiting mixed Hodge structures 1h
      Speaker: Dirk Kreimer
    • 10:45 11:00
      break 15m
    • 11:00 12:00
      From graph polynomials to limiting mixed Hodge structures - continued 1h
      Speaker: Dirk Kreimer
    • 12:00 12:30
      Discussion 30m
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