Qizhong Lin, Two classical Ramsey-Turán numbers involving triangles

In 1993, Erdős, Hajnal, Simonovits, Sós and Szemerédi proposed to determine the value of Ramsey-Turán density $\rho (3,q)$ for $q\ge 3$. Erdős et al. (1993) and Kim, Kim and Liu (2019) proposed two corresponding conjectures. However, we only know four values of this Ramsey-Turán density by Erdős et al. (1993). There is no progress on this classical Ramsey-Turán density since then. In this talk, I will introduce two new values of this classical Ramsey-Turán density. Moreover, the corresponding asymptotically extremal structures are weakly stable, which answers a problem of Erdős et al. (1993) for the two cases. Joint work with Xinyu Hu.