KPPY 81

Seungjai Lee, Eun-Kyung Cho, Jongyook Park, Sejeong Bang, Mitsugu Hirasaka

KPPY 81

Feb 21, 2017. 11:00am-6:00pm at PNU

Schedule
11:00am - 11:50 Seungjai Lee
NIMS
A survey on zeta functions of groups and rings
12pm - 1:25 Lunch
1:30 - 2:20 Eun-Kyung Cho
PNU
n finite groups which induces only commutative proper Schur rings
2:30 - 3:20 Jongyook Park
KIAS
On 2-walk-regular graphs
3:30 - 4:20 Sejeong Bang
Yeungnam University
Determination of geometric distance-regular graphs
4:30 - 5:20 Mitsugu Hirasaka
PNU
On finite metric spaces with some properties on distances and triangles

Abstracts



Seungjai Lee
A survey on zeta functions of groups and rings
Over the last few decades, zeta functions of groups and rings have become important tools in various areas of asymptotic group and ring theory. In this talk, I will introduce their definitions with brief history of their developments and their applications. I shall also present recent discoveries, and discuss further problems to solve.
Eun-Kyung Cho
n finite groups which induces only commutative proper Schur rings
Consider a group ring $\mathbb{C}[G]$ and a partition $\mathcal{P} = \{D_0=\{e\}, D_1, \cdots, D_d\}$ of $G$. Let $D_i^{*} = \{g^{-1} \mid g \in D_i\}$ and $\bar{D_i}$ is the sum of all the elements of $D_i$ for all $i \in \{0, 1, \cdots, d\}$. Then a subalgebra of $\mathbb{C}[G]$ generated by $\bar{D_0}, \bar{D_1}, \cdots, \bar{D_d}$ is called a Schur ring over $G$ and is denoted by $\mathfrak{G} =( G ; \mathcal{P})$. In this talk, we classify a group $G$ such that every proper Schur ring over it is commutative.
Jongyook Park
On 2-walk-regular graphs
A $t$-walk-regular graph is a common generalization of distance-regular graphs on the one hand and $t$-arc-transitive graphs on the other hand. We focus on the case where $t =2$ because $s$-walk-regular graphs are $t$-walk-regular if $s\geq t$ and many properties of distance-regular graphs can be generalized to $2$-walk-regular graphs. In this talk, we first introduce some known results that hold for $2$-walk-regular graphs but are not true in general for $1$-walk-regular graphs. And then we will generalize a known result of distance-regular graphs to the class of 2-walk-regular graphs. (This is joint work with Jack Koolen and Zhi Qiao.)
Sejeong Bang
Determination of geometric distance-regular graphs
A non-complete distance-regular graph is called {\it geometric} if there exists a set $\mathcal{C}$ of Delsarte cliques such that each edge lies in exactly one clique in $\mathcal{C}$. In this talk we study how to determine given distance-regular graphs with large valency are geometric or not.
Mitsugu Hirasaka
On finite metric spaces with some properties on distances and triangles
Let $(X,d)$ be a finite metric space with $|X|=n$. For a positive integer $k$ we define $A_k(X)$ to be the quotient set of all $k$-subsets of $X$ by isometry, and we denote $|A_k(X)|$ by $a_k$. The sequence $(a_1,a_2,\ldots,a_{n})$ is called the isometric sequence of $(X,d)$. In this talk we aim to characterize finite metric spaces with $a_2=a_3=4$.