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.
Group Leader
Administrative Support
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
Anastos M, Boyadzhiyska S, Rathke S, Rué J. 2025. On the chromatic number of powers of subdivisions of graphs. Discrete Applied Mathematics. 360, 506–511. View
Carbonero A, Koerts H, Moore B, Spirkl S. 2024. On heroes in digraphs with forbidden induced forests. European Journal of Combinatorics. 125, 104104. View
Lill J, Petrova KH, Weber S. 2024. Linear-time MaxCut in multigraphs parameterized above the Poljak-Turzík bound. 19th International Symposium on Parameterized and Exact Computation. IPEC: Symposium on Parameterized and Exact Computation, LIPIcs, vol. 321, 2. View
Anastos M, Auerbach B, Baig MA, Cueto Noval M, Kwan MA, Pascual Perez G, Pietrzak KZ. 2024. The cost of maintaining keys in dynamic groups with applications to multicast encryption and group messaging. 22nd International Conference on Theory of Cryptography. TCC: Theory of Cryptography, LNCS, vol. 15364, 413–443. View
Anastos M, Cooley O, Kang M, Kwan MA. 2024. Partitioning problems via random processes. Journal of the London Mathematical Society. 110(6), e70010. 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
