Topics and Lectures
Geometry, reduction and quantization
•Geometry of Dirac structures
Henrique Bursztyn
(IMPA, Brazil)
•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)
Abstract: The goal of these lectures is to give an introduction to the differential-geometric approach to moduli spaces of holomorphic bundles over compact Kahler manifolds. We shall only be concerned with the fundamental example of moduli spaces of stable holomorphic bundles over compact Riemann surfaces. After explaining the correspondence between holomorphic bundles with prescribed topological type and unitary connections on a fixed Hermitian bundle with that same topological type, we will focus on the notion of stable holomorphic bundle and state Donaldson's theorem, which gives a characterization of stable bundles in terms of the corresponding unitary connections. In particular, we shall explain how this leads to the Atiyah-Bott presentation of moduli spaces of stable bundles as infinite-dimensional symplectic quotients
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)
