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SUMMARY:Motivic periods and the cosmic Galois group (4/4)
DTSTART;VALUE=DATE-TIME:20150527T083000Z
DTEND;VALUE=DATE-TIME:20150527T103000Z
DTSTAMP;VALUE=DATE-TIME:20190627T130041Z
UID:indico-event-731@indico.math.cnrs.fr
DESCRIPTION:In the 1990's Broadhurst and Kreimer observed that many Feynma
n amplitudes in quantum field theory are expressible in terms of multiple
zeta values. Out of this has grown a body of research seeking to apply met
hods from algebraic geometry and number theory to problems in high energy
physics. This talk will be an introduction to this nascent area and survey
some recent highlights.\n \nMost strikingly\, ideas due to Grothendieck
(developed by Y. André) suggest that there should be a Galois theory of c
ertain transcendental numbers defined by the periods of algebraic varietie
s. Many Feynman amplitudes in quantum field theories are of this type.
P. Cartier suggested several years ago applying these ideas to amplitudes
in perturbative physics\, and coined the term `cosmic Galois group'. On
e of my goals will be to describe how to set up such a theory rigorously\,
define a cosmic Galois group\, and explore its consequences and unexpecte
d predictive power.\n \nTopics to be addressed will include:\n \n1) A
Galois theory of periods\, multiple zeta values.\n2) Parametric represen
tation of Feyman integrals and their mixed Hodge structures.\n3) Operads
and the principle of small graphs.\n4) The cosmic Galois group: results
\, counterexamples and conjectures.\n\nhttps://indico.math.cnrs.fr/event/7
31/
LOCATION:IHÉS Amphithéâtre Léon Motchane
URL:https://indico.math.cnrs.fr/event/731/
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