Vojtech Kaluza

Welcome to the home page of Vojtěch Kaluža.

I am currently a postdoc at the Institute of Science and Technology Austria (ISTA). I work in the group lead by Uli Wagner. Before that, I worked there as a Lise Meitner fellow funded by FWF and previously also as an IST fellow.
Before that, I was a post-doc at Institut für Mathematik, Universität Innsbruck for two years. I was working there with Michael Dymond on the project Lipschitz Mappings, Differentiability and Exceptional Sets funded by Austrian Science Fund (FWF).
Even before that, I was a Ph.D. student of Computer Science at Department of Applied Mathematics, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic. My supervisor was Martin Tancer and I was also co-advised by Eva Kopecká from University of Innsbruck.
During my undergdraduate studies of Computer Science at Charles University, my supervisor was Jiří Matoušek.

Research interests

My research interests lie in two areas at the interface of discrete and continuous worlds of mathematics. The first falls into topological and algebraic combinatorics. I am mostly concerned with questions about drawings of graphs, graph representations and topological and algebraic graph parameters. I also study the computational side of problems in this area.
In the second half of my research, I study geometry of Lipschitz and bilipschitz maps, typically in connection to discrete questions.

https://orcid.org/0000-0002-2512-8698

Grants

I was a recipient of a Lise Meitner grant award M 3100-N: Spectra and topology of graphs and of simplicial complexes funded by Austrian Science Fund (FWF). Here you can find more details about the project.

Publications

Michael Dymond, Vojtěch Kaluža: Extending bilipschitz mappings between separated nets. 2024+, Preprint on arXiv.
Vojtěch Kaluža, Vadym Koval: Three observations on the Colin de Verdière spectral graph parameter. 2024+, Preprint on arXiv.
Michael Dymond, Vojtěch Kaluža: Divergence of separated nets with respect to displacement equivalence. Geometriae Dedicata, Vol. 218, no. 15, 2024. doi:10.1007/s10711-023-00862-3. Preprint on arXiv.
Vojtěch Kaluža, Martin Tancer: Even maps, the Colin de Verdière number and representations of graphs. Combinatorica, Vol. 42 (Suppl 2), pp 1317–1345, 2022. doi:10.1007/s00493-021-4443-7. Extended abstract appeared at 2020 ACM-SIAM Symposium on Discrete Algorithms (SODA20). Preprint on arXiv.
Michael Dymond, Vojtěch Kaluža: Highly irregular separated nets. Israel Journal of Mathematics. Vol. 253, pp 501–554, 2023. doi:10.1007/s11856-022-2448-6. Preprint on arXiv.
Michael Dymond, Vojtěch Kaluža, Eva Kopecká: Mapping n grid points onto a square forces an arbitrarily large Lipschitz constant. Geometric and Functional Analysis, Vol. 28, Issue 3, pp 589–644, 2018. doi:10.1007/s00039-018-0445-z. Preprint on arXiv.
Éric Colin de Verdière, Vojtěch Kaluža, Pavel Paták, Zuzana Patáková, Martin Tancer: A Direct Proof of the Strong Hanani-Tutte Theorem on the Projective Plane. Journal of Graph Algorithms and Applications, Vol. 21, no. 5, pp 939-981, 2017, doi:10.7155/jgaa.00445. Extended abstract appeared at the 24th International Symposium on Graph Drawing (GD 2016). Preprint on arXiv.
Alfredo Hubard, Vojtěch Kaluža, Arnaud de Mesmay, Martin Tancer: Shortest path embeddings of graphs on surfaces. Discrete & Computational Geometry, Vol. 58, Issue 4, pp 921–945, 2017, doi:10.1007/s00454-017-9898-3. Extended abstract appeared at the 32nd International Symposium on Computational Geometry (SoCG 2016). Preprint on arXiv.
Vojtěch Kaluža: Density not realizable as the Jacobian determinant of a bilipschitz map. Journal of Applied Analysis, Vol. 22, no. 1, pp 37-47, 2016. doi:10.1515/jaa-2016-0004. Preprint on arXiv.

My Ph.D. thesis entitled "Metric and analytic methods" can be found here.

Teaching (učení in Czech)

On a separate page (partly in Czech)

Contact

Mailing address:

  Am Campus 1
  3400 Klosterneuburg
  Austria

Email: "vojtech.kaluza" then the at sign followed by "ist ac at" separated by dots instead of blanks
or
"kaluza" then the at sign followed by "kam mff cuni cz" separated by dots instead of blanks