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 theory; when a family F is union-closed (the union of sets of F is itself a set of
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 also introduce recent extremal problems.
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 k, but any proper subgraph has a chromatic number less than k. The problem remains open for any integer k ≥ 4. Our presentation will …
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 forcing an
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 every graph H, the class of graphs containing no H-pivot-minor is 𝜒-bounded, and also satisfies the (strong) Erdős-Hajnal property.
Website: https://www.matrix-inst.org.au/events/structural-graph-theory-downunder-iii/ Program Description: This program, jointly organised by MATRIX and the Discrete Mathematics Group of the Korean Institute for Basic Science (IBS), builds on the “Structural Graph Theory Downunder” programs held at MATRIX in 2019 and 2022. In this short intensive workshop, mathematicians from across the globe will come together to work on open …