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Alexander Sidorenko works on density inequalities in graph theory and the theory of hypergraphs. His name is associated with the Sidorenko conjecture, which compares copies of a fixed bipartite graph with the random-density benchmark.^[ref]

With David Conlon and Joonkyung Lee, he studied hypergraph failures of the analogous inequality. Their result turns such failures into improved extremal constructions, connecting analytic inequalities for densities with concrete forbidden-subgraph problems.^[ref]

Benny Sudakov studies combinatorics, especially extremal and probabilistic questions. His ETH author page documents work in these areas.^[ref]

With David Conlon, Jacob Fox and Choongbum Lee, he developed bounds for ordered Ramsey numbers. Their work compares the order-preserving problem with the ordinary Ramsey number and demonstrates a large gap for some ordered matchings.^[ref]

Choongbum Lee works on graph theory and Ramsey theory. His joint paper with David Conlon, Jacob Fox and Benny Sudakov investigates copies of a graph whose vertex order must be preserved.^[ref]

The ordered setting is sensitive to labeling: some ordered matchings have superpolynomial Ramsey numbers. Thus low ordinary degree does not by itself make an order-constrained embedding problem easy.^[ref]

David Conlon studies extremal graph theory and Ramsey theory. His joint work with Jacob Fox, Choongbum Lee and Benny Sudakov shows that imposing a vertex order can make Ramsey problems substantially harder, even for matchings.^[ref]

With Joonkyung Lee and Alexander Sidorenko, he also linked failures of a hypergraph analogue of the Sidorenko conjecture to improved extremal lower bounds. This turns a failed density inequality into information about constructions avoiding a specified hypergraph.^[ref]

Jacob Fox works on extremal combinatorics, Ramsey theory and algebraic and probabilistic methods in graph theory. His Stanford research page also identifies applications to computer science.^[ref]

With David Conlon, Choongbum Lee and Benny Sudakov, he studied ordered Ramsey numbers. Requiring the vertices of a monochromatic copy to appear in a prescribed order can force superpolynomial growth even when the underlying graph is a matching.^[ref]

Joonkyung Lee works on extremal combinatorics. With David Conlon and Alexander Sidorenko, he studied connections between the Sidorenko conjecture and extremal numbers.^[ref]

The graph conjecture concerns lower bounds on homomorphism densities for bipartite graphs. The paper investigates hypergraph analogues, where counterexamples exist, and uses those failures to improve lower bounds for the number of edges in a forbidden-configuration-free hypergraph.^[ref]