Talks

We adapt the grammar introduced by Chapuy, Fusy, Kang and Shoilekova to study bipartite graph families which are defined by their 3-connected components. More precisely, in this talk I will explain how to get the counting formulas for bipartite series-parallel graphs (and more generally of the Ising model over this family of graphs), as well as asymptotic estimates for the number of such graphs with a fixed size. This talk is based in a work in progress joint with Kerstin Weller.

... ist vielleicht nur für die Analytiker interessant.

We describe a general approach to the strong hypergraph regularity lemma, which we call 'regular slices', which avoids many of the usual technical complications and retains the features one would like to use in extremal hypergraph theory. This talk will avoid painful technical details in so far as that is possible and focus on an application, proving a hypergraph extension of the Erdos-Gallai theorem.

This is joint work with Julia Böttcher, Oliver Cooley and Richard Mycroft.

The blow-up lemma of Komlós, Sárközy and Szemerédi is an important tool for embedding large graphs H into dense graphs G. We recently obtained versions of this lemma for subgraphs G of sparse random and pseudo-random graphs. This has important applications in extremal graph theory on random graphs, but can also be used for the analysis of certain maker-breaker games.

In the talk I will explain our blow-up lemmas and describe their connection to maker-breaker games, after giving some necessary background.

Joint work with P. Allen, H. Hàn, Y. Kohayakawa, Y. Person.