A large part of extremal combinatorics focuses on the interactions between frequencies of local patterns in discrete structures. For example, how many triangles must there be in a graph with 25 vertices and 200 edges? How long can a sequence of real numbers be without containing a monotone sequence of length 42?

My main research focus is on problems of this type and their applications in other areas. Much of my work in extremal combinatorics is intimately linked to the recently developed analytic "limit theory" for combinatorial objects which has led to a deeper understanding of some of the key ideas in the area, such as the Szemeredi Regularity Lemma and the notion of quasirandomness.

More broadly, I am interested in a wide range of topics in combinatorics, graph theory, theoretical computer science and probability theory. For example, my past work includes results on graph colouring, bootstrap percolation, and computational complexity problems related to graph homomorphisms.

Interests

• extremal combinatorics
• probabilistic combinatorics
• combinatorial limits
• quasirandomness
• Ramsey theory
• extremal set theory
• graph colouring
• graph homomorphisms
• bootstrap percolation
• algorithms
• computational complexity

Courses

• Fall 2024: 听 听
• Spring 2025:
• Summer 2025: