Day-long geometry seminars with three talks on a common theme
Asymptotic geometry of Riemannian manifolds
Université libre de Bruxelles, 28th November 2017
The talks will take place at the Université libre de Bruxelles. The talks will take place in the Salle de Profs, on the 9th floor of building NO, Campus de la Plaine. Lunch will be in the same room, at 12.30. Lunch is provided to all registered participants. Registration is free, but necessary so we know how many people to cater for. Please register here by 14th November. Directions to the talks can be found here.
1.45 Olivier Biquard
3.15 Anda Degeratu
4.45 Michael Eichmair
Olivier Biquard. Einstein metrics, desingularization and non degeneracy.
I will explain a recent non degeneracy result for desingularizations of Einstein 4-orbifolds. This has two types of applications: first it provides an obstruction to the existence of families of desingularizations; second it gives in principle a recursive procedure to desingularize asymptotically hyperbolic Einstein orbifolds with higher singularities.
Anda Degeratu. Quasi-Asymptotically Conical Geometries.
In this talk we introduce the class of quasi-asymptotically conical (QAC) geometries, a less rigid Riemannian formulation of the QALE geometries introduced by Joyce in his study of crepant resolutions of Calabi-Yau orbifolds. Our set-up is in the category of real stratified spaces and Riemannian geometry. Given a QAC manifold, we identify the appropriate weighted Sobolev spaces, for which we prove the finite dimensionality of the null space for generalized Laplacians as well as their Fredholmness. We conclude with new examples of Ricci-flat Kähler metrics which have these type of asymptotic geometries. This talk is based on joint work with Rafe Mazzeo and with Ronan Conlon and Frederic Rochon.
Michael Eichmair. From Dido, Queen of Carthage, to the Geometry of Spacetime.
According to the initial value formulation of general relativity, all that is future and all that is past is contained in a glimpse of a spacetime. This correspondence between the physics of the evolving spacetime and the geometry of “initial data” for the Einstein equations is dramatically and famously non-linear. The work of H. Bray, G. Huisken, R. Schoen, S.-T. Yau, and others suggests that the classical question of isoperimetry - How much area is needed to enclose a given amount of volume in initial data for the spacetime? - plays a pivotal role in this correspondence. In my lecture, I will discuss the recent proofs with O. Chodosh and with O. Chodosh, Y. Shi, and H. Yu of several long-standing conjectures in this direction.
Getting to the ULB
The entire event will take place in the mathematics department of the Université libre de Bruxelles. The department is in building NO, marked on this map which also shows the public transport which serves the campus: metro station "Delta" (line 5) and buses 71, 72 and 95. Note only roads, and not footpaths are shown on this map, the footpaths appear on this alternative plan of the campus. The talks and lunch will be in the Salle de Profs on the 9th floor of NO.
Most international visitors will arrive at Gare du Midi (where the Eurostar and Thalys terminals are). From here the easiest route to the ULB is by metro. Take line 2 or 6 in the direction "Elisabeth", and change at "Arts-Loi" for line 5, direction "Hermann Debroux", which will stop at "Delta". The journey should take approximately 30 minutes.
Click on the seminar names to see the speakers, titles and abstracts.
- Mélanie Bertelson (Université libre de Bruxelles)
- Simone Gutt (Université libre de Bruxelles)
- Reto Müller (Queen Mary's College, London)
- Dmitri Panov (King's College, London)
- Felix Schulze (University College, London)
- Michael Singer (University College, London)
- Guiseppe Tinaglia (King's College, London)