Curriculum Vitae

Personal

Married, two children (11 and 6 years old).

Education

2015 Habilitation, Bielefeld University, Germany.
Thesis: Compactness of moduli spaces in some problems inspired by higher dimensional gauge theory.
2006 PhD, Georg-August University of Goettingen, Germany.
Thesis: Generalized Seiberg-Witten equations and hyperKaehler geometry.
Supervisor Prof.Dr. Victor Pidstrygach.
1997-2002 Five-year B.Sc/M.Sc integrated degree in Mathematics; National University of Lviv, Ukraine.
Diploma with distinction.

Employment

from 2021
 ULB;
Chargé de Cours (Assistant Professor).
2017-2021
 Freiburg University;
PostDoc (supported by the Simons Collaboration on Special Holonomy).
2009-2017
 Bielefeld University;
Assistant Professor (Akademischer Rat a.Z.; fixed-term position).
2006-2009 Bielefeld University;
PostDoc (Wissenschaftlicher Mitarbeiter).

Visiting positions

2019-2020 Stanford University;
Visiting Researcher.
2010-2012 Imperial College London;
Visiting Researcher (supported by the DFG).

Publications/Preprints

1. A. Haydys. Seiberg-Witten monopoles and flat PSL(2;R)-connections, Adv. Math. 409 (2022).
2. A. Haydys. Introduction to gauge theory, arXiv:1910.10436
3. A. Haydys and B. Xu. Special Kähler structures, cubic differentials and hyperbolic metrics, Selecta Math. 26, 37 (2020), arXiv:1807.08550.
4. 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
5. M. Callies and A. Haydys. Affine special Kaehler structures in real dimension two, In Spectral Structures and Topological Methods in Mathematics, EMS Series of Congress Reports, pp. 221–233, Zürich: European Mathematical Society, 2019; arXiv:1710.05211
6. A. Haydys. G2 instantons and the Seiberg-Witten monopoles. In Gromov-Witten Theory, Gauge Theory and Dualities edited by P. Bouwknegt, B. Parker and B.-L. Wang (to appear). arXiv:1703.06329.
7. 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
8. A. Haydys. Isolated singularities of affine special Kaehler metrics in two dimensions. Commun. Math. Phys., 340(3):1231-1237, 2015; arXiv:1505.00462
9. A. Haydys, Th.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
10. A. Haydys. Dirac operators in gauge theory, In New ideas in low-dimensional topology edited by L.Kauffman and V.Manturov, volume 56 of Ser. Knots Everything, pp. 161-188. World Sci. Publ., Hackensack, NJ, 2015; arXiv:1303.2971
11. A. Haydys. Fukaya-Seidel category and gauge theory, J. Symplectic Geom. 13(1):151-207, 2015. arXiv:1010.2353
12. A. Haydys. Gauge theory, calibrated geometry and harmonic spinors, J. Lond. Math. Soc. (2), 86(2):482-498, 2012. arXiv:0902.3738
13. A. Haydys. HyperKahler and quaternionic Kahler manifolds with S1-symmetries. J. Geom. Phys. 58(2008), no. 3, 293-306. arXiv: 0706.4473
14. A. Haydys. Nonlinear Dirac operator and quaternionic analysis. Comm.  Math. Phys. 281(2008), 251-261,arXiv:0706.0389

Grants/Awards

since 2017 Principal Investigator;
Research Training Group "Cohomological methods in Geometry''.
2013-2017 Principal Investigator;
Project "Algebraic and analytic aspects of holomorphic Lagrangian fibrations'' (together with S.Rollenske; CRC 701) funded by the DFG.

PostDocs
2016-2017 Dr. Martin Callies.
2015 Dr. Ryouke Takahashi.
2014-2015 Dr. Giovanni Bazzoni.
2010-2012 Research Fellowship of the DFG;
Research project "High and low dimensional gauge theory and exceptional geometry".
Host Institution: Imperial College London.
2007-2009 Reserch project
"Gauge theory over low and high dimensional manifolds and exceptional geometry" supported by Bielefeld University.
2002-2005 Scholarship of the research training group "Groups and Geometry", Georg-August University of Goettingen.

Selected Recent Invited Talks

2020 Workshop “Geometry and Analysis of Moduli Spaces”, London, UK.
2019 Minisymposium on Gauge Theory and Partial Differential Equations, La Quinta, USA.
Berkeley Mathematical Physics Seminar, Berkeley, USA.
Workshop “Geometric and analytic aspects of moduli spaces”, Hanover, Germany.
Pure Math Colloquium, University of Waterloo, Canada.
2018 Workshop on Special Metrics and Gauge Theory, Madrid, Spain.
25th Goekova Geometry and Topology conference, Goekova, Turkey.
Geometry and Physics Seminar, CalTech, USA.
Workshop "Gauge Theory and Special Holonomy'', London, UK.
2017 Workshop "The Analysis of Gauge-Theoretic Moduli Spaces", Banff, Canada.
Workshop on G2 Manifolds and Related Topics, Toronto, Canada.
Mathematical Congress of the Americas, Special session on Gauge theory and special geometry, Montreal, Canada.
Symposium in Geometry and Differential Equations, Beijing, China.
Workshop "Gauge Theory and Categorification", UCLA, Los Angeles, USA.
2016 9th Brussels-London geometry seminar "Gauge theory'', University College London, London, UK.

Workshop "Recent Developments in the Mathematical Study of Gauge Theory'', Simons Center, Stony Brook, USA.

Inaugural Conference of Simons Collaboration on Special Holonomy in Geometry, Analysis, and Physics, Simons Center, Stony Brook, USA.

Workshop "General Relativity: from Geometry to Amplitudes'', Cambridge, UK.

Conference "Gromov-Witten theory, Gauge Theory and Dualities'', Kioloa, Australia.
2015 Mathematics Colloquium, Bielefeld University, Germany.

CUHK/UM Joint International Workshop in Geometry, Hong Kong, China.

Mini-Workshop "Singularities in G2-geometry'', Oberwolfach, Germany.

Invited Lectures

2019 Introduction to gauge theory, 2019 PCMI summer school "Quantum Field Theory and Manifold Invariants'', Park City, USA (6 lectures).
2018 Integrable systems and special Kaehler geometry, University of Science and Technology of China, Hefei, China (6 lectures).