PostDoc position in Brussels

The differential geometry group at the Université libre de Bruxelles offers a 3 year postdoc position. 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.

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.
Applications will be considered on a rolling basis. There is no deadline, however applications received by September 15, 2022 will have some preference. For more information, candidates can contact Andriy Haydys andriy.haydys[AT]ulb.be.

Research projects

Gauge theory

The aim of this project is a construction of invariants of compact G2-manifolds via gauge-theoretic methods. A program for constructing such invariants was pioneered by Donaldson and Thomas. Roughly speaking, one would like to define an invariant of G2-manifolds which would remain constant along isotopies of G2-metrics by counting certain G2-instantons. One of the main problems of this approach is that the number of G2-instantons does not need to be constant along isotopies of G2-metrics. Conjecturally, one should be able to obtain an invariant of a G2-manifold that remains constant along isotopies of G2-structures by counting G2-instantons together with certain Seiberg-Witten monopoles on associative submanifolds. Some details of this approach can be found for example in Haydys' paper G2 instantons and the Seiberg-Witten monopoles.

Selected publications:

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

Special Kähler and related geometries

Special Kähler structures appear in geometry as natural structures on certain important moduli spaces and as the structure of the base of a holomorphic Lagrangian fibration. These structures also appear in physics, for example in the low energy limit of N = 2 supersymmetric Yang-Mills theory in dimension four.

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.

Selected publications:

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

Some Recorded Talks