# Andriy Haydys

Haydys' research interests include in particular:

- gauge theory and its applications;
- Riemannian manifolds with special holonomy groups and related geometries;
- geometric analysis.

The differential geometry group at the ULB is looking to recruit a PhD student with full funding for 4 years, with no associated teaching duties. The position may be started after 01.04.2023 and preferably before 01.10.2023. Further details.

Speakers include Rafe Mazzeo (Stanford), Victor Nistor (Université de Lorraine), and Alessandro Pigati (Courant Institute). Financial support is available for PhD students and postdocs. Further details.

A. Haydys. Seiberg-Witten monopoles and flat PSL(2;R)-connections, Adv. Math. 409 (2022), arXiv:2001.07589. |

A. Haydys. The infinitesimal multiplicities and orientations of the blow-up set of the Seiberg–Witten equation with multiple spinors. Adv. Math. 343 (2019), 193–218; arXiv:1607.01763. |

A. Haydys, T.Walpuski. A compactness theorem for the Seiberg-Witten equation with multiple spinors in dimension three. Geom. Funct. Anal. (GAFA), 25(6):1799-1821, 2015; arXiv:1406.5683 |

A. Haydys. Gauge theory, calibrated geometry and harmonic spinors, J. Lond. Math. Soc. (2), 86(2):482-498, 2012. arXiv:0902.3738 |

Since a complete special Kähler metric is necessarily flat, a singular special Kähler metric is a relevant object of study. From the integrable system point of view, singularities of special Kähler structures correspond to singular fibers of the corresponding holomorphic Lagrangian fibration. From the moduli space point of view, singularities correspond to the "boundary points", i.e., degenerations of the structures under consideration. The main goal of this project is to understand singularities of special Kähler structures in a systematic way.

A. Haydys and B. Xu. Special Kähler structures, cubic differentials and hyperbolic metrics, arXiv:1807.08550 |

M. Callies and A. Haydys. Local models of isolated singularities for affine special Kähler structures in dimension two, IMRN, DOI:10.1093/imrn/rny165, arXiv:1711.09118 |

A. Haydys. Isolated singularities of affine special Kaehler metrics in two dimensions. Commun. Math. Phys., 340(3):1231-1237, 2015; arXiv:1505.00462 |

- Topology of the blow up locus for the Seiberg-Witten equation, Stony Brook, USA, 2016.
- G2-instantons and the Seiberg-Witten monopoles (this is a shorter version of the two talks with the identical title below), Cambridge, UK, 2016.
- A compactness theorem for the Seiberg-Witten equations with multiple spinors, Stony Brook, USA, 2014.
- G2-instantons and the Seiberg-Witten monopoles I, Stony Brook, USA, 2014.
- G2-instantons and the Seiberg-Witten monopoles II, Stony Brook, USA, 2014.
- Fukaya-Seidel category and gauge theory, Banff, Canada, 2013.