Research interest: low dimensional topology, singularity theory of complex surfaces and mappings, immersion theory, algebraic geometry, topology of quantum systems

Quantum mechanics meets singularity theory: With my physicist collaborators we study degeneracy points of physical systems. These systems are described by a parameter dependent family of matrices (e.g. the Hamiltonian map in the case of quantum systems), with coincident eigenvalues at certain points, which are called degeneracy points. The characterization of the degeneracy naturally leads to singularity theoretical methods. The topology has had a revolutionary influence in this area in the recent decades, and we expect a similar one from singularity theory. Joint work with György Frank, András Pályi, Dániel Varjas, Zoltán Guba, Péter Vrana.

A talk about this topic.

MSc and PhD research topic

Singularity theory meets immersion theory:  My PhD work deals with holomorphic map germs, whose images define certain type of non-isolated surface singularities. The restriction of such germ to the  boundary defines an immersion of spheres. I compared the immersion invariants, like the Smale invariant, Ekholm-Szűcs invariant, with the invariants of the complex singularity, like the cross cap number, triple point number, and the Milnor fibre of the singularity. A future project is to extend the new methods to more general families of singularities. Joint work with András Némethi, András Sándor, Tamás Terpai, Roberto Giménez Conejero, András Szűcs.

A talk with A. Sándor and another one With R. Giménez Conejero.