MODERN MATHEMATICS METHODS IN PHYSICS: Diffeology, Categories and Toposes and Non-commutative Geometry
Over the past decades, physicists have become accustomed to working on infinite dimensional spaces (function spaces, groups of diffeomorphisms…), or on singular spaces (symplectic reductions, moduli spaces…). The notion of space has traversed very radical transformations, both in pure mathematics and in mathematical physics. Over time, several approaches have been identified: traditional functional analysis, non-commutative geometry, diffeology and toposes. The objective of this summer school is to introduce these recent notions of space in mathematics and/or physics (such as diffeologies, schemes, topoi, stacks, spin networks, homotopy types, noncommutative spaces, supermanifolds, etc.). The lectures will be given by: Serap Gürer, Galatasaray University, Istanbul Turkey (Diffeology) Patrick Iglesias-Zemmour, CNRS, Aix-Marseille University, France (Diffeology) Murad Özaydın, University of Oklahoma, USA (Non-commutative Geometry) Urs Scheiber, Academy of the Sciences, Prague, Czechia (Categories and Toposes)
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