On October 4, 2022, Zixiang Xu (徐子翔) from the IBS Extremal Combinatorics and Probability Group gave a talk at the Discrete Math Seminar on the Turán numbers of bipartite graphs and recent approaches. The title of his talk was “On the degenerate Turán problems“.

## Welcome Nika Salia and Zixiang Xu, new members of the IBS Extremal Combinatorics and Probability Group

The IBS discrete mathematics group welcomes Dr. Nika Salia and Dr. Zixiang Xu (徐子翔), new research fellows at the IBS Extremal Combinatorics and Probability Group from September 1, 2022.

Dr. Nika Salia received his Ph.D. from the Central European University in 2021 under the supervision of Prof. Ervin Győri.

Dr. Zixiang Xu (徐子翔) received his Ph.D. from the Capital Normal University of China in 2022 under the supervision of Prof. Gennian Ge.

## Zixiang Xu (徐子翔), On the degenerate Turán problems

For a graph $F$, the Turán number is the maximum number of edges in an $n$-vertex simple graph not containing $F$. The celebrated Erdős-Stone-Simonovits Theorem gives that \[ \text{ex}(n,F)=\bigg(1-\frac{1}{\chi(F)-1}+o(1)\bigg)\binom{n}{2},\] where $\chi(F)$ is the chromatic number of $H$. This theorem asymptotically solves the problem when $\chi(F)\geqslant 3$. In case of bipartite graphs $F$, not even the order of magnitude is known in general. In this talk, I will introduce some recent progress on Turán numbers of bipartite graphs and related generalizations and discuss several methods developed in recent years. Finally, I will introduce some interesting open problems on this topic.