For the near future, the seminar will be held via Zoom. If you would like to receive the regular weekly announcements then please e-mail me and I can add you to the e-mail list.

Date | Speaker | Title |

6 October | ||

13 October | Sebastian Heller (Hannover) | The energy of holomorphic sections of the Deligne-Hitchin moduli space |

20 October | Georgios Kydonakis (MPIM Bonn) | Poisson structures on moduli spaces of Higgs bundles over stacky curves |

27 October | Ben Sibley (Université libre de Bruxelles) | Compactifcations of Hermitian-Yang-Mills moduli space and the Yang-Mills flow on projective manifold |

3 November | ||

10 November 4pm this week only | Paul Feehan (Rutgers) | Virtual Morse-Bott theory on analytic spaces, moduli spaces of SO(3) monopoles, and applications to four-manifolds (slides) |

17 November | Lynn Heller (Hannover) | Area Estimates for High genus Lawson surfaces via DPW |

24 November | Jason Lotay (Oxford) | Deformed \(G_2\)-instantons (slides) |

1 December | Eloise Hamilton (IMJ-PRG) | Moduli spaces for unstable Higgs bundles of rank 2 and their geometry |

Date | Speaker | Title |

19 January | Chikako Mese (Johns Hopkins) | Holomorphic Rigidity of Teichmuller space |

26 January | ||

2 February | ||

9 February | ||

16 February | Mark Haskins (Duke) | Solitons in Bryant's G_2-Laplacian flow (slides) |

23 February | ||

2 March | Sushmita Venugopalan (IMSc Chennai) | Tropical Fukaya Algebras |

9 March | ||

16 March | Chris Woodward (Rutgers) | Morse flow trees and deformations of exact Lagrangians |

Date | Speaker | Title |

20 April | ||

27 April | ||

4 May | ||

11 May | Alastair King (Bath) | Categorification of perfect matchings |

15 June | Zeno Huang (CUNY) | TBA |

In the first part, we recall basic concepts of hyper-Kähler manifolds and their twistor spaces. For hyper-Kähler spaces admitting a circle action (and some additional conditions) we explain the construction (by Haydys and Hitchin) of a holomorphic line bundle with a meromorphic connection on its twistor space. The energy of a section is given by the residue of the pull-back of the meromorphic connection. It is shown that the energy on the spaces of twistor lines coincides with the moment map for the circle action. In the second part of the talk we consider the particular case of the Higgs bundle moduli space. Its twistor space can be identified with the Deligne-Hitchin moduli space of \(\lambda\)-connections. We prove a natural formula for the energy of a section of the Deligne-Hitchin moduli spaces in terms of a Serre-type pairing. Finally, we compute the energy for a class of examples given by Willmore surface.

The talk is based on joint work with F. Beck and M. Röser, and on joint work with L. Heller.

This is joint work with Hao Sun and Lutian Zhao.

This work is spread out over several papers, and is partly joint work with Richard Wentworth, and with Daniel Greb, Matei Toma, and Richard Wentworth.

This is joint work with Sebastian Heller and Martin Traizet.

This is joint work with Johannes Nordström and also in part with Rowan Juneman at Bath.

This is joint work with Chris Woodward.