On January 26, 2021, Tuan Tran from the IBS Discrete Mathematics Group gave a talk at the Discrete Math Seminar on a result towards the conjecture of Erdős and Kleitman on the size of an s-saturated family of subsets of {1,2,…,n}. The title of his talk was “Minimum saturated families of sets“.

## Tuan Tran, Minimum saturated families of sets

A family $\mathcal F$ of subsets of [n] is called s-saturated if it contains no s pairwise disjoint sets, and moreover, no set can be added to $\mathcal F$ while preserving this property. More than 40 years ago, Erdős and Kleitman conjectured that an s-saturated family of subsets of [n] has size at least $(1 – 2^{-(s-1)})2^n$. It is a simple exercise to show that every s-saturated family has size at least $2^{n-1}$, but, as was mentioned by Frankl and Tokushige, even obtaining a slightly better bound of $(1/2 + \varepsilon)2^n$, for some fixed $\varepsilon > 0$, seems difficult. We prove such a result, showing that every s-saturated family of subsets of [n] has size at least $(1 – 1/s)2^n$. In this talk, I will present two short proofs. This is joint work with M. Bucic, S. Letzter and B. Sudakov.

## 2020 Combinatorics Workshop (2020 조합론 학술대회) was held on August 24 online

On August 24, Monday, the 2020 Combinatorics Workshop (2020 조합론 학술대회) was held online due to the COVID-19 pandemic. This local workshop series began in 2004 and has been continued to be one of the biggest annual gathering of people in combinatorics located in Korea. Due to the COVID-19 pandemic, it has been reduced to a one-day online conference on Zoom. It was hosted by Kyung Hee University and IBS Discrete Mathematics Group.

The workshop website: https://cw2020.combinatorics.kr

## There were 5 invited speakers.

**Sejeong Bang (방세정)**, Yeungnam University,*Geometric distance-regular graphs***Ringi Kim (김린기)**, KAIST,*Decomposing planar graphs into graphs with degree restrictions***Sangwook Kim (김상욱)**, Chonnam National University,*Combinatorics of lattice path matroid polytopes***Jinyoung Park (박진영)**, Institute for Advanced Study,*Tuza’s Conjecture for random graphs***Jongyook Park (박종육)**, Kyungpook National University,*On distance-regular graphs with induced subgraphs $K_{r,t}$*

## There were 4 contributed talks.

**Byung-Hak Hwang (황병학)**, Seoul National University,*Acyclic orientation polynomials***Jaeseong Oh (오재성)**, Seoul National University,*On linearization coefficients of q-Laguerre polynomials***Jun Seok Oh (오준석)**, Incheon National University,*An inverse Erdős-Ginzburg-Ziv theorem for finite groups***Tuan Tran**, IBS Discrete Mathematics Group,*The singularity of random combinatorial matrices*

## 2020 Combinatorics Workshop

Combinatorics Workshop (조합론 학술대회) is the biggest annual conference in combinatorics in Korea. It was firstly held in 2004 by the Yonsei University BK21 Research Group. It has been advised by the committee of discrete mathematics of the Korean Mathematical Society since 2013. The aim of this workshop is to bring active researchers with different backgrounds to discuss recent and prospective advances in combinatorics and related areas.

Originally, we planned an offline workshop. However, COVID 19 is more spreading and many participants are worried about attending an offline conference. So the schedule and venue are changed as an online workshop with Zoom. I hope that all participants generously understand this sudden change.

# Invited Speakers

- Sejeong Bang (방세정), Yeungnam University
- Ringi Kim (김린기), KAIST
- Sangwook Kim (김상욱), Chonnam National University
- Jinyoung Park (박진영), Institute for Advanced Study
- Jongyook Park (박종육), Kyungpook N. University

# Contributed speakers

- Byung-Hak Hwang (황병학), Seoul National University
- Jaeseong Oh (오재성), Seoul National University
- Jun Seok Oh (오준석), Incheon National University
- Tuan Tran, Institute for Basic Science (IBS)

More information is available on the website https://cw2020.combinatorics.kr.

## Tuan Tran gave a talk on the anti-concentration phenomena at the Discrete Math Seminar

On August 18, 2020, Tuan Tran from IBS Discrete Mathematics Group gave a talk on the anti-concentration phenomena and its consequences to the random matrix theory. The title of his talk is “Anti-concentration phenomena”.

## Tuan Tran, Anti-concentration phenomena

Let $X$ be a real random variable; a typical anti-concentration inequality asserts that (under certain assumptions) if an interval $I$ has small length, then $\mathbb{P}(X\in I)$ is small, regardless the location of $I$. Inequalities of this type have found powerful applications in many branches of mathematics. In this talk we will discuss several recent applications of anti-concentration inequalities in extremal combinatorics, as well as random matrix theory. The talk is partially based on joint work with Matthew Kwan and Benny Sudakov.

## Welcome Ben Lund and Tuan Tran, new research fellows in the IBS Discrete Mathematics Group

The IBS discrete mathematics group welcomes Dr. **Ben Lund** and Dr. **Tuan Tran**, new research fellows at the IBS discrete mathematics group from August 1, 2020.

**Ben Lund** received his Ph.D. from the Department of Mathematics at Rutgers University in 2017 under the supervision of Prof. Shubhangi Saraf. Before joining the IBS, he was a postdoc at Princeton University and a postdoc at the University of Georgia.

**Tuan Tran** received his Ph.D. from the Department of Mathematics at the Freie Universität Berlin in 2015 under the supervision of Prof. Tibor Szabó. Before joining the IBS, he was a lecturer at Hanoi University of Science and Technology, a postdoc at ETH Zürich, and a postdoc at Czech Academy of Sciences. He won the IBS Young Scientist Fellowship.