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Spring 2017

Leeds Geometry Seminar

Organiser: Gerasim Kokarev

Time and venue:
Wednesday 3pm, Roger Stevens LT12. Coffee/Tea served in the Common Room after 4pm.

1 February 2017
Jurgen Berndt (KCL) The coindex of symmetry
Abstract. The coindex of symmetry is a geometric invariant that measures in how far a homogeneous Riemannian manifold fails to be a Riemannian symmetric space. We discuss some examples, some general structure theory for compact homogeneous Riemannian manifolds in relation to this invariant, and classifications for small coindex of symmetry. This is joint work with Carlos Olmos (Cordoba) and Silvio Reggiani (Rosario).

8 February 2017 AGIS Colloquium
Bernd Schroers (Heriot-Watt University) Integrable vortex tubes in three dimensions
Abstract. In this talk I will explain how one can combine a rather wide range of ideas and results from the literature - the work of Loss and Yau on zero-modes of a magnetic 3d Dirac operator, a dimensional reduction of the Seiberg-Witten equations, integrable vortex equations in 2d - to obtain linked vortex tubes as exact solutions of a spinorial vortex equation in 3d. There is a new, Lorentzian version of this story which I will sketch as well. This talk is based on joint work with my student Calum Ross.

22 February 2017
Michael Singer (UCL) Monopoles and the Sen Conjecture
Abstract. The Sen conjecture, made in 1994, makes precise predictions about the existence of L^2 harmonic forms on the monopole moduli spaces. For each positive integer k, the moduli space M_k of monopoles of charge k is a non-compact smooth manifold of dimension 4k, carrying a natural hyperkaehler metric. Thus studying Sen's conjectures requires a good understanding of the asymptotic structure of M_k and its metric. This is a challenging analytical problem, because of the non-compactness of M_k and because its asymptotic structure is at least as complicated as the partitions of k. For k=2, the metric was written down explicitly by Atiyah and Hitchin, and partial results are known in other cases. In this talk, I shall introduce the main characters in this story and describe recent work aimed at proving Sen's conjecture.

24 February 2017
Yorkshire and Durham Geometry Day (to be held at the University of Durham)

1 March 2017
Andrea Mondino (Warwick) Structure of Non-smooth spaces with Ricci curvature lower bounds
Abstract. The idea of compactifying the space of Riemannian manifolds satisfying Ricci curvature lower bounds goes back to Gromov in the '80s and was pushed by Cheeger and Colding in the '90s who investigated the structure of the spaces arising as Gromov-Hausdorff limits of smooth Riemannian manifolds satisfying Ricci curvature lower bounds. A completely new approach via optimal transportation was proposed by Lott-Villani and Sturm almost ten years ago; with this approach one can a give a precise meaning of what means for a non smooth space to have Ricci curvature bounded from below by a constant. This approach has been refined in the last years by a number of authors and a number of fundamental tools have now been established (for instance the Bochner inequality, the splitting theorem, etc.), permitting to give further insights in the theory. In the seminar I will give an overview of the topic with emphasis on the structure of such non smooth spaces (i.e. tangent cones and rectifiability properties).

15 March 2017
Reto Buzano (Queen Mary University of London) The moduli space of two-convex embedded spheres and tori.
Abstract. It is interesting to study the topology of the space of smoothly embedded n-spheres in R^{n+1}. By Smale's theorem this spcae is contractible for n=1 and by Hatcher's proof of the Smale conjecture, it is also contractible for n=2. These results are of great importance generalising in particuler the Schoenflies theorem and Cerf theorem. In this talk I will explain how mean curvature flow with surgery can be used to study a higher-dimensional variant of these results, proving in particular that the space of 2-convex embedded spheres is path connected in every dimension n. We then also look at the space of 2-convex embedded tori where the question is more intriguing and the result in particular depends on the dimension n. This is joint work with Robert Haslhofer and Or Hershkovits.

22 March 2017
Stergios Antonakoudis (Cambridge) The complex geometry of Teichmüller spaces and bounded symmetric domains.
Abstract. From a complex analytic perspective, Teichmüller spaces and symmetric spaces can be realised as contractible bounded domains, which have several features in common but also exhibit many differences. In this talk we will study isometric maps between these two important classes of bounded domains equipped with their intrinsic Kobayashi metric.

26 April 2017
Martin Svensson (The University of Southern Denmark) Harmonic maps into G2/SO(4) and their twistor lifts
Abstract. Burstall and Rawnsley have shown how the canonically fibered flag manifolds sit inside the twistor space of a compact, simply connected inner Riemannian symmetric space. It is known that a harmonic map from a surface into an inner Riemannian symmetric space of classical type has a twistor lift into such a flag manifold if and only if it is nilconformal in the sense that its derivative is nilpotent. In this talk, I will show that this result can be generalised to harmonic maps into the exceptional inner symmetric space G_2/SO(4). I will describe the structure of the canonically fibered flag manifolds over this space and the construction of the twistor lifts of nilconformal harmonic maps. I will also show how almost complex maps into $S^6$ can be used to construct harmonic maps into G_2/SO(4). The talk will be based on joint work with John C. Wood.

3 May 2017
Yorkshire and Durham Geometry Day at Leeds

Previous Geometry Seminars:

Academic Year 2016/17: Autumn 2016
Last modified: 25 Aug 2016