Motives in Relation to Mathematical Physics
The theory of motives, founded by Alexandre Grothendieck in the 60ies, originates in algebraic geometry and proves to be a versatile tool to study generalised (co)homology theories.
"Contrary to what occurs in ordinary topology, one finds oneself confronting a disconcerting abundance of different cohomological theories. One has the distinct impression (but in a sense that remains vague) that each of these theories 'amounts to the same thing', that they 'give the same results'. In order to express this kinship of these different cohomological theories, I formulated the notion of 'motive' associated to an algebraic variety. By this term I want to suggest that it is the 'common motive' (or 'common reason') behind this multitude of cohomological invariants attached to an algebraic variety, or indeed, behind all cohomological invariants that are a priori possible" (Alexandre Grothendieck, Récoltes et semailles: Réflexions et témoignages sur un passé de mathématicien. Université des Sciences et Technologies du Languedoc, Montpellier, et Centre National de la Recherche Scientifique, 1986. [Translation from: Barry Mazur, What is a Motiv, Notices of the AMS, Vol 51(10), 2004, p. 1215])
Via string theory, motives became a tool in mathematical physics, useful e.g. in the computation of Euler numbers of orbifolds. Rather puzzling results and conjectures emerged from this realm, e.g. the concept of mirror symmetry. Motivic integration was used for example by Kontsevich. Even more recently it was appreciated that multi zeta values and polylogarithms appearing in perturbative quantum field theoretical calculations (of toy models) are of a `Feynman' motivic origin. The motivic Galois theory used by Connes and Marcolli in renormalisation theory is another appearance of this intriguing structure in mathematical physics.
The joint workshop on 'Motives in Relation to Mathematical Physics' tries to provide a forum for mathematicians and physicist to discuss recent developments in the theory and application of motives.