## Rob Morris gave a talk showing the sketch of the proof that the diagonal Ramsey number is less than (4-𝜀)^k at the Discrete Math Seminar

During the Discrete Math Seminar held on May 2, 2023, Rob Morris of IMPA presented on the recent breakthrough regarding the diagonal Ramsey number, specifically demonstrating that $R(k,k)<(4-\varepsilon)^k$. The title of his talk was “An exponential improvement for diagonal Ramsey.”

## Rob Morris gave a colloquium talk at KAIST on Ramsey Theory

On April 27, 2023, Rob Morris from IMPA gave a colloquium talk on Ramsey Theory at the Colloquium of KAIST Mathematical Sciences. The title of his talk was “Ramsey theory: searching for order in chaos.” Rob Morris is currently visiting IBS and will give a seminar talk at IBS on May 2 with more details on his latest theorem on diagonal Ramsey numbers.

## Rob Morris, Ramsey theory: searching for order in chaos

In many different areas of mathematics (such as number theory, discrete geometry, and combinatorics), one is often presented with a large “unstructured” object, and asked to find a smaller “structured” object inside it. One of the earliest and most influential examples of this phenomenon was the theorem of Ramsey, proved in 1930, which states that if n = n(k) is large enough, then in any red-blue colouring of the edges of the complete graph on n vertices, there exists a monochromatic clique on k vertices. In this talk I will discuss some of the questions, ideas, and new techniques that were inspired by this theorem, and present some recent progress on one of the central problems in the area: bounding the so-called “diagonal” Ramsey numbers. Based on joint work with Marcelo Campos, Simon Griffiths and Julian Sahasrabudhe.

## Rob Morris, An exponential improvement for diagonal Ramsey

The Ramsey number $R(k)$ is the minimum n such that every red-blue colouring of the edges of the complete graph on n vertices contains a monochromatic copy of $K_k$. It has been known since the work of Erdős and Szekeres in 1935, and Erdős in 1947, that $2^{k/2} < R(k) < 4^k$, but in the decades since the only improvements have been by lower order terms. In this talk I will sketch the proof of a very recent result, which improves the upper bound of Erdős and Szekeres by a (small) exponential factor.

Based on joint work with Marcelo Campos, Simon Griffiths and Julian Sahasrabudhe.

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