Noticias en español
Spread measures on perfect matchings in regular pairs.
Abstract: The notion of spread distributions on copies of a given graph (or family of graphs) has played a crucial role in recent developments in probabilistic combinatorics, particularly in studying thresholds in random graphs. In this talk, I will show how to construct a spread distribution on perfect matching in regular pairs, which can be used together with the regularity lemma to find well-behaved embeddings of sparse graphs.
Read MoreHamiltonicity in pseudorandom graphs: absorbing paths.
Abstract: In this second talk, we will introduce the “extendability method” for embedding sparse structures in expander graphs and we will use it to construct efficient absorbers to solve the Hamiltonicity problem in pseudorandom graphs.
Read MoreHamiltonicity in pseudorandom graphs: Pósa rotation.
Abstract: In this series of talks, we will study different approaches to the Hamiltonicity problem in sparse pseudorandom graphs. In this first talk, we will review the celebrated “extension-rotation” technique pioneered by Pósa in the 70s and how to use it in pseudorandom graphs to find Hamilton cycles.
Read MoreAbstract: On 14/5 I gave a talk revolving around the fat minor conjecture. On 15/5 a paper appeared on Arxiv claiming to disprove it. I will report on this new development and I will attempt to offer a comprehensive view of the new questions that it raises, such as “Is this for real?” and “What now?”.
Read MoreCoarse Graph Theory I – The Questions
Resumen: Coarse graph theory is concerned with the large-scale geometric properties of infinite graphs, especially the properties preserved by quasi-isometries. Although such inquiries have been raised since the 80’s, it was usually in the context of Cayley graphs and geometric group theory. Recently the topic migrated to graph theory with intriguing outcomes. Eventually, the field of coarse graph theory was officially inaugurated and systematically treated in a paper by Georgakopoulos and Papasoglu. In this talk, I will explain the basics of coarse graph theory, exploreits...
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