# KCL2019.08

KAIST Combinatorics Lab. Workshop

It is a triannual (three-times-a-year) seminar organized by academic genealogy from Professor Dongsu Kim in * KAIST Combinatorics Laboratory*, which KCL stands for. The aim of this seminar is to bring together active combinatorialists to discuss recent and prospective advances in

*and related areas. The style of talk tends to be less formal.*

**algebraic combinatorics**### Information

**Title**KAIST Combinatorics Lab. Workshop 2019.08 (KCL2019.08)**Date**August 12 (Monday), 2019**Venue**Room 31318, Sungkyunkwan University, Suwon

### Program

**12:00 - 13:55**Welcome reception**13:55 - 14:00**Opening Address / Message from Dennis**14:00 - 16:00**Lecture 1 by Seunghyun Seo**Title.**Combinatorics on hyperplane arrangements.**Abstract.**A hyperplane arrangement is a collection of finitely many affine hyperplanes in some vector space (which for us will usually be over the real numbers.) We will give an introduction to the theory of hyperplane arrangements, focusing on their combinatorial properties. Topics will include the number of regions, intersection lattices, characteristic polynomials, and graphical arrangements. Some special arrangements will be analyzed, such as the braid, Catalan, Shi and Linial arrangements. We also present some recent progress on calculating characteristic polynomials of certain hyperplane arrangements.

**16:00 - 16:30**Coffee Break**16:30 - 17:30**Lecture 2 by U-keun Song**Title.**Rational generating functions**Abstract.**In this talk, we will review a general class of generating functions which is called rational generating functions. We will see a well-known role of rational generating functions about linear homogeneous Diophantine equations. And as an application, we will enumerate the number of nonnegative integer matrices such that every row and column sums are the same, namely, magic squares.

**17:30 - 17:55**Lightning Talks (about 3 minutes for each)**17:55 - 18:00**Closing Remarks**18:00 - 20:00**Dinner

### Participants

Dongsu Kim, KAIST

Seunghyun Seo, Kangwon National University

Heesung Shin, Inha University

Jang Soo Kim, Sungkyunkwan University

Sun-mi Yun, Sungkyunkwan University

U-keun Song, Sungkyunkwan University

Jihyeug Jang, Sungkyunkwan University

Taehyun Eom, KAIST

Sangwook Kim, Chonnam National University

JiSun Huh, Sungkyunkwan University

Minho Song, Sungkyunkwan University

SoHyeon Gyeong, Sungkyunkwan University

### Organizer

Jang Soo Kim, Sungkyunkwan University

### Host and Sponsor

Sungkyunkwan University

Applied algebra and Optimization Research Center (AORC)

National Research Foundation