Yorkshire and Durham Geometry Days
A Yorkshire and Durham Geometry Day will take place on
Friday March 8, 2019
in the Department of Mathematics at Durham University.
10:00 Coffee Mathematics Department Common Room CM211
11:00 Fernando Galaz-Garcia
(Karlsruhe) in CM301
In Riemannian geometry, collapse imposes strong geometric and topological restrictions on the spaces on which it occurs.
In the case of Alexandrov spaces, which are metric generalizations of complete Riemannian manifolds with a uniform lower sectional
curvature bound, collapse is fairly well understood in dimension three. In this talk, I will discuss the geometry and topology of
sufficiently collapsed three-dimensional Alexandrov spaces: when the space is irreducible, it is modeled on one of the eight
three-dimensional dimensional Thurston geometries, excluding the hyperbolic one.
This extends a result of Shioya and Yamaguchi, originally formulated for Riemannian manifolds, to the Alexandrov setting.
(Joint work with Luis Guijarro and Jesús Núñez-Zimbrón).
- "Geometry and topology of sufficiently collapsed three-dimensional Alexandrov spaces"
12:00 Lunch break
1:15 Martin Kell (Tuebingen) in
Abstract: In this talk I will prove the existence of optimal transport maps in the Riemannian and Lorentzian setting.
In case the cost function is just the length this will lead to a solution to the Monge problem in both the classical as
well as the relativistic setting. The proof is rather elementary and relies on a very weak
notion of lower Ricci curvature. It also works for a wider class of metric spaces having (weakly) non-branching geodesics,
e.g. Alexandrov spaces and so-calld RCD-spaces.
- "Transport maps and non-branching geodesics in Riemannian and Lorentzian geometries"
2:15 Tea break in CM211
3:00 Stefan Suhr (Bochum)
The Ricci curvature is the basic ingredient in the Einstein equations of general relativity. In recent years the interpretation of Ricci curvature in
Riemannian geometry has changed fundamentally via its characterization in terms of convexity properties of e.g. the Shannon-Bolzmann entropy of optimal
transportation. In my talk I will explain the recent development of an analogous characterization of Ricci curvature and the
Einstein equation in Lorentzian geometry.
- "Optimal transportation and the Einstein equation"
4:00 Tea break in CM211
4:30 Monica Musso (Bath) in CM301
Abstract: A classical problem for the two-dimensional Euler flow for an incompressible
fluid confi ned to a smooth domain is that of fi nding regular solutions with highly concentrated vorticities around N moving vortices. The formal dynamic
law for such objects was fi rst derived in the 19th century by Kirkhoff and Routh. We devise a gluing approach for
the construction of smooth N-vortex solutions. We capture in high precision the core of each vortex as a scaled fi nite
mass solution of Liouville's equation plus small, more regular terms.
This work is in collaboration with J. D. Avila, M. del Pino, J. Wei.
- "Gluing methods for vortex dynamics in Euler flows"
5:45 Leave for dinner at Grey College from CM211
Durham is easy to get to by car and train, and so is the Department of Mathematics, located on the Science Site. Click here for relevant information.
Yorkshire and Durham Geometry Days are jointly organised by the Universities of Durham, Leeds and York, and occur at a
frequency of three meetings per academic year. Financial support is provided by the London Mathematical Society through a Scheme 3 grant,
currently administered by the University of York. Additional support is provided by the Department of Mathematics,
local organizers are:
Bolton & Wilhelm Klingenberg,
University of Durham
Derek Harland &
Gerasim Kokarev, University
McIntosh & Chris
Wood, University of York