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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.




Team


Current Projects

Random graphs | Random matrices | Extremal combinatorics | Ramsey theory | Combinatorial design theory | Probabilistic inequalities | Connections to theoretical computer science


Publications

Mies S, Moore B, Smith-Roberge E. 2025. Beyond the pseudoforest strong Nine Dragon Tree theorem. European Journal of Combinatorics. 130(12), 104214. View

Christoph M, Petrova KH, Steiner R. 2025. A note on digraph splitting. Combinatorics Probability and Computing. 34(4), 559–564. View

Anastos M, Kwan MA, Moore B. 2025. Smoothed analysis for graph isomorphism. Proceedings of the 57th Annual ACM Symposium on Theory of Computing. STOC: Symposium on Theory of Computing, 2098–2106. View

Lichev L, Schapira B. 2025. Color-avoiding percolation on the Erdős–Rényi random graph. Annales Henri Lebesgue. 8, 35–65. View

Dvořák Z, Moore B, Seifrtová M, Šámal R. 2025. Precoloring extension in planar near-Eulerian-triangulations. European Journal of Combinatorics. 127, 104138. View

View All Publications

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
2024 Austrian Mathematical Society (ÖMG) Prize
2020 SIAM Dénes Kőnig Prize
2020-2023 NSF Grant
2019 ETH Medal


Additional Information

View Matthew Kwan’s website
Mathematics at ISTA



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