Matthew Kroeker, Average flat-size in complex-representable matroids

Room B332 IBS (기초과학연구원)

Melchior’s Inequality (1941) implies that, in a rank-3 real-representable matroid, the average number of points in a line is less than three. This was extended to the complex-representable matroids by Hirzebruch in 1983 with the slightly weaker bound of four. In this talk, we discuss and sketch the proof of the recent result that, in

Zichao Dong, Convex polytopes in non-elongated point sets in $\mathbb{R}^d$

Room B332 IBS (기초과학연구원)

For any finite point set $P \subset \mathbb{R}^d$, we denote by $\text{diam}(P)$ the ratio of the largest to the smallest distances between pairs of points in $P$. Let $c_{d, \alpha}(n)$ be the largest integer $c$ such that any $n$-point set $P \subset \mathbb{R}^d$ in general position, satisfying $\text{diam}(P) < \alpha\sqrt{n}$ (informally speaking, `non-elongated'), contains a

Ander Lamaison, Uniform Turán density beyond 3-graphs

Room B332 IBS (기초과학연구원)

The uniform Turán density $\pi_u(F)$ of a hypergraph $F$, introduced by Erdős and Sós, is the smallest value of $d$ such that any hypergraph $H$ where all linear-sized subsets of vertices of $H$ have density greater than $d$ contains $F$ as a subgraph. Over the past few years the value of $\pi_u(F)$ was determined for

Sebastian Wiederrecht, Packing even directed circuits quarter-integrally

Room B332 IBS (기초과학연구원)

We prove the existence of a computable function $f\colon\mathbb{N}\to\mathbb{N}$ such that for every integer $k$ and every digraph $D$ either contains a collection $\mathcal{C}$ of $k$ directed cycles of even length such that no vertex of $D$ belongs to more than four cycles in $\mathcal{C}$, or there exists a set $S\subseteq V(D)$ of size at

Jie Han (韩杰), Perfect matchings in dense uniform hypergraphs

Room B332 IBS (기초과학연구원)

There has been a raising interest on the study of perfect matchings in uniform hypergraphs in the past two decades, including extremal problems and their algorithmic versions. I will introduce the problems and some recent developments.

Linda Cook, On polynomial degree-boundedness

Room B332 IBS (기초과학연구원)

We prove a conjecture of Bonamy, Bousquet, Pilipczuk, Rzążewski, Thomassé, and Walczak, that for every graph $H$, there is a polynomial $p$ such that for every positive integer $s$, every graph of average degree at least $p(s)$ contains either $K_{s,s}$ as a subgraph or contains an induced subdivision of $H$. This improves upon a result

Evangelos Protopapas, Erdős-Pósa Dualities for Minors

Room B332 IBS (기초과학연구원)

Let $\mathcal{G}$ and $\mathcal{H}$ be minor-closed graphs classes. The class $\mathcal{H}$ has the Erdős-Pósa property in $\mathcal{G}$ if there is a function $f : \mathbb{N} \to \mathbb{N}$ such that every graph $G$ in $\mathcal{G}$ either contains (a packing of) $k$ disjoint copies of some subgraph minimal graph $H \not\in \mathcal{H}$ or contains (a covering of)

Casey Tompkins, On graphs without cycles of length 0 modulo 4

Room B332 IBS (기초과학연구원)

Bollobás proved that for every $k$ and $\ell$ such that $k\mathbb{Z}+\ell$ contains an even number, an $n$-vertex graph containing no cycle of length $\ell \bmod k$ can contain at most a linear number of edges. The precise (or asymptotic) value of the maximum number of edges in such a graph is known for very few

Eero Räty, Positive discrepancy, MaxCut and eigenvalues of graphs

Room B332 IBS (기초과학연구원)

The positive discrepancy of a graph $G$ of edge density $p$ is defined as the maximum of $e(U) - p|U|(|U|-1)/2$, where the maximum is taken over subsets of vertices in G. In 1993 Alon proved that if G is a $d$-regular graph on $n$ vertices and $d = O(n^{1/9})$, then the positive discrepancy of $G$

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