Homepage of Jan Grebík
Address:
Mathematics Institute
University of Warwick
Coventry CV4 7AL, UK
email: jan.grebik [at] warwick.ac.uk
202122, Term 3,
Warwick's Combinatorics Seminar, Wednesdays 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]
Preprint

(with Z. Vidnyánszky) Ramsey, expanders, and Borel chromatic numbers, submitted, [arXiv]

(with S. Brandt, Y. Chang, C. Grunau, V. Rozhoň, Z. Vidnyánszky) Deterministic Distributed algorithms and Descriptive Combinatorics on Δregular trees
, submitted, [arXiv]

(with R. Greenfeld, V. Rozhoň, T. Tao) Measurable tilings by abelian group actions, submitted, [arXiv]

(with S. Brandt, Y. Chang, C. Grunau, V. Rozhoň, Z. Vidnyánszky) On Homomorphism Graphs, submitted, [arXiv]

(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, accepted to ITCS, [arXiv]

(with V. Rozhoň) Classification of Local Problems on Paths from the Perspective of Descriptive Combinatorics, submitted, [arXiv], extended abstract accepted at EUROCOMB 2021.

(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), submitted, [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]

Borel equivalence relations induced by actions of tsi Polish groups, submitted, [arXiv]

Approximate Schreier decorations and approximate König’s line coloring Theorem, accepted to Annales Henri Lebesgue, [arXiv]

(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, accepted to JCTA . [arXiv]
Publications

(with S. Geschke and B. D. Miller) Scrambled Cantor sets, Proc. Amer. Math. Soc. 149 (2021), no. 10, 4461–4468., [arXiv]

(with M. Doležal, J. Hladký, I. Rocha, V. Rozhoň) Relating the cut distance and the weak* topology for graphons, J. Combin. Theory Ser. B 147 (2021), 252–298. [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]
202122, Term 1, minicourse on
Distributed Computing, Random Processes and Descriptive Combinatorics, Tuesdays 1pm