Magyar változat
Research
My main research interest is in moduli spaces of
tame and wild harmonic bundles on Riemann surfaces.
See my Google Scholar profile .
My latest publications:
- 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