学术报告（刘济豪 2024.5.17）

Abstract：In this talk, I will present several results on the optimal bounds for algebraic invariants of surfaces. Specifically, I will discuss our findings of the 1-gap of R-complementary thresholds, the smallest volume of ample log surfaces with reduced boundary, the smallest minimal log discrepancy of klt Calabi-Yau surfaces, and the minimal accumulation point of volumes of stable surfaces. These results answer questions posed by V. Alexeev and W. Liu, and J. Kollár, and also reprove a recent result by L. Esser, B. Totaro, and C. Wang. As an application, I will also discuss our work on finding and classifying all exceptional Fano surfaces (Fano surfaces with Tian’s alpha invariant strictly greater than 1) that are not 1/11-klt. We have identified 25 such surfaces up to isomorphism. This talk is based on joint works with V. V. Shokurov and Wenfei Liu.