Jeck Lim, Sums of linear transformations

Zoom ID: 870 0312 9412 (ibsecopro) [CLOSED]

We show that if $L_1$ and $L_2$ are linear transformations from $\mathbb{Z}^d$ to $\mathbb{Z}^d$ satisfying certain mild conditions, then, for any finite subset $A$ of $\mathbb{Z}^d$, \ This result corrects and confirms the two-summand case of a conjecture of Bukh and is best possible up to the lower-order term for many choices of $L_1$ and

O-joung Kwon (권오정), Graph minor theory and beyond

Room 1501, Bldg. E6-1, KAIST

One of the important work in graph theory is the graph minor theory developed by Robertson and Seymour in 1980-2010. This provides a complete description of the class of graphs that do not contain a fixed graph H as a minor. Later on, several generalizations of H-minor free graphs, which are sparse, have been defined

Amadeus Reinald, Twin-width and forbidden subdivisions

Room B332 IBS (기초과학연구원)

Twin-width is a recently introduced graph parameter based on vertex contraction sequences. On classes of bounded twin-width, problems expressible in FO logic can be solved in FPT time when provided with a sequence witnessing the bound. Classes of bounded twin-width are very diverse, notably including bounded rank-width, $\Omega ( \log (n) )$-subdivisions of graphs of

Chengfei Xie, On the packing densities of superballs in high dimensions

Zoom ID: 870 0312 9412 (ibsecopro) [CLOSED]

The sphere packing problem asks for the densest packing of nonoverlapping equal-sized balls in the space. This is an old and difficult problem in discrete geometry. In this talk, we give a new proof for the result that for $ 1<p<2 $, the translative packing density of superballs (a generalization of $\ell^p$ balls) in $\mathbb{R}^n$

Ben Lund, Radial projections in finite space

Room B332 IBS (기초과학연구원)

Given a set $E$ and a point $y$ in a vector space over a finite field, the radial projection $\pi_y(E)$ of $E$ from $y$ is the set of lines that through $y$ and points of $E$. Clearly, $|\pi_y(E)|$ is at most the minimum of the number of lines through $y$ and $|E|$. I will discuss

Xizhi Liu, Hypergraph Turán problem: from 1 to ∞

Zoom ID: 870 0312 9412 (ibsecopro) [CLOSED]

One interesting difference between (nondegenerate) Graph Turán problem and Hypergraph Turán problem is that the hypergraph families can have at least two very different extremal constructions. In this talk, we will look at some recent progress and approaches to constructing hypergraph families with at least two different extremal constructions. Based on some joint work with

Eric Vigoda, Computational phase transition and MCMC algorithms

Room B332 IBS (기초과학연구원)

This talk will highlight recent results establishing a beautiful computational phase transition for approximate counting/sampling in (binary) undirected graphical models (such as the Ising model or on weighted independent sets). The computational problem is to sample from the equilibrium distribution of the model or equivalently approximate the corresponding normalizing factor known as the partition function. We show that when correlations die

Sepehr Hajebi, Holes, hubs and bounded treewidth

Zoom ID: 869 4632 6610 (ibsdimag)

A hole in a graph $G$ is an induced cycle of length at least four, and for every hole $H$ in $G$, a vertex $h\in G\setminus H$ is called a $t$-hub for $H$ if $h$ has at least $t$ neighbor in $H$. Sintiari and Trotignon were the first to construct graphs with arbitrarily large treewidth

Kevin Hendrey, Product Structure of Graph Classes with Bounded Treewidth

Room B232 IBS (기초과학연구원)

The strong product $G\boxtimes H$ of graphs $G$ and $H$ is the graph on the cartesian product $V(G)\times V(H)$ such that vertices $(v,w)$ and $(x,y)$ are adjacent if and only if $\max\{d_G(v,x),d_H(w,y)\}=1$. Graph product structure theory aims to describe complicated graphs in terms of subgraphs of strong products of simpler graphs. This area of research was initiated

Jinyoung Park (박진영), Thresholds 1/2

Room B332 IBS (기초과학연구원)

Thresholds for increasing properties of random structures are a central concern in probabilistic combinatorics and related areas. In 2006, Kahn and Kalai conjectured that for any nontrivial increasing property on a finite set, its threshold is never far from its "expectation-threshold," which is a natural (and often easy to calculate) lower bound on the threshold.

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