## Younjin Kim (김연진) gave a talk on the number of k-dimensional corner-free subsets in the k-dimensional grid at the Discrete Math Seminar

On April 11, 2022, Younjin Kim (김연진) from POSTECH gave a talk at the Discrete Math Seminar on the number of k-dimensional corner-free subsets of the k-dimensional grid {1,2,…n}^k. The title of her talk was “On the extremal problems related to Szemerédi’s theorem”.

## Younjin Kim (김연진), On the extremal problems related to Szemerédi’s theorem

In 1975, Szemerédi proved that for every real number $\delta > 0$ and every positive integer $k$, there exists a positive integer $N$ such that every subset $A$ of the set $\{1, 2, \cdots, N \}$ with $|A| \geq \delta N$ contains an arithmetic progression of length $k$. There has been a plethora of research related to Szemerédi’s theorem in many areas of mathematics. In 1990, Cameron and Erdős proposed a conjecture about counting the number of subsets of the set $\{1,2, \dots, N\}$ which do not contain an arithmetic progression of length $k$. In the talk, we study a natural higher dimensional version of this conjecture, and also introduce recent extremal problems related to Szemerédi’s theorem.

기초과학연구원 수리및계산과학연구단 이산수학그룹
대전 유성구 엑스포로 55 (우) 34126
IBS Discrete Mathematics Group (DIMAG)
Institute for Basic Science (IBS)
55 Expo-ro Yuseong-gu Daejeon 34126 South Korea
E-mail: dimag@ibs.re.kr, Fax: +82-42-878-9209