Tuan Tran, Minimum saturated families of sets
Room B232 IBS (기초과학연구원)A family $\mathcal F$ of subsets of is called s-saturated if it contains no s pairwise disjoint sets, and moreover, no set can be added to $\mathcal F$ while preserving …
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Discrete Math Seminar
Doowon Koh (고두원), On the cone restriction conjecture in four dimensions and applications in incidence geometry
Room B232 IBS (기초과학연구원)Main purpose of this talk is to introduce a connection between restriction estimates for cones and point-sphere incidence theorems in the finite field setting. First, we review the finite field …
Martin Ziegler, Quantitative Coding and Complexity Theory of Continuous Data
Room B232 IBS (기초과학연구원)Specifying a computational problem requires fixing encodings for input and output: encoding graphs as adjacency matrices, characters as integers, integers as bit strings, and vice versa. For such discrete data, the actual encoding …
Minki Kim (김민기), Rainbow paths and rainbow matchings
Room B232 IBS (기초과학연구원)We prove that if $n \geq 3$, then any family of $3n-3$ sets of matchings of size $n$ in any graph has a rainbow matching of size $n$. This improves …
Kevin Hendrey, A unified half-integral Erdős-Pósa theorem for cycles in graphs labelled by multiple abelian groups
Room B232 IBS (기초과학연구원)Erdős and Pósa proved in 1965 that there is a duality between the maximum size of a packing of cycles and the minimum size of a vertex set hitting all …
Debsoumya Chakraborti, Some classical problems in graph saturation
Room B232 IBS (기초과학연구원)Graph saturation is one of the oldest areas of investigation in extremal combinatorics. A graph $G$ is called $F$-saturated if $G$ does not contain a subgraph isomorphic to $F$, but …
Se-Young Yun (윤세영), Regret in Online Recommendation Systems
Room B232 IBS (기초과학연구원)We propose a theoretical analysis of recommendation systems in an online setting, where items are sequentially recommended to users over time. In each round, a user, randomly picked from a …
Hong Liu (刘鸿), Nested cycles with no geometric crossing
Room B232 IBS (기초과학연구원)In 1975, Erdős asked the following question: what is the smallest function $f(n)$ for which all graphs with $n$ vertices and $f(n)$ edges contain two edge-disjoint cycles $C_1$ and $C_2$, …
Casey Tompkins, 3-uniform hypergraphs avoiding a cycle of length four
Room B232 IBS (기초과학연구원)We show that that the maximum number of of edges in a $3$-uniform hypergraph without a Berge-cycle of length four is at most $(1+o(1)) \frac{n^{3/2}}{\sqrt{10}}$. This improves earlier estimates by …
Rutger Campbell, Matroid orientability and representability
Room B232 IBS (기초과학연구원)In this talk we will have a brief introduction to oriented matroids and their relation to real-representability.