Log canonical singularities and Kawamata log terminal singularities are important for studying birational geometry even in positive characteristic.
On the other hand, F-singularities are also important to control pathlogical phenomena in positive characteristic.
In birational geometry in positve characteristic, we are interested in the relationship between singularities in minimal model theory and F-singularities.
In this talk, I will first introduce relations between singularities in minimal model theory and F-singularities.
Then, I will introduce the notion of quasi-F-splitting, which is introduced by Yobuko, and the idea that using quasi-F-splitting can lead to better relations in the two-dimensional case.
The talk is based on joint work with Kenta Sato and Shunsuke Takagi.