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.
Team
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
Publications
Campbell R, Hörsch F, Moore B. 2024. Decompositions into two linear forests of bounded lengths. Discrete Mathematics. 347(6), 113962. View
Kwan MA, Sah A, Sawhney M, Simkin M. 2023. Substructures in Latin squares. Israel Journal of Mathematics. 256(2), 363–416. View
Anastos M. 2023. Constructing Hamilton cycles and perfect matchings efficiently. Proceedings of the 12th European Conference on Combinatorics, Graph Theory and Applications. EUROCOMB: European Conference on Combinatorics, Graph Theory and Applications, 36–41. View
Kwan MA, Sah A, Sauermann L, Sawhney M. 2023. Anticoncentration in Ramsey graphs and a proof of the Erdős–McKay conjecture. Forum of Mathematics, Pi. 11, e21. View
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
ReX-Link: Matthew Kwan
Career
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