Date | Speaker | Title |

8 October | ||

15 October | ||

22 October | ||

29 October | ||

5 November | Andrea Appel (Edinburgh) | Quantisation via differential twists |

12 November | ||

19 November | Yuuji Tanaka (Oxford) | On two generalisations of Hitchin's equations in four dimensions from Theoretical Physics |

26 November | Andrew Dancer (Oxford) | Symplectic duality and implosion |

3 December | Johan Martens (Edinburgh) | A general approach to the Hitchin connection |

Date | Speaker | Title |

14 January | ||

21 January | Alina Vdovina (Newcastle) | \(C^*\)-algebras coming from cube complexes and buildings |

28 January | Nuno Romao (Augsburg) | Pochhammer states on Riemann surfaces |

4 February | ||

11 February | ||

18 February | Matthew Young (MPIM Bonn) | Unoriented Dijkgraaf-Witten theory |

25 February | Mathew Bullimore (Durham) | Symplectic Vortices and Symplectic Duality |

3 March | Aron Wall (Cambridge) | The Maximin Method: How to Prove Holographic Entropy Inequalities |

10 March | Samuel Borza (Durham) | Measure Contraction Property of generalised Grushin planes |

Date | Speaker | Title |

14 April | ||

21 April | ||

28 April | Ben Davison (Edinburgh) | Strong positivity for quantum cluster algebras |

5 May | ||

12 May | Yue Fan (Maryland) | Construction of the moduli space of Higgs bundles using analytic methods (video) |

26 May | Jan Swoboda (Heidelberg) | Moduli spaces of parabolic Higgs bundles: their ends structure and asymptotic geometry (video) |

2 June | Victoria Hoskins (Nijmegen) | On the motive of the moduli space of Higgs bundles |

9 June | ||

16 June | ||

23 June | Szilard Szabo (Budapest) | Geometry of Hodge moduli spaces in the Painlevé cases |

30 June |

This is joint work with Frances Kirwan and Amihay Hanany.

This is joint work with Baier, Bolognesi and Pauly.

This is joint work with Marcel Bökstedt.

Since the dynamical version of AdS/CFT involves Lorentzian geometries, it is important to be able to prove the corresponding inequalities for asymptotically AdS geometries. In this case, we have to use extremal surfaces instead of globally minimal ones, making it more difficult to prove global inequalities. But by reformulating extremal surfaces in terms of an equivalent "maximin" variational principle, elegant proofs can be constructed. (Unlike the static case, these results require use of the null curvature condition.)

The classical version of this question was settled in the affirmative by Gross, Hacking, Keel and Kontsevich. I will present a proof of the quantum version of this positivity, due to joint work with Travis Mandel, based on results in categorified Donaldson-Thomas theory obtained in joint work with Sven Meinhardt.

In my talk, I will mostly take up this latter point of view and give an introduction to Higgs bundles on Riemann surfaces both in the smooth and the parabolic setting. In the parabolic case, i.e. in the situation where the Higgs bundles are permitted to have poles in a discrete set of points, I will discuss recent joint work with L. Fredrickson, R. Mazzeo and H. Weiß concerning the asymptotic geometric structure of their moduli spaces. Here the focus lies on the hyperkähler metric these spaces are naturally equipped with. One implication of a recent conjectural picture due to Gaiotto-Moore-Neitzke suggests that this metric is asymptotic to a so-called semiflat model metric which comes from the description of the moduli space as a completely integrable system.

We shall also discuss several open questions in the case where the Riemann surface is a four-punctured sphere and these moduli spaces turn out to be gravitational instantons of type ALG.