FNRS Contact Group in Differential Geometry
The 2012 FNRS contact group in differential geometry will take place 18-19 December, at the Université Libre de Bruxelles. The talks will be in the Salle Solvay. This is right next to the lifts on the fifth floor of building NO, which houses the mathematics department, on Campus de la Plaine of the university.
The conference is being organised by Mélanie Bertelson and Joel Fine. If you have any questions (e.g., concerning the schedule, travel arrangements or booking accommodation) then please do not hesitate to contact us.
The conference poster is available to those of you who want to help us publicise the conference by putting it up on the walls around your department.
The confirmed speakers are
- Vincent Borrelli
- Stefan Friedl
- Kirill Krasnov
- Dmitri Panov
- Patrick Popescu-Pampu
- Sobhan Seyfaddini
- Richard Thomas
- Michel Willem
There will be a conference lunch on the 18th December at La Mirabelle. Please let us know in advance whether or not you will be able to attend the lunch by emailing Mélanie Bertelson. Unfortunately participants will have to pay for their own lunch, since we do not have the funds to pay for everybody.
The precise schedule of talks will be confirmed nearer the time, but will be along the following lines.
Tuesday 18th December
9.30-10.30 Patrick Popescu-PampuStein fillings of Lens spaces with standard contact structures are Milnor fibres.I will present steps in the proof of the conjecture of Lisca connecting Stein fillings of Lens spaces with their standard contact structure and deformations of singularities of toric surfaces. This is joint work with Andras Némethi.
11.00-12.00 Stefan FriedlRecent developments in 3-manifold topologyIan Agol and Dani Wise recently showed that fundamental groups of hyperbolic 3-manifolds are “virtually special”. This result implies in particular the virtual Haken and the virtual fibering conjecture. In this survey talk we will explain the meaning of “virtually special” and we will summarize some of the implications.
15.00-16.00 Vincent BorrelliFlat tori in three-dimensional spaceIn the mids 1950s, Nash and Kuiper proved a bewildering theorem: any m-dimensional Riemannian manifold admitting an embedding in an Euclidean space E^n (n>m) can be C^1 isometrically embedded in the same Euclidean space. The result was then really a surprise, in part because of its numerous counterintuitive implications. For instance, it follows from that theorem that there exist C^1 isometric embeddings of flat tori into E^3 (a flat torus is a quotient E^2/L where L=Ze_1+Z e_2 is a lattice). In the 70-80's, Gromov turned the results of Nash into generic tools for solving undetermined system of partial differential equations: the Convex Integration theory. This theory offers a systematic approach and opens the door to a deeper understanding of Nash-Kuiper embeddings. We shall focus on the geometric structure of embedded flat tori obtained by the convex integration process. We shall also present the first pictures of an embedded flat torus.
16.30-17.30 Michel WillemPoincaré inequality and a relative isoperimetric inequalityWe consider various aspects of the Poincaré inequality in the space of functions of bounded variations. In particular we describe the relations between the optimal Poincaré inequality and some relative isoperimetric inequalities
Wednesday 19th December
9.30-10.30 Kirill KrasnovTwo variational principles for General Relativity, with two proofs of local rigidity of anti-self-dual Einstein metrics.I will explain two (related) reformulations of Einstein's General Relativity (in 4 dimensions). Both encode the Riemannian metric on a manifold into some other object. Thus, in one of the formulations (known as Plebanski formulation in the physics literature) the metric is encoded in a triple of two-forms, or, equivalently, an sl(2)-valued two-form. In another formulation the metric is encoded in an SO(3) connection on the manifold. In both formulations, the Einstein condition is a certain second-order PDE on the basic field. Again for both formulations, the Einstein condition arises by extremizing a certain functional in the field space. I will then discuss the linearization of the field equations (and the two functionals) around an anti-self-dual (ASD) Einstein metric. Both formulations can be used to give a simple proof of the local rigidity of the ASD Einstein metrics. The proof is particularly remarkable in the second, gauge-theoretic formulation, because in this case the functional whose critical points are Einstein metrics turns out to be convex (around an ASD Einstein metric).
11.00-12.00 Richard ThomasThe Göttsche conjectureI will discuss the Göttsche conjecture and generalisations (recently proved in increasing generality by Tzeng, Li, Kool, Shende, Thomas and Rennemo). In particular I will explain a simple proof that should generalise to symplectic geometry.
14.00-15.00 Dmitri PanovHyperbolic geometry and symplectic manifolds.This talk is based on joint works with Joel Fine and Anton Petrunin. We prove that every finitely presented group is the fundamental group of a compact three-dimensional hyperbolic orbifold and deduce the same result for compact symplectic six dimensional manifolds with c_1=0.
15.30-16.30 Sobhan SeyfaddiniC^0 limits of Hamiltonian paths and spectral invariants.After briefly reviewing spectral invariants, I will write down an estimate, which under certain assumptions, relates the spectral invariants of a Hamiltonian to the C^0-distance of its flow from the identity. Time permitting I will present a few applications to Hofer geometry