Stefan Glock

Hello! I'm an Assistant Professor at the Faculty of Computer Science and Mathematics at University of Passau.

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News

We have funding available for academic guests. If you are interested to visit UoP for a few weeks to collaborate on a project, please contact me.

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Contact

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Research overview

I am broadly interested in the study of discrete mathematical structures, which have important manifestations in algebra, geometry, number theory, optimization, probability theory, statistical physics, theoretical computer science and topology. Most of my research topics can be located within the following areas:

• Extremal Combinatorics
• Ramsey Theory
• Design Theory
• Discrete Geometry
• Graph Theory
• Probabilistic Combinatorics

Some highlights of my research include the resolution of several long-standing open problems, in particular:

• the existence problem of Steiner systems posed by the geometer Jakob Steiner in 1853 (second proof)
• the "Oberwolfach problem" posed by Ringel in 1967
• a conjecture of Erdős from 1973 on high girth triple systems (asymptotic version)
• a conjecture of Erdős and Lovász from 1973 on the intersection spectrum of intersecting hypergraphs
• a problem from the 80s on the largest hole in random graphs
• a conjecture of Chung, Diaconis and Graham from 1989 on Euler tours

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Publications and preprints

Submitted

• On the (k+2,k)-problem of Brown, Erdős and Sós for k=5,6,7
  with Jaehoon Kim, Lyuben Lichev, Oleg Pikhurko and Shumin Sun


• Tight Hamilton cycles with high discrepancy
  with Lior Gishboliner and Amedeo Sgueglia


• Hamilton cycles in pseudorandom graphs
  with David Munhá Correia and Benny Sudakov

Accepted / To appear

• Optimal Hamilton covers and linear arboricity for random graphs
  with Nemanja Draganić, David Munhá Correia and Benny Sudakov
  Proceedings of the American Mathematical Society, accepted


• Conflict-free hypergraph matchings
  with Felix Joos, Jaehoon Kim, Marcus Kühn and Lyuben Lichev
  Journal of the London Mathematical Society, accepted


• On the (6,4)-problem of Brown, Erdős and Sós
  with Felix Joos, Jaehoon Kim, Marcus Kühn, Lyuben Lichev and Oleg Pikhurko
  Proceedings of the American Mathematical Society, accepted

2023

• New results for MaxCut in H-free graphs
  with Oliver Janzer and Benny Sudakov
  Journal of the London Mathematical Society 108 (2023), 441-481 ☞


• The existence of designs via iterative absorption: hypergraph F-designs for arbitrary F
  with Daniela Kühn, Allan Lo and Deryk Osthus
  Memoirs of the American Mathematical Society 284 (2023), monograph 1406 ☞

2022

• The n-queens completion problem
  with David Munhá Correia and Benny Sudakov
  Research in the Mathematical Sciences 9 (2022), Art. 41 ☞


• Short proofs for long induced paths
  with Nemanja Draganić and Michael Krivelevich
  Combinatorics, Probability & Computing 31 (2022), 870-878 ☞


• The largest hole in sparse random graphs
  with Nemanja Draganić and Michael Krivelevich
  Random Structures & Algorithms 61 (2022), 666-677 ☞


• The intersection spectrum of 3-chromatic intersecting hypergraphs
  with Matija Bucić and Benny Sudakov
  Proceedings of the London Mathematical Society 124 (2022), 680-690 ☞


• An average degree condition for independent transversals
  with Benny Sudakov
  Journal of Combinatorial Theory, Series B 154 (2022), 370-391 ☞

2021

• Extremal aspects of graph and hypergraph decomposition problems
  with Daniela Kühn and Deryk Osthus
  in: Surveys in Combinatorics 2021,
  London Mathematical Society Lecture Note Series 470, pp. 235-265 ☞


• Counting Hamilton cycles in Dirac hypergraphs
  with Stephen Gould, Felix Joos, Daniela Kühn and Deryk Osthus
  Combinatorics, Probability & Computing 30 (2021), 631-653 ☞


• Decompositions into isomorphic rainbow spanning trees
  with Daniela Kühn, Richard Montgomery and Deryk Osthus
  Journal of Combinatorial Theory, Series B 146 (2021), 439-484 ☞


• Resolution of the Oberwolfach problem
  with Felix Joos, Jaehoon Kim, Daniela Kühn and Deryk Osthus
  Journal of the European Mathematical Society 23 (2021), 2511-2547 ☞

2020

• A rainbow blow-up lemma for almost optimally bounded edge-colourings
  with Stefan Ehard and Felix Joos
  Forum of Mathematics, Sigma 8 (2020), e37 ☞


• Pseudorandom hypergraph matchings
  with Stefan Ehard and Felix Joos
  Combinatorics, Probability & Computing 29 (2020), 868-885 ☞


• Euler tours in hypergraphs
  with Felix Joos, Daniela Kühn and Deryk Osthus
  Combinatorica 40 (2020), 679-690 ☞


• Minimalist designs
  with Ben Barber, Daniela Kühn, Allan Lo, Richard Montgomery and Deryk Osthus
  Random Structures & Algorithms 57 (2020), 47-63 ☞


• A rainbow blow-up lemma
  with Felix Joos
  Random Structures & Algorithms 56 (2020), 1031-1069 ☞


• On a conjecture of Erdős on locally sparse Steiner triple systems
  with Daniela Kühn, Allan Lo and Deryk Osthus
  Combinatorica 40 (2020), 363-403 ☞

2019 and before

• Triple systems with no three triples spanning at most five points
  Bulletin of the London Mathematical Society 51 (2019), 230-236 ☞


• On the decomposition threshold of a given graph
  with Daniela Kühn, Allan Lo, Richard Montgomery and Deryk Osthus
  Journal of Combinatorial Theory, Series B 139 (2019), 47-127 ☞


• Optimal path and cycle decompositions of dense quasirandom graphs
  with Daniela Kühn and Deryk Osthus
  Journal of Combinatorial Theory, Series B 118 (2016), 88-108 ☞


• On the f-matching polytope and the fractional f-chromatic index
  International Journal of Computer Mathematics 92 (2015), 1135-1142 ☞

Unpublished

• Note on induced paths in sparse random graphs


• A note on dense bipartite induced subgraphs

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Talks

upcoming:

• Discrete Mathematics Seminar, Beijing, 7.5.2024
• Berlin-Poznań-Hamburg-Warsaw Seminar, 24.-25.5.2024

previous:

• Birmingham Combinatorics Seminar, 15.2.2023
• Discrete Maths Meeting, Vienna, 24.11.2023
• FCT, Trier, 18.-21.9.2023
• EUROCOMB, Prague, 28.8.-1.9.2023
• Discrete Maths Meeting, Vienna, 14.4.2023
• KOLKOM, Paderborn, 18.-19.11.2022
• 29th British Combinatorial Conference, Lancaster, 14.7.2022
• Third Southwestern German Workshop on Graph Theory, Heidelberg, 27.6.2022
• Discrete Mathematics Seminar, Princeton, 14.4.2022
• CS Colloquium, Ariel University, 6.4.2022
• Combinatorics, Physics and Probability Seminar, Harvard, 14.12.2021
• Workshop on Developments in Combinatorics, Shandong University, 26.10.2021
• Combinatorics Seminar, Ilmenau, 14.10.2021
• Mittagsseminar, Zürich, 12.10.2021
• Graz Combinatorics Seminar, 24.9.2021
• EUROCOMB, Barcelona, 8.9.2021
• 8th European Congress of Mathematics, Portorož, 24.6.2021
• CanaDAM, 25.5.2021
• Extremal and Probabilistic Combinatorics Webinar, 12.4.2021
• Mittagsseminar, Zürich, 16.3.2021
• Canadian Mathematical Society winter meeting, Montreal, 4.12.2020
• Mathematisches Kolloquium, Karlsruhe, 29.9.2020
• DMV-Jahrestagung, Chemnitz, 15.9.2020
• Mathematisches Kolloquium, Ulm, 31.1.2020
• ITS Fellows' Seminar, Zürich, 10.12.2019
• KOLKOM, Paderborn, 8.-9.11.2019
• Mittagsseminar, Zürich, 3.10.2019
• DMV-Jahrestagung, Karlsruhe, 26.9.2019
• BCC, Birmingham, 1.8.2019
• RSA, Zürich, 18.7.2019
• Combinatorics Seminar, Prague, 9.11.2018
• Oberseminar Diskrete Mathematik und Algebra, Ilmenau, 19.10.2018
• 1st Southwestern German Workshop on Graph Theory 2018, Karlsruhe, 31.8.2018
• ICGT, Lyon, 11.7.2018
• Combinatorics Seminar, Warwick, 29.6.2018
• Symposium Diskrete Mathematik 2018, Graz, 16.6.2018
• Combinatorics Seminar, IIAS, Jerusalem, 30.4.2018
• Extremal Combinatorics conference, Warwick, 18.9.2017
• RSA, Gniezno, 9.8.2017
• DIMAP Seminar, Warwick, 20.6.2017
• CanaDAM, Toronto, 15.6.2017
• Seminar on Combinatorics, Games and Optimisation, LSE (London), 23.2.2017
• Bristol Combinatorics Seminar, 14.2.2017
• Oxford Combinatorial Theory Seminar, 7.2.2017
• Birmingham Combinatorics Seminar, 2.2.2017
• SIAM Discrete Mathematics, Atlanta, 8.6.2016
• EUROCOMB, Bergen, 3.9.2015
• Birmingham Combinatorics Seminar, 28.5.2015
• Birmingham Young Mathematician Colloquium, 13.5.2015
• Oberseminar Diskrete Mathematik und Algebra, Ilmenau, 19.6.2014
• KOLKOM, Ilmenau, 8.11.2013

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Short CV

I studied mathematics at Technische Universität Ilmenau from 2009 to 2014. I obtained my PhD from the University of Birmingham in 2018, under the supervision of Daniela Kühn and Deryk Osthus. My dissertation `Decompositions of Graphs and Hypergraphs' was the runner-up for the Richard-Rado-Preis 2018. I continued to be a Research Fellow (postdoc) in Birmingham, before joining ETH Zürich in 2019. There, I was a Junior Fellow in the Institute for Theoretical Studies, and a member of the Combinatorics Research Group of Benny Sudakov. Since 1 September 2022, I hold a tenure-track professorship at the University of Passau.