Time:10:00-11:00, Monday, April 10, 2023
Venue:E4-201, Yungu Campus, Westlake University
Speaker：Jihao Liu, Northwestern University
Title：Optimal Bounds for Algebraic Invariants of Surfaces
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, and the smallest minimal log discrepancy of klt Calabi-Yau 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, none of which have been previously documented in the literature. If time allows, I will also touch upon a question we have developed regarding the 1-gap of R-complementary thresholds and the 1-gap of minimal log discrepancies in high dimensions. This is an ongoing joint work with V. V. Shokurov.
