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:
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
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
2020 SIAM Dénes Kőnig Prize
2020-2023 NSF grant
2019 ETH Medal
2019 NWMA (New World Mathematics Awards) Silver Medal