# Andriy Haydys

Haydys' research interests include in particular:

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

We look for a strong candidate with a PhD working in a field of geometry and/or geometric analysis currently represented at the differential geometry group. The position has no teaching requirements attached and the knowledge of French is not required, however a good command of English is expected. The position is equipped with a travel grant of approximately 2000 euro per year which can be used for attending conferences and/or inviting collaborators. The contract of the successful candidate can start on any preferred date between October 1, 2022 and preferably by December 30, 2022.

The position is funded by the ARC grant “Transversality and reducible solutions in the Seiberg-Witten theory with multiple spinors”. The successful candidate will be expected to collaborate on problems related to this as well as pursue their own research projects.

To apply for this position, please send the following as a single pdf file to andriy.haydys[AT]ulb.be:

- motivation letter (including a preferred starting date of the contract);
- brief CV, including a publication list and the names and contact details of at least 2 established researchers that can provide a reference letter;
- brief research statement;
- copy of your PhD thesis.

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.