Marcelo Sales, On Pisier type problems
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We give a summary on the work of the last months related to Frankl's Union-Closed conjecture and its offsprings. The initial conjecture is stated as a theorem in extremal set …
In 1977, Erdős and Hajnal made the conjecture that, for every graph
Extremal Combinatorics studies the maximum or minimum size of finite objects (numbers, sets, graphs) satisfying certain properties. In this talk, I introduce the conjectures I solved on Extremal Combinatorics, and …
In 1993, Erdős, Hajnal, Simonovits, Sós and Szemerédi proposed to determine the value of Ramsey-Turán density
In this talk, we will discuss the problem of determining the maximum number of edges in an n-vertex k-critical graph. A graph is considered k-critical if its chromatic number is …
Configurations of axis-parallel boxes in
We consider the spanning tree embedding problem in dense graphs without bipartite holes and sparse graphs. In 2005, Alon, Krivelevich and Sudakov asked for determining the best possible spectral gap …
Pivot-minors can be thought of as a dense analogue of graph minors. We shall discuss pivot-minors and two recent results for proper pivot-minor-closed classes of graphs. In particular, that for …
In 2006, Tao established the Gaussian counterpart of the celebrated Green-Tao theorem on arithmetic progressions of primes. In this talk, I will explain the extension of Tao's theorem and the …