Stijn Cambie, Recent progress on the Union-closed conjecture and related

Room B332 IBS (기초과학연구원)

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 $\mathcal F$), then $\mathcal F$ contains an

Paul Seymour, A loglog step towards the Erdős-Hajnal conjecture

Zoom ID: 869 4632 6610 (ibsdimag)

In 1977, Erdős and Hajnal made the conjecture that, for every graph $H$, there exists $c>0$ such that every $H$-free graph $G$ has a clique or stable set of size at least $|G|^c$; and they proved that this is true with $|G|^c$ replaced by $2^{c\sqrt{\log |G|}}$. There has no improvement on this result (for general

Younjin Kim (김연진), Problems on Extremal Combinatorics

Room B332 IBS (기초과학연구원)

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.

Qizhong Lin, Two classical Ramsey-Turán numbers involving triangles

Zoom ID: 224 221 2686 (ibsecopro)

In 1993, Erdős, Hajnal, Simonovits, Sós and Szemerédi proposed to determine the value of Ramsey-Turán density $\rho(3,q)$ for $q\ge3$. Erdős et al. (1993) and Kim, Kim and Liu (2019) proposed two corresponding conjectures. However, we only know four values of this Ramsey-Turán density by Erdős et al. (1993). There is no progress on this classical

Tianchi Yang, On the maximum number of edges in k-critical graphs

Room B332 IBS (기초과학연구원)

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

István Tomon, Configurations of boxes

Room B332 IBS (기초과학연구원)

Configurations of axis-parallel boxes in $\mathbb{R}^d$ are extensively studied in combinatorial geometry. Despite their perceived simplicity, there are many problems involving their structure that are not well understood. I will talk about a construction that shows that their structure might be more complicated than people conjectured.

Jie Han, Spanning trees in expanders

Zoom ID: 224 221 2686 (ibsecopro)

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 $(n,d,\lambda)$-graph to be $T(n, \Delta)$-universal. In this talk, we introduce our recent work on this conjecture.

James Davies, Two structural results for pivot-minors

Room B332 IBS (기초과학연구원)

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.

MATRIX-IBS Workshop: Structural Graph Theory Downunder III

MATRIX, Australia

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

Shin-ichiro Seki, On the extension of the Green-Tao theorem to number fields

Zoom ID: 897 6822 0619 (ibsecopro) [04/19 only]

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 Green-Tao theorem to the case of general number fields. Our combinatorial tool is the relative hypergraph removal lemma by Conlon-Fox-Zhao. I will discuss the difficulties

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