Topics and Lectures
Geometry, reduction and quantization
•Geometry of Dirac structures
Henrique Bursztyn
(IMPA, Brazil)
Abstract: Dirac structures were introduced by Courant and Weinstein around 20 years ago, motivated by the study of mechanical systems with constraints. Examples of Dirac structures naturally associated with symplectic geometry include closed 2-forms (e.g. the restriction of a symplectic form to a constraint submanifold) and Poisson manifolds (e.g. the quotient of a symplectic manifold by a Lie group acting freely and properly via symplectomorphisms). A key ingredient in the theory of Dirac structures is the so-called Courant bracket, which gives a unified way to view many known integrability conditions in geometry. The first of these lectures will provide an introduction to Dirac structures, with basic definitions, properties and examples. The remaining lectures will discuss recent developments and applications of the theory.
Topics should include, if time permits, Lie theoretic aspects of Dirac geometry (e.g. integration of Dirac structures and equivariant cohomology), connections with generalized momentum map theories (e.g. quasi-hamiltonian and quasi-Poisson spaces), as well as generalized complex structures and supergeometry.
•Cohomological formulae for the equivariant index of a transversally
elliptic operator
Paul-Emile Paradan
(Montpellier, France)
• Holomorphic structures and unitary connections on Hermitian vector bundles
Florent Schaffhauser
(Keio, Japan)
Multizeta, polylogarithms and periods in quantum field theory
• Iterated integrals in quantum field theory
Francis Brown
(Paris VII, France)
• A Prologomon to Renormalization
Sylvie Paycha
(Clermont-Ferrand, France)
• Introduction to Feynman integrals
Stefan Weinzierl
(Mainz, Germany)
Geometry of quantum fields and the standard model
• Geometric issues in Quantum Field Theory and String Theory
Luis J. Boya
(Zaragoza, Spain)
• Geometric Aspects of the Standard Model and the Mysteries of Matter
Florian Scheck
(Mainz, Germany)
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