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Kwan Group

Combinatorics and Probability

Combinatorics is the area of mathematics concerned with finite structures and their properties. This subject is enormously diverse and has connections to many different areas of science: for example, objects of study include networks, sets of integers, error-correcting codes, voting systems, and arrangements of points in space.

Kwan’s group studies a wide range of combinatorial questions, with a particular focus on the interplay between combinatorics and probability. On the one hand, surprisingly often it is possible to use techniques or intuition from probability theory to resolve seemingly non-probabilistic problems in combinatorics (this is the so-called probabilistic method, pioneered by Paul Erdős). On the other hand, combinatorial techniques are of fundamental importance in probability theory, and there are many fascinating questions to ask about random combinatorial structures and processes.

On this site:


Current Projects

Perfect matchings in random hypergraphs | Subgraph statistics in Ramsey graphs | Permanents of random matrices | Partitioning problems in graphs and hypergraphs | Random designs | Transversal bases in matroids | Extremal problems on extension complexity of polytopes | Polynomial Littlewood–Offord problems | Ordered embedding problems


Anastos M, Fabian D, Müyesser A, Szabó T. 2023. Splitting matchings and the Ryser-Brualdi-Stein conjecture for multisets. Electronic Journal of Combinatorics. 30(3), P3.10. View

Anastos M. 2023. A note on long cycles in sparse random graphs. Electronic Journal of Combinatorics. 30(2), P2.21. View

Anastos M. 2023. Fast algorithms for solving the Hamilton cycle problem with high probability. Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms. SODA: Symposium on Discrete Algorithms vol. 2023, 2286–2323. View

Cooley O, Kang M, Pikhurko O. 2022. On a question of Vera T. Sós about size forcing of graphons. Acta Mathematica Hungarica. 168, 1–26. View

Cooley O, Kang M, Zalla J. 2022. Loose cores and cycles in random hypergraphs. The Electronic Journal of Combinatorics. 29(4), P4.13. View

View All Publications

ReX-Link: Matthew Kwan


since 2021 Assistant Professor, Institute of Science and Technology Austria (ISTA)
2018 – 2021 Szegő Assistant Professor, Stanford University, USA
2018 DSc., ETH Zurich, Switzerland

Selected Distinctions

2023-2028 ERC Starting Grant
2020 SIAM Dénes Kőnig Prize
2020-2023 NSF Grant
2019 ETH Medal
2019 NWMA (New World Mathematics Awards) Silver Medal

Additional Information

View Matthew Kwan’s website
Mathematics at ISTA

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