My mathematical interest is in situations where methods of algebraic topology (e.g. sheaf cohomology) can be applied to yield information on the solutions of a geometrically meaningful differential operator (e.g. the Laplace-operator or the Dirac-operator on a manifold).
My main research topic is Complex Geometry, more precisely the relation between integrable connexions and Higgs bundles on a complex curve, known as non-abelian Hodge theory, and various incarnations of the Fourier transform.
Recently, I am also interested in the relation between the space of Fuchsian differential equations and the moduli space of logarithmic integrable connections.
I am a member of the Differential Topology and Algebraic Geometry group of the Rényi Institute of Mathematics. I am an organizer of the Seminar of Young Researchers (FIKUSZ) at the Rényi Institute. I have a teaching position at the Technical University of Budapest.
Click here for my short curriculum (in html format), or here for a detailed version (pdf file).
Here are the informal notes of my talk on Hitchin's equations and Fourier transform on curves, held in March 2007 at the Lie algebras and moduli spaces seminar of the Technical University of Budapest. And here the slides of my talk on Fourier transform and the Deligne-Simpson problem (in Hungarian!), held at the Rényi Institute's Young Research Fellow Symposium on the 17th of November, 2008.
Click here for the list of my publications on arXiv, and search for 'Szabo' AND 'Sz' as well as for 'Szabo' AND 'Szilard'.