The University of Geneva and the EPF Lausanne invite you to the Journée Georges de Rham 2018 which will take place at the University of Geneva, Sciences II building, in the A150 auditorium.
The Journée Georges de Rham has been introduced in 1991 by the Troisième cycle Romand de mathématiques. It convenes mathematicians not only of the CUSO universities, but also from the whole of Switzerland and from abroad and stimulates interaction between professors, postdocs and PhD students. The organisers invite two speakers of international reputation who present their vision of contemporary mathematics and of future developments. A particular aim is to offer doctoral students a modern high class perspective of mathematical sciences and to establish contacts on an international level and with other research groups.
This year, the speakers are Nigel Hitchin and Francis Brown from the Mathematical Institute at the University of Oxford.
Francis Brown: De Rham Integration
Among G. de Rham's most celebrated contributions is the theorem which states that integration of differential forms along chains defines a pairing between the cohomology theory which bears his name and singular cohomology. For algebraic varieties, this theorem was subsequently refined by Grothendieck, who defined a version of de Rham cohomology constructed out of algebraic differential forms. It is the starting point for the theory of periods. After reviewing this material, I will explain why it is natural in this context to consider a kind of `integration' of differential forms paired, not with chains, but with (duals of) differential forms. This leads to new classes of numbers and functions with several applications ranging from number theory to theoretical physics.
Nigel Hitchin: Integrable systems and algebraic geometry
Completely integrable Hamiltonian systems are an important concept in many areas of mathematics and include classical examples like the equations for a spinning top or the geodesics on an ellipsoid. A huge range of examples comes from considering the algebraic geometry of moduli spaces of Higgs bundles on a curve. The talk will focus on the geometry of the singular locus for these systems and how certain constructions in algebraic geometry such as blow-ups and Hecke correspondences help to understand the structure of this locus.
15:00-16:00: F. Brown's talk on "De Rham Integration"
16:00-16:30: Coffee/Tea Break
16:30-17:30: N. Hitchin's talk on "Integrable systems and algebraic geometry"