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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: 11.00 Coffee and Reception 11.30 Eirik Eike Svanes (Jussieu) Moduli of Heterotic Geometries. Abstract. I will review some recent developments of certain SU(3) and G2 structure geometries with bundles, referred to as heterotic compactifications in the string theory community. After a brief overview of the infinitesimal moduli of heterotic SU(3) geometries, I turn to the corresponding seven dimensional story. There are many similarities between the two situations, but also crucial differences that I will expand upon. Finally, I will report on some recent progress in understanding the finite deformations in six dimensions. We will see that the Maurer-Cartan equation of the corresponding differentially graded Lie algebra can be understood as the equation of motion of an effective theory derived from a holomorphic functional on the moduli space, known as the heterotic superpotential. This effective theory has features which combine and generalise aspects of both Holomorphic Chern-Simons and Kodaira-Spencer theory. 12.30 Lunch 13.30 Marcos Jardim (UNICAMP) Instanton sheaves and complex instantons. Abstract. Instanton bundles were introduced by Atiyah, Drinfeld, Hitchin and Manin in the late 1970s as the holomorphic counterparts, via twistor theory, to anti-self-dual SU(r) connections (a.k.a. instantons) on the sphere S^4. We will revise the ADHM construction of instanton sheaves on CP^3, along with some recent results regarding the basic geometrical features of their moduli spaces. Finally, we outline the construction of the corresponding SL(r,C) instanton connections of R^4. 14.30 Marie-Amelie Lawn (Imperial) A spinorial representation of submanifolds in space forms. Abstract. We give a spinorial representation of submanifolds of any dimension and codimension into Riemannian space forms in terms of the existence of particular spinors. As an application we will give a new concise proof of the fundamental theorem of submanifold theory. 15.30 Tea Break 16.00 Mark Gross (Cambridge) A general mirror symmetry construction. Abstract. Mirror symmetry was first discovered by string theorists circa 1990 as a duality between two very different Calabi-Yau manifolds. Since then, there have been many constructions of mirror pairs which apply to specific families of Calabi-Yau manifolds, but no construction which works in all cases. I will outline a recently announced construction due to myself and Siebert which produces mirrors in all cases that mirrors are expected to exist. 17.30 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. Financial support is provided by the London Mathematical Society through a Scheme 3 grant, currently administered by the University of York. 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/ydgd2017.html
Last modified: 28 April 2017 |