# 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. Funding is also available to support travel to conferences and workshops. The position may be started after 01.04.2023 and preferably before 01.10.2023.

The differential geometry group at the ULB is a dynamic research group with an excellent international reputation and a lively community of PhD students and postdoctoral researchers. The members of the group have extensive collaborations and links with other research institutions from around the globe. The group is active in Riemannian geometry, symplectic geometry, gauge theory and geometric analysis. ULB features an excellent mathematics department providing a stimulating research environment.

As a PhD student you will carry out mathematical research in the context of the research project "Topological methods in enumerative geometry of G2 manifolds" funded jointly by FNRS and DFG. You will be based in Brussels and work with Andriy Haydys and cosupervised by Sebastian Goette (Freiburg).

You are expected to have a masters degree (or equivalent) in mathematics, or to obtain such a degree before the starting date of the PhD project. A working proficiency in English is necessary, however knowledge of French or German is not required.

To apply, please send the following documents to Andriy Haydys as a single PDF-file:- Letter of motivation, no longer than 2 pages, providing information about your mathematical interests.
- CV.
- A brief description of masters thesis (or any project that you may have carried out) and the master thesis itself (draft if not yet ready).
- The names and e-mail addresses of two referees.
- Copies of degrees / university transcripts or a list of all master courses taken (including grades, when available).

If you have any questions about the position, please contact Andriy Haydys.

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.