arXiv subjects

Gergő Pintér

Publications and source records attributed to Gergő Pintér.

23 records · Page 2Linked to original sources

arXiv2021

Evaluating the Effect of the Financial Status to the Mobility Customs

In this article, we explore the relationship between cellular phone data and housing prices in Budapest, Hungary. We determine mobility indicators from one months of Call Detail Records (CDR) data, while the property price data are used to characterize the socioeconomic status at the Capital of Hungary. First, we validated the proposed methodology by comparing the Home and Work locations estimation and the commuting patterns derived from the cellular network dataset with reports of the national mini census. We investigated the statistical relationships between mobile phone indicators, such as Radius of Gyration, the distance between Home and Work locations or the Entropy of visited cells, and measures of economic status based on housing prices. Our findings show that the mobility correlates significantly with the socioeconomic status. We performed Principal Component Analysis (PCA) on combined vectors of mobility indicators in order to characterize the dependence of mobility habits on socioeconomic status. The results of the PCA investigation showed remarkable correlation of housing prices and mobility customs.

cs.SI↗

arXiv2020

Topological charge distributions of an interacting two-spin system

Quantum systems are often described by parameter-dependent Hamiltonians. Points in parameter space where two levels are degenerate can carry a topological charge. Here we theoretically study an interacting two-spin system where the degeneracy points form a nodal loop or a nodal surface in the magnetic parameter space, similarly to such structures discovered in the band structure of topological semimetals. We determine the topological charge distribution along these degeneracy geometries. We show that these non-point-like degeneracy patterns can be obtained not only by fine-tuning, but they can be stabilized by spatial symmetries. Since simple spin systems such as the one studied here are ubiquitous in condensed-matter setups, we expect that our findings, and the physical consequences of these nontrivial degeneracy geometries, are testable in experiments with quantum dots, molecular magnets, and adatoms on metallic surfaces.

cond-mat.mes-hall↗

arXiv2019

On certain complex surface singularities

The thesis deals with holomorphic germs $ Φ: (\mathbb{C}^2, 0) \to (\mathbb{C}^3,0) $ singular only at the origin, with a special emphasis on the distinguished class of finitely determined germs. The results are published in two articles (arXiv:1404.2853 and arXiv:1902.01229), joint with András Némethi. In Chapter 3 of the thesis we study the associated immersion $ S^3 \looparrowright S^5 $, while Chapter 5 contains an algorithm providing the Milnor fibre boundary of the non-isolated hypersurface singularity determined by the image of $ Φ$. These results create bridges between different areas of complex singularity theory and immersion theory. The background of these topics is summerized in Chapter 1, 2 and 4.

math.AT↗

arXiv2019

The boundary of the Milnor fibre of certain non-isolated singularities

Let $ Φ: ({\mathbb C}^2, 0) \to ( {\mathbb C}^3, 0) $ be a finitely determined complex analytic germ and let $(\{f=0\},0)$ be the reduced equation of its image, a non-isolated hypersurface singularity. We provide the plumbing graph of the boundary of the Milnor fibre of $f$ from the double-point-geometry of $Φ$.

math.AG↗

arXiv2014

Immersions associated with holomorphic germs

A holomorphic germ Φ: (C^2, 0) \to (C^3, 0), singular only at the origin, induces at the links level an immersion of S^3 into S^5. The regular homotopy type of such immersions are determined by their Smale invariant, defined up to a sign ambiguity. In this paper we fix a sign of the Smale invariant and we show that for immersions induced by holomorphic gems the sign-refined Smale invariant is the negative of the number of cross caps appearing in a generic perturbation of Φ. Using the algebraic method we calculate it for some families of singularities, among others the A-D-E quotient singularities. As a corollary, we obtain that the regular homotopy classes which admit holomorphic representatives are exactly those, which have non-positive sign-refined Smale invariant. This answers a question of Mumford regarding exactly this correspondence. We also determine the sign ambiguity in the topological formulae of Hughes-Melvin and Ekholm-Szucs connecting the Smale invariant with (singular) Seifert surfaces. In the case of holomorphic realizations of Seifert surfaces, we also determine their involved invariants in terms of holomorhic geometry.

math.AG↗