Homepage of Jan Grebík

I am a research assistant at the University of Warwick working with O. Pikhurko and a member of the Leverhulme Research Project Grant RPG-2018-424 "Measurable Combinatorics". Before that I was student researcher at the Mathematics Institute of the Czech Academy of Sciences (2015-2019), student researcher at the Institute of Computer Science of the Czech Academy of Sciences (2018) and I completed my PhD at the Charles University in Prague in 2020 (thesis submitted September 2019) working under supervision of David Chodounský. I am interested in descriptive set theory, combinatorics, ergodic theory and Borel equivalence relations. Here is my [CV]

Vašek gave a nice introductory tutorial on connections between Distributed Algorithms, Finitary Factors, and Descriptive Combinatorics, see his webpage for videos and links to relevant papers.

Preprint

• (with S. Brandt, Y. Chang, C. Grunau, V. Rozhoň, Z. Vidnyánszky) Local Problems on Trees from the Perspectives of Distributed Algorithms, Finitary Factors, and Descriptive Combinatorics, preprint, [arXiv]
• (with V. Rozhoň) Classification of Local Problems on Paths from the Perspective of Descriptive Combinatorics, preprint, [arXiv]
• (with V. Rozhoň) Local Problems on Grids from the Perspective of Distributed Algorithms, Finitary Factors, and Descriptive Combinatorics (Previous, now irrelevant, title: Of Toasts and Tails), preprint, [arXiv]
• (with O. Pikhurko) Large Deviation Principles for Block and Step Graphon Random Graph Models, submitted, [arXiv]
• (with C. T. Conley, O. Pikhurko) Divisibility of Spheres with Measurable Pieces, submitted, [arXiv]
• (with Z. Vidnyánszky) Tall \(F_\sigma\) subideals of tall analytic ideals, accepted to Proc. Amer. Math. Soc., [arXiv]
• Dichotomy for tsi Polish groups II: \(\mathbb{E}_3\)-dichotomy, preprint, [pdf]
• Dichotomy for tsi Polish groups I: Classification by countable structures, preprint, [pdf]
• (with S. Geschke and B. D. Miller) Scrambled Cantor sets, accepted to Proc. Amer. Math. Soc., [arXiv]
• Approximate Schreier decorations and approximate König’s line coloring Theorem, submitted, [pdf]
• (with I. Rocha) Fractional Isomorphism of Graphons, accepted to Combinatorica. [arXiv], extended abstract appeared in the proceedings of Eurocomb 2019.
• (with M. Doležal, J. Hladký, I. Rocha, V. Rozhoň) Cut distance identifying graphon parameters over weak* limits, submitted. [arXiv]

Publications

• (with M. Doležal, J. Hladký, I. Rocha, V. Rozhoň) Relating the cut distance and the weak* topology for graphons, Journal of Combinatorial Theory, series B, Volume 147, 2021, 252-298. [arXiv]
• (with O. Pikhurko) Measurable versions of Vizing's theorem, Adv. Math. 374 (2020), 107378, 40 pp. [arXiv]
• σ-lacunary actions of Polish groups, Proc. Amer. Math. Soc. 148 (2020), 3583-3589. [arXiv]
• (with M. Hrušák) No minimal tall Borel ideal in the Katětov order, Fund. Math. 248 (2020), no. 2, 135–145. [arXiv]
• (with C. Uzcategui) Bases and selectors for tall families, J. Symb. Log. 84 (2019), no. 1, 359–375. [arXiv]

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• (with S. Gabriyelyan, J. Kakol, L. Zdomskyy) Topological properties of function spaces over ordinals, Rev. R. Acad. Cienc. Exactas Fı́s. Nat. Ser. A Math. RACSAM 111 (2017), no. 4, 1157–1161. [arXiv]
• (with S. Gabriyelyan, J. Kakol, L. Zdomskyy) The Ascoli property for function spaces, Topology Appl. 214 (2016), 35–50. [arXiv]
• An example of a Fraı̈ssé class without a Katětov functor, Appl. Categ. Structures 26 (2018), no. 1, 1–6. [arXiv]
• (with D. Chodounsky, V. Fischer) Free sequences in \(\mathcal{P}(\omega)/\operatorname{fin}\), Arch. Math. Logic 58 (2019), no. 7-8, 1035–1051. [arXiv]
• A rigid Urysohn-like metric space, Proc. Amer. Math. Soc. 145 (2017), no. 9, 4049–4060. [arXiv]
• Ultrafilter extensions of asymptotic density, Comment. Math. Univ. Carolin. 60 (2019), no. 1, 25–37. [pdf]

Notes

• Borel selector for hypergraphons. [pdf]