prof. Fard's seminars at SISSA - change of time

[Emanuele Tuillier Illingworth]

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MATHEMATICAL PHYSICS SECTOR ACTIVITIES
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Prof. Kurusch E. Fard
(LMIA, Université de Haute Alsace, Mulhouse France)

will hold 2 seminars:




Tuesday 5 May at 15.00 in SISSA lecture room C

title: The combinatorics of Bogoliubov's recursion in perturbative
renormalisation

abstract: In this talk we describe various combinatorial aspects of
perturbative renormalisation using the language of connected graded Hopf
algebras. The analog of Bogoliubov's preparation map on the Lie algebra
of Feynman graphs is identified with the Magnus expansion.




Thursday 7 May at 14.30 in SISSA lecture room D


title: The pre-Lie relation, rooted trees and the Magnus expansion

abstract: W. Magnus' classical paper on the exponential solution of
differential equations for a linear operator received much attention
since its appearance in 1954, both in applied mathematics as well as
physics. In this talk we review recent work on the classical Magnus
expansion, unveiling a new structure by using the language pre-Lie
algebras as well as Hopf algebras of rooted trees. The pre-Lie relation
implies a reduction in the number of terms in the Magnus expansion. This
observation has to be seen in the light of the computation of
commutators in particular numerical integration schemes, which is a
major expense of many algorithms. Hence it appears to make sense to look
for ways to reduce the number of commutators. Motivations as well as
applications, ranging from numerical methods to the process of
renormalisation in perturbative quantum field theory, naturally appear.