Recent Results on Ramsey Numbers

Ramsey Theory is the study of inevitable structure, with examples occurring in various areas, including Graph Theory, Number Theory and Geometry. In this mini-course we discuss recent major advances, including the new lower bound on R(4, k) and the exponential improvement for the upper bound on diagonal Ramsey numbers.

References:
[1] F. Botler, M. Collares, T. Martins, W. Mendon¸ca, R. Morris and G. Mota, Combinatória, XXXIII Colóquio Brasileiro de Matemática (SBM/IMPA).
[2] M. Campos, S. Griffiths R. Morris and J. Sahasrabudhe, An exponential improvement for diagonal Ramsey, arXiv:2303.09521
[3] D. Conlon, J. Fox and B. Sudakov, Recent developments in graph Ramsey theory, Surveys in Combinatorics, 424 (2015), 49–118.
[4] S. Mattheus and J. Verstraete, The asymptotics of r(4, t), arXiv:2306.04007