Speaker: 이준경 교수 (Prof. Joonkyung Lee, Hanyang University) Date: June 28th.(Tue) 2022, 15:00-16:00 Place: AORC Seminar Room(SKKU, General Studies Bd. 3F) Title: Ramsey multiplicity and common graphs Abstract: A graph H is common if the number of monochromatic copies of H in a 2-edge-colouring of the complete graph is minimised by the random colouring. Burr and Rosta, extending a famous conjecture by Erdős, conjectured that every graph is common. The conjectures by Erdős and by Burr and Rosta were disproved by Thomason and by Sidorenko, respectively, in the late 1980s. Collecting new examples for common graphs had not seen much progress since then, although very recently, a few more graphs are verified to be common by the flag algebra method or the recent progress on Sidorenko's conjecture. I will give an overview on both old and new results in the area, including Sidorenko's theorem proving commonality of odd cycles and some recent results on tripartite common graphs. Joint work with Andrzej Grzesik, Bernard Lidický, and Jan Volec.