Bjarne Schülke
Currently, I am a Young Scientist Fellow (YSF) at the Institute for Basic Science in the ECOPRO group lead by Hong Liu. Before that, from 2021 to 2024, I was a Harry Bateman Instructor in Mathematics at Caltech mentored by David Conlon. From 2018 to 2021, I was a PhD student at the University of Hamburg under the supervision of Christian Reiher and Mathias Schacht.
My research area is extremal and probabilistic combinatorics. Topics that I am excited about include variants of the hypergraph Turán problem, spanning structures in graphs and hypergraphs, and various problems in extremal set theory.
Selected publications
Separating hypergraph Turán densities, with H. Liu, S. Wang, H. Yang, and Y. Zhang, submitted.
Hypergraphs accumulate, with D. Conlon, to appear in Int. Math. Res. Not..
Hypergraphs with arbitrarily small codegree Turán density, with S. Piga, submitted.
r-cross t-intersecting families via necessary intersection points, with P. Gupta, Y. Mogge, and S. Piga, Bull. London Math. Soc. 55 (2023), 1447-1458.
On extremal problems concerning the traces of sets, with S. Piga, J. Combin. Theory Ser. A 182 (2021), Paper No. 105447, 15 pp.
All publications
See also my arXiv.
Lagrangians are attained as uniform Turán densities, with D. King and M. Sales, submitted.
Separating hypergraph Turán densities, with H. Liu, S. Wang, H. Yang, and Y. Zhang, submitted.
Hypergraphs accumulate, with D. Conlon, to appear in Int. Math. Res. Not..
Simplicial Turán Problems, with D. Conlon and S. Piga, submitted.
Hypergraphs with arbitrarily small codegree Turán density, with S. Piga, submitted.
Beyond the broken tetrahedron, with A. Chen, submitted.
A local version of Katona's intersecting shadow theorem, with M. Sales, Combinatorica (2023), 43, 1075-1080.
The codegree Turán density of tight cycles minus one edge, with S. Piga and M. Sales, Combin. Probab. Comput. (2023), 32(6), 881-884.
r-cross t-intersecting families via necessary intersection points, with P. Gupta, Y. Mogge, and S. Piga, Bull. London Math. Soc. 55 (2023), 1447-1458.
A pair-degree condition for Hamiltonian cycles in 3-uniform hypergraphs, Combin., Probab. and Comput. (2023), 32(5), 762-781..
Decomposing hypergraphs into cycle factors, with F. Joos and M. Kühn, J. Combin. Theory Ser. B 158 (2023), 136–175.
On extremal problems concerning the traces of sets, with S. Piga, J. Combin. Theory Ser. A 182 (2021), Paper No. 105447, 15 pp.
On Hamiltonian cycles in hypergraphs with dense link graphs, with J. Polcyn, Chr. Reiher, and V. Rödl, J. Combin. Theory Ser. B 150 (2021), 17–75.
Convex graphon parameters and graph norms, with J. Lee, Israel J. Math. 242 (2021), 549–563.
Short proof that Kneser graphs are Hamiltonian for n ≥ 4k, with J. Bellmann, Discrete Math. 344 (2021), Paper No. 112430, 2 pp.
Covering 3-edge-coloured random graphs with monochromatic trees, with Y. Kohayakawa, G. Mota, and W. Mendonça, SIAM J. Discrete Math. 35 (2021), 1447–1459.
Embedding spanning subgraphs in uniformly dense and inseparable graphs, with O. Ebsen, G.S. Maesaka, Chr. Reiher, and M. Schacht, Random Structures Algorithms 57 (2020), 1077–1096.
Minimum pair degree condition for tight Hamiltonian cycles in 4-uniform hypergraphs, with J. Polcyn, Chr. Reiher, V. Rödl, A. Ruciński, and M. Schacht, Acta Math. Hungar. 161 (2020), 647–699 (Special issue dedicated to Endre Szemerédi's 80th birthday).
Extended abstracts
Maximum size of r-cross t-intersecting families, with P. Gupta, Y. Mogge, and S. Piga, Procedia Computer Science (2022)
On extremal problems concerning the traces of sets, with S. Piga, Extended Abstracts EuroComb 2021 (2021)
Minimum pair-degree for tight Hamiltonian cycles in 4-uniform hypergraphs, with Chr. Reiher, V. Rödl, A Ruciński, and M. Schacht, Acta Math. Univ. Comenian (2019)
Covering 3-coloured random graphs with monochromatic trees, with Y. Kohayakawa, W. Mendonça, and G. Mota, Acta Math. Univ. Comenian (2019)
Powers of Hamiltonian cycles in \mu-inseparable graphs, Acta Math. Univ. Comenian (2019)