报告人：刘济豪（美国西北大学）

时  间：2023年4月12日上午09:00-11:00

地  点：厦大海韵园实验楼111报告厅

内容摘要:

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.

个人简介：

刘济豪是美国西北大学的 Boas 助理教授。他于2021年3月在美国犹他大学获得博士学位，导师是 Christopher Hacon。刘济豪的研究领域是代数几何，在双有理几何中的极小模型理论、低维簇的具体界等前沿问题中取得优秀的成果，已有多篇论文发表/接收在《中国科学-数学》，《Osaka J. Math.》，《Int. J. Math.》，《Math. Nachr.》等杂志。

联系人：刘文飞