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The lectures will hold in MALL1, Level 8, School of Mathematics, The University of Leeds. Coffee and tea will be served on Level 9. Programme: 11.30 Coffee and Reception 12:00 Ian McIntosh (York) The (geometric) Toda equations for noncompact symmetric spaces over compact Riemann surfaces Abstract. The Toda equations arise in many different geometric settings and for those of us who keep running into them it is often difficult to establish which version comes from where. The aim of this talk is to characterise one source: those which come from primitive harmonic maps into noncompact symmetric spaces. This is essentially an exercise in Lie algebra theory. I will also talk about when one can apply well-established existence methods (from abelian gauge theory) to equations of this type. These methods only apply to a minority of the versions of Toda available. None of the methods used are new: the purpose of the exercise is to provide a useful classification. For all of these equations there are Higgs bundles lurking about. I will hopefully have time to explain how they fit in as well. 13.00 Lunch 14.00 Ilka Agricola (Marburg) Spectral theory on naturally reductive homogeneous spaces - theory and experiments Abstract. The explicit computation of the spectrum of the Laplacian on closed Riemannian manifolds is a challenging task that only succeeds under strong symmetry assumptions. After the classical examples of spheres, projective spaces, and flat tori, Riemannian symmetric spaces G/K were the first large class of manifolds for which the spectrum could be computed explicitly via representation theoretic tools. The crucial point is that the connection induced from the canonical principal fibre bundle projection G →G/K is just the Levi-Civita connection, and the Laplacian can be identified with the Casimir operator. For homogeneous spaces, this approach fails. I will explain how connections with torsion are used to „classify“ homogeneous spaces and how the task can be achieved for large families of naturally reductive homogeneous metrics. Many examples like Aloff-Wallach manifolds will be used to illustrate the results; in fact, explicit spectra were computed using Python and are available as a Jupyter notebook. 15.00 Yang Li (Cambridge) Large mass limit of G2 and Calabi-Yau monopoles Abstract. I will discuss some recent progress on the Donaldson Segal programme, and in particular how calibrated cycles arise from the large mass limit of G2 and Calabi Yau monopoles. 16.00 Tea Break 16.30 Luis J. Alías (Murcia) Maximum principles at infinity and geometric applications Abstract. In this lecture we will introduce some new forms of maximum principles at infinity on complete, non-compact Riemannian manifolds. We will also show some of their applications to different geometric topics like Bernstein-type results for entire graphs and, more generally, for hypersurfaces immersed into a Riemannian manifold endowed with a Killing vector field. Our results are part of our joint work with Antonio Caminha and F. Yure do Nascimento, from Universidade Federal do Ceará at Fortaleza (Brazil). 18.00 Dinner in the city Travel: Leeds is easily accessible by train and has direct inter-city links with major destinations in the UK. In particular, if you are travelling from London, there is a direct high-speed train from King's Cross railway station with average journey time of 140 minutes. From the railway station, the University campus is within walking distance of approximately 15-20 minutes. The Google map of the university campus can be found here; on the campus map from the university web-pages the School of Mathematics is located in the building number 84. History and organizers: 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. The current local organizers are: Previous organizers: John Wood (Leeds, 2000-2015), Jurgen Berndt (Hull, 2000-2004), Martin Speight (Leeds, 2003-2016). Archive of previous meetings can be found here.
http://www1.maths.leeds.ac.uk/~pmtgk/ydgd/ydgd2019.html
Last modified: 27 June 2025 |