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.

Jinyoung Park (박진영), Thresholds 2/2

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.

Noam Lifshitz, Product free sets in the alternating group

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

A subset of a group is said to be product free if it does not contain the product of two elements in it. We consider how large can a product free subset of $A_n$ be? In the talk we will completely solve the problem by determining the largest product free subset of $A_n$. Our proof

Seunghun Lee (이승훈), Inscribable order types

Room B332 IBS (기초과학연구원)

We call an order type inscribable if it is realized by a point configuration where all extreme points are all on a circle. In this talk, we investigate inscribability of order types. We first show that every simple order type with at most 2 interior points is inscribable, and that the number of such order

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