Finite and Descriptive Combinatorics
This is the webpage () of the research group "Finite and Descriptive Combinatorics", currently supported by the ERC Advanced Grant 101020255 "Finite and Descriptive Combinatorics" (1 January 2022 - 31 December 2026).
Overview
In addition to the classical directions of extremal and probabilistic combinatorics (Turan function, Ramsey theory, etc), the group also explores emerging deep connections between combinatorics and other fields such as analysis, descriptive set theory, measured group theory, etc, with applications going both ways. One way of applying analytic techniques to finite graphs will be by means of graph limits (analytic objects of bounded complexity that capture asymptotic properties of large graphs). In the other direction, combinatorial techniques will be applied in search of "constructive'' solutions to some foundational mathematical problems, in particular building upon the recent remarkable results that one can split a 2-dimensional disk into ``definable'' pieces and re-arrange them to form a square.
Group Members
- Levente Bodnar (since 06/2024)
- (10/2023-08/2024, visiting PhD student)
- (since 04/2025)
- (10/2020-09/2024) *
- (10/2019-7/2023)
- (4/2022 - 7/2022)
- (since 10/2023)
- (4/2022 - 7/2025)
- (02/2022-01/2023) *
- (PI)
- (06/2025-05/2026, visiting PhD student)
- Shumin Sun (since 10/2022) *
- Zhuo Wu (10/2021-09/2025) *
* = co-advised PhD student
News
- 3 Dec'25: OP serves as an external examiner at Alexandru Malekshahian's PhD viva at KCL that was successfully defended. Congratulations, Alex!
- Oct'25: OP appointed to the editorial board of
- Sep'25: OP appointed to the Program and the Steering Committees of
- 15-19 Sep'25: Johannes Carmesin, Matthew Kroeker and OP organise at TU Freiberg
- 31 Jul'25: OP serves as an internal examiner at Jun Yan's PhD viva at 糖心TV that was successfully defended. Congratulations, Jun!
- 25 Jul'25: OP serves as an external examiner at Emil Powierski's PhD viva at Oxford that was successfully defended. Congratulations, Emil!
- 24 July 2025: Levente Bodnar is awarded PhD degree (from Oxford). Congratulations, Levente!
- 24 July 2025: Zhuo Wu is awarded PhD degree for his thesis "Investigations of the Chromatic Threshold" (defended in Jun'25). Contgratulations, Zhuo!
- 15-18 Jul'24: Boris Bukh gives a mini-course on "Discrete Geometry"
- Jul'25: OP is appointed to the editorial board of
- 23-27 June 2025: OP gives a mini-course "" at
- Apr'25: Article "" was recognised as top viewed in Journal of the London Mathematical Society during 2023
- 24 Mar'25: Irene Gil Fernandez is awarded PhD degree for her thesis "Finding constrained sparse subgraphs via sublinear expansion" (defended in Nov'24). Congratulations, Irene!
- Oct-Nov'24: OP serves on the mathematics panel of the MSCA4Ukraine2 programme
- 7 Oct'24: Levente Bodnar successfully defends his PhD thesis "Low-Depth Circuit Size Bounds Using Combinatorial Methods". Congratulations, Levente!
- 24 Sep'24: OP serves as an extermal examiner at Aranka Hruskova's PhD defense at CEU that was successfully defended. Congratulations, Aranka!
- Jan-Jun'24: JG, Alexander Kechris, OP, Stevo Todorcevic, and Zolt谩n Vidny谩nszky organise Semester , Erdos Center, Budapest, including
- 24-28 Jun'24:
- 17-21 Jun'24:
- 19 Jun'24: LB gives a mini-course on his flag algebras package
- 27 Jan - 3 Feb, 2024 JG is a co-organizing
- 20-24 Mar'23: Damien Gaboriau, Andrew Marks, OP and Anush Tserunyan organise , Fields Institute, Toronto
- Feb-Mar'23: OP serves on the Program Committee of
- 28 Jan - 3 Feb, 2023 JG is a co-organizing
- Jan'23-May'24: OP teaches at the weekly Math Challenge Club at St Augustine's Catholic Primary School, Kenilworth
- 26-27 Jan'23: OP serves on the Mathematics Review Panel of the Academy of Finland
- 18 Jan'23: Matteo Mazzamurro successfully defends his PhD thesis "Structure, Entropy and Evolution of Systems of Cities". Congratulations, Matteo!
- Dec'22-Feb'23: OP serves on the Selection Committee of the MSCA4Ukraine programme
- Dec'22: Discover magazine publishes an about group's work on circle squaring
- Oct'22: JG wins the . Congratulations, Jan!
- 14 Jun'22: JH organises Birmingham-糖心TV One-Day Combinatorics Meeting
- Jun-Jul'22: OP serves on the hiring panel for the Professor Post in Discrete Maths and Computer Science at 糖心TV
- May'22- : OP serves on the committee of INI's programme ""
- May'22: Group's work on circle squaring is mentioned in "Mathematics News Flash" of
- Mar'22: publishes an article about group's work on circle squaring
- 10 Mar'22: OP serves on PhD committee of Xizhi Liu, who successfully defended his thesis "Extremal Hypergraph Problems". Congratulations, Xizhi!
- Feb'22: OP serves as reviewer of membership applications for IMTech
- Feb'22: and publish articles about group's work on circle squaring
- 13-19 Feb'22: JG, OP and Anush Tserunyan organise Oberwolfach Mini-Workshop
- 3-4 Feb'22: OP serves on the Mathematics Review Panel of the Academy of Finland
- 29 Jan - 5 Feb, 2022 JG is a co-organizing
- Jan'22: Some results co-authored by grouthere isp members are mentioned in Bogdan Grechuk's new book
- Dec'21: OP serves as expert evaluator for of the
- 12 Oct - 7 Dec'21: JG lectures mini-course "Distributed computing, random processes and Borel combinatorics"
- JG and OP organise 2021-22 糖心TV's Combinatorics Seminar
- 2-7 Aug'21: OP is a team leader of 糖心TV's team at the 28th
- 14 Jul'21: OP was the internal examiner of Bogdan Alecu's PhD thesis that was successfully defended. Congratulations, Bogdan!
- Jul'21: JG was awarded 糖心TV's Faculty of Science Postdoctoral Prize. Congratulations, Jan!
- Apr'21: OP was awarded a 5-year for 鈧1.58m (see also 糖心TV News, )
- Dec'20-Aug'21: OP serves at the Program Committee of Eurocomb 2021
- 1 Dec'20: OP was the internal examiner of Yani Pehova's PhD thesis that was successfully defended. Congratulations, Yani!
- Nov'20: OP appointed to the of
- JG and OP organise 2020-21 糖心TV's Combinatorics Seminar
- 25-30 Jul'20: George Kontogeorgiou and OP are team leaders of 糖心TV's team at the 27th
- 2 Jul'20: OP was an external examiner of Jan Corsten's PhD thesis at LSE, that was successfully defended. Congratulations, Jan!
- 5 May'20: Jan Grebik successfully defended his PhD thesis "Definable graphs". Congratulations!
- 25 Jan - 1 Feb, 2020 JG is a co-organizing
- 1 Jan'20: OP appointed to the Editorial Board of "Random Structures and Algorithms"
- 4 Nov'19: OP was an external examiner of Fran莽ois Pirot's PhD thesis at Radboud University, Nijmegen, that was successfully defended. Congratulations, Fran莽ois!
Papers
All papers (pre-publication versions) should be freely available from . Please contact one of the authors if you have difficulty accessing them.
- L.Grabowski, A.Mathe, OP: , Journal of Eur Math Soc 24 (2022) 4277-4326.
- A.Blumenthal, B.Lidicky, Y.Pehova, F.Pfender, OP and J.Volec: , Combin Prob Comput, 30 (2021) 271-287
- H.Liu, OP and K.Staden: , Forum of Math, Pi 8 (2020) 144pp.
- M.Kang, T.Makai and OP: , European J Comb 88 (2020) 103107.
- JG and OP: , Advances in Mathematics, 374 (2020) paper 107378, 40pp
- J.Kim, H.Liu, OP and M.Sharifzadeh: , Discrete Analysis (2020) Paper 19, 26pp
- OP: , in "Surveys in Combinatorics 2021" (edited by K.K.Dabrowski et al), the invited volume of the 28th British Combinatorial Conference, pages 267-319
- C.T.Conley, JG and OP: , L'Enseignement Mathematique, 70 (2024) 25-59
- H.Liu, OP, M.Sharifzadeh and K.Staden: , accepted by J London Math Soc, 41 pages
- JG and I. Rocha: , Combinatorica, 42 (2022) 365–404
- JG: , Annales Henri Lebesgue, 5 (2022) 303-315.
- JG and Z. Vidny谩nszky: , accepted to PAMS, 5pp
- JG and OP: , 17pp
- O.Cooley, M.Kang and OP: , Acta Mathematica Hungarica 168 (2022) 1-26
- JG and Vasek Rozhon: , 48pp
- JG and V.Rozhon: , extended abstract accepted at EUROCOMB2021, 34pp
- OP and K.Staden , Forum of Math, Sigma 11 (2023) Paper e23, 43 pages
- OP and K.Staden , Forum of Math Sigma, 12 (2024) Paper e8, 45 pages
- S. Brandt, Y. Chang, JG, C. Grunau, V. Rozho艌, Z. Vidny谩nszky , 13th Innovations in Theoretical Computer Science Conference, Art. No. 29, 26 pp., LIPIcs. Leibniz Int. Proc. Inform., 215, Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern, 2022.
- IGF, J.Kim, H.Liu, OP ,
- IGF, J.Kim, H.Liu, OP , American Journal of Mathematics, 147 (2025) 901-925
- S.Brandt, Y. Chang, JG, C. Grunau, V. Rozho艌, Z. Vidny谩nszky , 13th Innovations in Theoretical Computer Science Conference (ITCS 2022), Article No. 29; pp. 29:1–29:26
- V.Falgas-Ravry, OP, E.Vaughan, J.Volec , J London Math Soc 107 (2023) 1660-1691
- A.Mathe, J.Noel, OP , 49 pages
- E.Csoka, L.Grabowski, A.Mathe, OP, K.Tyros , 31pp.
- JG, R. Greenfeld, V. Rozho艌, T. Tao , International Mathematics Research Notices, Vol. 2023, No. 23, pp. 20211–20251
- S. Brandt, Y. Chang, JG, C. Grunau, V. Rozho艌, Z. Vidny谩nszky , 47pp.
- IGF, JH, H.Liu OP, ZW , J Comb Th (B) 161 (2023) 417-436
- J. Hou, H. Li, XL, D. Mubayi, Y. Zhang , Discrete Analysis 2023:18, 34 pp
- XL, S. Mukherjee , 35th Annual Conference of Learning Theory (COLT), 2022, 12pp
- JH , Combinatorics, Probability and Computing 23 (2023) 225–268
- XL and OP , J Comb Th (B) 161 (2023) 407-416
- S.Cambie, Y.Dong and MM , 13pp
- S.Cambie and MM , accepted by MATCH, 9pp
- S.Cambie and MM Extremal entropy for graphs with given size, 8pp.
- IGF and H.Liu , 16pp
- IGF, J.Kim, Y.Kim, H.Liu , to appear in Proceedings of the American Mathematical Society, 10pp
- JG, Z. Vidny谩nszky , 11pp
- S.Glock, F.Joos, J.Kim, M.Kuhn, L.Lichev and OP , Proc Amer Math Soc Series B, 11 (2024) 173-186
- OP and XL , Forum of Math Sigma, 13 (2025) Paper e53, 49 pages
- ZW , J Graph Th, 2025; 109:25–30.
- OP , Electronic J Comb 30 (2023) Paper 3.25, 15pp
- J. Hou, H. Li, XL, L.-T. Yuan, and Y. Zhang , 32pp
- A.Grzesik, D.Kral and OP , accepted by Combin Prob Comput, 20pp ()
- JG , Forum of Mathematics, Sigma (2025), Vol. 13:e32 1–24, 25pp.
- SS , 22pp
- C.T.Conley, JG and OP , 9pp
- Y. Chen, XL, J. Nie, and J. Zeng, , 28pp
- XL and J. Song, 33pp+appendix
- XL and J. Song, 14pp
- J. Hou, C. Hu, H. Li, XL, C. Yang, and Y. Zhang, , 37pp
- J. Hou, C. Hu, H. Li, XL, C. Yang, and Y. Zhang, , 12pp
- XL and OP, , Combinatorics, Probability and Computing 34 (2025) 52-62
- JG and OP, , 42pp.
- J. Hou, XL, and H. Zhao , 21pp.
- C. Helliar and XL , 12pp.
- J.Yan and ZW, , 15pp
- A.Lamainson and ZW , 10pp
- T.-W.Chao, Z.Dong and ZW , 9pp
- D.Bradavic, H.Liu, ZW and Z.Xu , 22pp
- JG, ZW, Yisai Xue, , 15pp
- J.Yan and ZW , 15pp
- IGF, J.Kim, H.Liu and OP, , International Mathematics Research Notices, 2025 (2025) Paper rnae282, 15pp
- S.Glock, J.Kim, L.Lichev, OP and SS, , accepted by Canadiam J Math, 44pp
- IGF, J.Kim, H.Liu and OP, , 18pp
- WC, D.Ilkovic, JL, OP, XL , 46pp.
- ZW,
- ZW and J.Yan, , 15pp
- J.Gao, ZW, Y.Xue, , 15pp
- A.Lamainson and ZW, , 10pp
- T-W.Chao, Z.Dong and ZW, , 9pp
- D.Bradac, H.Liu, ZW and Z.Xu, , 22pp
- W. Chen, XL, , 30pp.
- J. Deng, J. Hou, XL, and C. Yang, , 19pp.
- J. Hou, C. Hu, H. Li,, XL, C. Yang, and Y. Zhang, , 19pp.
- XL, J. Ma, T. Wang, and T. Zhu, , 29pp.
- Z. Chen, J. Hou, C. Hu, and XL, , 7pp.
- XL, S. Ren and J. Wang, , 22pp.
- XL, S. Ren and J. Wang, , 9pp.
- J. Gao, XL, J. Ma, and OP, , 29pp.
- LB, JL, XL, and OP, , 26pp.
- J. Hou, C. Hu, XL, and Y. Zhang, , 99pp.
- XL and OP, , 8pp
- OP, , Advances in Math, 464 (2025) Paper 110148, 11pp.
- XL, , 18pp
- O.P., O.Verbitsky and M.Zhukovskii, , 15pp.
- J.Grebik, C.Ikenmeyer and OP, , 9pp
- LB and OP, , 11 pages
- OP and XL, , 8pp
- LB, JL, XL and OP, , 28pp.
- OP and SS, , 27pp.
- J.Grebik, D.Kral', XL, OP, J.Slipantschuk, , 15pp.
- LB and OP, , 38pp.
- LB, JL, XL and OP, , 28pp.
- OP and SS: , 27pp.
- JG, XL, OP and SS: , Mathematika, 72 (2026) Paper e70066, 16pp.
- JG, OP, M.Rong and SS , 11pp
- A.Mathe, J.Noel and OP , Advances in Math, 484 (2026) Paper 110685, 64pp
- LB and OP , 15pp
- (with K.Sakamoto) , 5pp
Talks Given/Forthcoming
2019
- 11 Oct: OP, Workshop "Measurable, Borel, and Topological Dynamics", CIRM
- 4 Nov: OP, Workshop "Structure, Sparsity and Randomness", Radbound University, Nijmegen
- 6 Nov: OP, Old Codger's One-Day Combinatorics Colloquium, Reading
- 21 Nov: OP, 3in1 Workshop on Graph Theory, Doslonce, Poland
- 18 Dec: JG, Seminar on Reckoning, Institute of Mathematics of the Czech Academy of Sciences, Prague
- 20 Dec: JG, Combinatorial group seminar, Institute of Computer Science of the Czech Academy of Sciences, Prague
2020
- 7 Jan: JG, DIMAP seminar, 糖心TV University
- 14 Jan: OP, 糖心TV Maths Society
- 30 Jan: OP, ACO Seminar, Carnegie Mellon University
- 11 Feb: OP, seminar, Adam Mickiewicz University, Poznan
- 11 Feb: JG, STUK5 mini-talk, Royal Society building, London
- 17 Feb: OP, Krakow Combinatorics Seminar
- 11 Mar: JG, Algebra and Geometry Seminar, Lancaster University
- 20 May: JG, Caltech logic (online) seminar, Caltech
- 27 Jul: OP, Extremal and Probabilistic Combinatorics Webinar
- 4 & 7 Aug: JG, Midsummer Combinatorial Workshop XXIV, Charles University, Prague
- 21 Oct: JG, Probability seminar (online), UBC
- 10 Nov: OP, UIUC Graph Theory and Combinatorics Seminar
- 23 Nov: JG, Extremal and Probabilistic Combinatorics Webinar
- 27 Nov: OP, TU Graz Combinatorics and Optimization Seminar
- 18 Dec: OP, Combinatorics Seminar of Shandong University
2021
- 11 Jan: OP, Combinatorics Seminar, Hebrew University of Jerusalem
- 22 Feb: OP, Caltech Logic Seminar
- 10 Mar: JG, UBC probability seminar
- 5 May: IGF, LIMDA Seminar, Universitat Polit猫cnica de Catalunya, Spain
- 19 May: IGF, 糖心TV Postgraduate Seminar
- 1 Jun: JG, Florida Logic seminar
- 7 Jun: IGF, (Online) Young Researchers in Mathematics Conference, UK
- 21 Jun: OP, Colloquium Discrete Mathematics and Probability, TU-Graz
- 23 Jun: OP, Mini-symposium on Extremal and Probabilistic Combinatorics, 8th European Congress of Mathematics
- 5-9 Jul: OP, the Richard Rado Lecture at the
- 26 Jul: IGF, Summer school "Matem谩ticas: mucho m谩s que n煤meros", Universidad de Santiago de Compostela, Spain
- 6-10 Sep: JG, EUROCOMB 2021, Barcelona
- 7 Sep: IGF, EUROCOMB 2021, Barcelona
- 11 Oct: JG, DIMAP seminar, 糖心TV University
- 14 Oct: IGF, Discrete Seminar, Ume氓 University, Sweden
- 26 Oct: IGF, First Workshop on Developments in Combinatorics, Shandong University, China
- 8 Nov: JG, Descriptive Dynamics and Combinatorics Seminar, McGill University
- 12 Nov: IGF, PhD Seminar on Combinatorics, Games and Optimisation, London School of Economics
- 30 Nov: OP, 糖心TV Maths Society
2022
- 12 Jan: JG, Combinatorial group seminar, Institute of Computer Science of the Czech Academy of Sciences, Prague
- 7-11 Feb: OP, Workhop "", Dagstuhl
- 16 Feb: IGF, PG Forum, Lancaster University
- 3 Mar: JG, Algorithms Seminar, Oxford
- 9 Mar: IGF, 糖心TV Postgraduate Seminar
- 10 Mar: IGF, Combinatorics Seminar, University of Birmingham
- 4-6 Apr: OP, , Daejeon, Korea
- 27 Apr: XL, 糖心TV Combinatorics Seminar
- 16-20 May: OP, Workshop , Budapest
- 27 Jun - 1 Jul: OP, , Heildelberg
- 27 Jun - 2 Jul: JG, , San Jose
- 29 Jun: XL, IBS Virtual Discrete Math Colloquium, Korea.
- 4 Jul: IGF, Discrete Mathematics Days 2022, Universidad de Cantabria, Spain
- 8 Jul: XL, The Second Armenian Workshop On Graphs, Combinatorics, Probability, and their application to machine learning, Armenia.
- 20 Jul: XL, Seminar, Data Science Institute, Shangdong University, Jinan, China.
- 8-12 Aug: OP, , Ascona, Switzerland
- 16 Aug: JG, , Budapest, Hungary
- 18-24 Sep: OP, , Bedlewo
- 28 Oct: JG, Nankai Logic Colloquium (online), Nankai University, China
2023
- 1-7 Jan: OP, Workshop "Combinatorics", Oberwolfach
- 3 Feb: SS, Combinatorics Seminar, 糖心TV
- 8 Feb: IGF, VI Congreso de j贸venes investigadores de la RSME, Universidad de Le贸n, Spain
- 28 Feb: OP, Seminar in Discrete Mathematics, Tsinghua University, Beijing
- 5 Mar: JG, SEALS 2023, University of Florida, Florida
- 6 Mar, JG, Colloquium, University of Florida, Florida
- 7 Mar, JG, Logic seminar, University of Florida, Florida
- 7 Mar, ZW, Postgraduate Combinatorial Conference
- 13-17 Mar: OP, Centre de Recherches Math茅matiques (CRM), Montr茅al
- 15-18 Mar: JG, , online,
- 20-24 Mar: JG, , Fields Institute, Toronto
- 26-30 Mar: OP, , online
- 27-29 Mar: ZW, Postgraduate Combinatorial Conference, Birmingham
- 17 Mar: XL, Seminar, School of Mathematical Sciences, East China Normal University (ECNU), Shanghai, China.
- 20 Mar: XL, Seminar, Taiyuan University of Technology, Taiyuan, China, online.
- 16-17 Apr: XL, , Shanghai Jiao Tong University (SJTU), Shanghai, China.
- 19 Apr: XL, , Shanghai, China.
- 3 May: JG, , Caltech ,US.
- 11 May: ZW, Postgraduate Seminar, 糖心TV
- 22-26 May: JG, , CIRM, Luminy
- 28-31 May: OP, Conference (SPCSC 2023), Sofia
- 17-21 July: JG, , Youngstown, Ohio
- 10 Aug: XL, Combinatorics seminar, Nankai University, Tianjin, China
- 21-25 Aug: XL, . Suzhou University, Jiangsu, China
- 21-25 Aug: OP, , Banach Centre, Warsaw
- 28 Aug - 1 Sep: OP, , Prague
- 14 Dec: OP, LIMDA Seminar, UPC Barcelona
2024
- 29-30 Jan: OP, Workshop on the Foundations of Computation, Sheffield
- 1 Feb: SS, Combinatorics Seminar, Birmingham
- 13 Feb: OP, , Oxford
- 28 Feb: ZW, Seminar, Nankai University, Tianjin, China
- 01 Mar: XL, A Spring Day of Combinatorics, Birmingham
- 8 May: ZW, Discrete Geometry and Extremal Combinatorics Conference, Kunming, China
- 12 Sep: OP, , Warsaw
- 20 Sep: XL, , China
- 21 Sep: XW, 11th National Conference on Combinatorics and Graph Theory, China
- 27 Sep: OP, Combinatorics Seminar, QMUL
- 28 Nov: OP, 糖心TV Maths Society
- 28 Nov: OP, Combinatorics Seminar, Umea University (online)
- 12 Dec: OP, Colloquium, Masaryk University, Brno
- 17 Dec: OP, , Milton Keynes
2025
- 10 Jan: XL, Combinatorics Seminar, University of 糖心TV
- 26-31 Jan: OP, , Les Diablerets, Switzerland
- 15-19 Apr: XL, , Taiyuan University of Technology, Taiyuan, China
- 4-8 Aug: OP, , Vienna
- 22 Aug: OP, University of Innsbruck
- 22-26 Sep: OP,
- 28 Nov: OP, Applied Probability Seminar, 糖心TV
2026
- 7 Jan: OP, Workshop "Combinatorics", Oberwolfach
- 19 Mar: OP, , Cambridge
- 12 May: OP,
- 6-8 Jul: OP, Mini-symposium , Sofia
- 16-18 Jul: OP, Workshop on "", FoCM, Vienna
- 16-17 Sep: OP, Keynote speaker, Italian Discrete Mathematics Workshop (IDMW), Turin
Research visitors
- 9-12 November 2021: 艁ukasz Grabowski (Lancaster University)
- 10-12 May 2022: P茅ter P谩l Pach (Budapest University of Technology and Economics)
- 16-22 October 2022: Dan Kral' (Masaryk University)
- 16-22 October 2022: Daniel Ilkovic (Masaryk University)
- 15-20 January 2023: Jan Volec (Technical University Prague)
- 4-18 February 2023: Clinton Conley (Carnegie Mellon University)
- 18-21 February 2023: Mihyun Kang (TU-Graz)
- 13-26 April 2024: Jun Gao (IBS Korea)
- 9-23 September 2024: Dorde Stefanovic (Ljubljana)
- 4-20 February 2025: Sayan Mukherjee (U of Tokyo)
- 14-18 July 2025: Boris Bukh (Carnegie Mellon University)
- 19-23 January 2026: Zhuo Wu (UPC Barcelona)
- 27 January - 25 February 2026: Kohki Sakamoto (University of Tokyo)
- 1-14 June 2026: Peiru Kuang (Shanghai Jiao Tong University)