Homepage of Jan Grebík
Address:
Mathematics Institute
University of Warwick
Coventry CV4 7AL, UK
email: jan.grebik [at] warwick.ac.uk
202021, Term 3,
Warwick's Combinatorics Seminar, Fridays 2pm
I am a research assistant at the University of Warwick working with O. Pikhurko and a member of the Leverhulme Research Project Grant RPG2018424 "Measurable Combinatorics".
Before that I was student researcher at the Mathematics Institute of the Czech Academy of Sciences (20152019), 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, 252298. [arXiv]

(with O. Pikhurko) Measurable versions of Vizing's theorem, Adv. Math. 374 (2020), 107378, 40 pp. [arXiv]

σlacunary actions of Polish groups, Proc. Amer. Math. Soc. 148 (2020), 35833589. [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]

(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. 78, 1035–1051. [arXiv]

A rigid Urysohnlike 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]