Posztdoktori kutató
Oktatás
2024 autumn:
- Topological methods in condensed matter physics - special course with Levente Rózsa
- Vector and Matrix Algebra (physicist-engineering)
2023 autumn: BME, Department of Theoretical Physics
2018 - 2021: Eötvös Lorand University, Department of Analysis
- Calculus for economic students (ELTE GTI, economists)
- Set theory and logic (mathematics teachers)
- Popular Mathematics (interdisciplinar course)
I gave lectures and seminars at
- Budapest Business School (BGE) (2010 – 2013),
- Budapest University of Technology and Economics (BME) (2013 – )
- Eötvös Loránd University (ELTE) (2015 – )
in the following topics: analysis, calculus, probability theory, vector calculus, operations analysis, popular mathematics.
In 2022 I taught in the high school Forrás Waldorf in Győr.
Kutatás
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.
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.
Válogatott közlemények
Quantum mechanics meets singularity theory:
- György Frank, Dániel Varjas, G. P., András Pályi: Birth quota of non-generic degeneracy points, Arxiv, (2022)
- György Frank, Dániel Varjas, Péter Vrana, G. P., András Pályi: Topological charge distributions of an interacting two-spin system, Physical Review B. 105(3), (2022)
- Zoltán Guba, György Frank, G. P., András Pályi: Weyl-points in ball-and-spring mechanical systems, Arxiv, (2023)
Singularity theory meets immersion theory:
- G. P., R. Giménez Conejero: Signature of the Milnor fiber of parametrized surfaces, Arxiv, (2024)
- G. P., András Sándor: Cross caps, triple points and a linking invariant for finitely determined germs, Revista Matematica Complutense (2023) (opec access)
- András Némethi, G. P.: Immersions associated with holomorphic germs, Comment. Math. Helv., 90, (2015), 513-541.
Ismeretterjesztő könyveim (magyarul) // Popular science books (in Hungarian):
Előadások
Conference lectures
- Magyar Fizikus Vándorgyűlés (in Hungarian), 2022, programfüzet
- Tatra conference in Low-dimensional topology, Male Ciche, Poland, August of 2015
Seminar lectures
- Stony Brook University, 2019
- University of Strasbourg (IRMA), 2019
- Warwick University, 2017
- University of Valencia, 2017
- BME, Department of Geometry, Department of Theoretical Physics (regularly)
- Rényi Institute, AGDT Seminar (regularly), videos: 1, 2, 3
- ELTE, Department of Analysis (regularly)
Ismeretterjesztő előadásim (főleg magyarul) // Popolar science talks (mostly in Hungarian)
- Térteremtés -TEDxYouth (with English subtitles), 2016
- Térteremtés - Mindenki Akadémiája (M5) (2017)
- Mi a lyuk? - Budapest Science Meetup (2017)
- A változás pillanata - Famelab (2018)
- A teremtés szabadsága - Csopa Cafe (2017)
- Új világok teremtése könyvbemutató (2020)
- Milyen térben él egy kvantumbit? - Kutatók Éjszakája a Rényiben (2022)
- Bepillantás a topológiába és magasabb dimenziókba Euler tételén keresztül - Rátz László Vándorgyűlés (2023)
- Rendszeres MateMorfózis ismeretterjesztő szeánszok szórakozóhelyeken és fesztiválokon (2011-től napjainkig), néhány videó
Linkek
MateMorfózis tudományos ismeretterjesztés és a zenéim // Popolar science MathMorphosis and my music:
My old research homepage: renyi.hu/lapker