My main research interest is in moduli spaces of tame and wild harmonic bundles on Riemann surfaces.

See my Google Scholar profile .

- Hitchin WKB-problem and P = W conjecture in lowest degree for rank 2 over the 5-punctured sphere , The Quarterly Journal of Mathematics (December 2022)
- Perversity equals weight for Painlevé spaces, Adv. Math. (2021) ,
- joint with András Némethi:
The Geometric P=W Conjecture in the Painlevé Cases via Plumbing Calculus, IMRN Volume 2022, Issue 5, Pages 3201-3218
## Talks

- Hitchin's equations and Fourier transform on curves
(informal notes typed by Zs. Szilágyi, pdf), March 2007,
*Lie algebras and moduli spaces Seminar*of the Technical University of Budapest. - Nahm transform for parabolic integrable connections on the Riemann sphere (slides, pdf), 29th of August 2007, Workshop on Non-linear integral transforms: Fourier-Mukai and Nahm, Centre de Recherches Mathématiques, Montreal.
- Nahm transform for parabolic integrable connections on the Riemann sphere (slides, pdf), 3rd of March 2008, Geometry and Analysis Seminar, University of Oxford.
- Knots and their
invariants (slides in Hungarian, ps), 3rd of June 2008,
*Young Professors' Symposium*, Technical University of Budapest. - Nahm transform for parabolic integrable connections on the Riemann sphere (slides, pdf), 11th of June 2008, Mini-workshop on Krichever-Novikov algebras, Luxembourg.
- The Hitchin system and Mirror symmetry (slides in Hungarian, pdf), 30th of August 2008, Integrability Summer School, Physics Department of the Eötvös Loránd University, Budapest.
- Fourier transform and the Deligne-Simpson problem (slides in
Hungarian, pdf), 17th of November, 2008,
*Young Research Fellow Symposium*of the Rényi Institute . - Deformations of logarithmic connections and apparent singularities (slides, pdf), 14th of July 2009, Kyoto RIMS Workshop on Non-abelian Hodge theory and Geometry of Twistor structures
- The geometry of the basic instanton moduli space over the multi-Taub--NUT space (slides, pdf), 20th of July 2009, Kobe Kobe Workshop on Geometry of Moduli Spaces
- The geometry of the basic instanton moduli space over the multi-Taub--NUT space, 1st of February 2010, Dublin Theoretical Physics Colloquium.
- Nahm transform for parabolic integrable connections on the Riemann sphere 4th of August 2014, Singapore Conference on The Geometry, Topology and Physics of Moduli Spaces of Higgs Bundles
- Hyper-K\"ahler isometry of Fourier--Laplace--Nahm transform 15 June 2015, Warwick, Fourier--Mukai, 34 years on
- Spectral data for irregular Higgs bundles, 8 October 2015, Chennai Fifty Years of the Narasimhan-Seshadri Theorem
- Irregular Higgs bundles on curves and sheaves on ruled surfaces 14 Jan. 2016, Lausanne, Workshop - Higgs bundles and Hitchin system - VBAC2016
- Spectral representation of irregular Higgs bundles on curves 16 June 2016, Simons Center for Geometry and Physics, Stony Brook, New Trends in Higgs bundles, branes and quantization
- Elementary transformations of singular oper-like objects, 8 December 2016, Kobe University Algebraic Geometry and Integrable Systems, Kobe 2016
- Nahm transform for parabolic harmonic bundles on the Riemann sphere with regular residues 13 February 2017, Perimeter Institute for Theoretical Physics, Waterloo, Hitchin systems in Mathematics and Physics
- Perversity equals weight for Painlevé spaces June 2018, CIRM Luminy Gauge theory and complex geometry, VBAC2018
- On mathematical results of Stephen Hawking 15 October 2018, Rényi Institute Colloquium
- Perversity equals weight for Painlevé spaces 10 December 2018, Kobe Conformal field theory, isomonodromy tau-functions and Painlevé equations
- 2 May 2019, Dijon Geometry and Integrable Systems
- P = W conjecture and its geometric version for Painlevé spaces 25 June 2019, Kyoto Moduli Spaces, Representation Theory and Quantization
- Geometry of Hodge moduli spaces in the Painlevé cases 23 June 2020, University of York Geometry, Analysis and Mathematical Physics Seminar
- Sheaf-counting and wall-crossing on Painlevé moduli spaces 8 October 2020, SZTE Bolyai Institute Kerékjártó Seminar
- Asymptotic Hodge theory in the Painlevé cases 4 December 2020, University of California, Santa Barbara Differential Geometry Seminar
- Asymptotic analysis of non-abelian Hodge theory in rank 2 10 March 2021 Web-seminar on Painlevé Equations and related topics
- WKB-analysis of Hitchin system in rank 2 5 October 2021 Workshop on Toda equations, parabolic Higgs bundles, and related topics, Waseda University
- P=W conjecture in lowest degree in Garnier case with 5 parabolic points 11 February 2022 Algebraic Geometry and Integrable Systems, Kobe University (online)
- Quantum spectra of birational surfaces 11 January 2023 Web-seminar on Painlevé Equations and related topics
- Canonical coordinates for moduli spaces of rank two irregular connections on curves 20 October 2023 Complex Lagrangians, Mirror Symmetry and Quantization, Banff International Research Station

- Hitchin's equations and Fourier transform on curves
(informal notes typed by Zs. Szilágyi, pdf), March 2007,