报告题目：Syzygies of algebraic varieties
报告人：牛文博，美国阿肯色大学副教授
时间：2023年5月29日（周一）15:00-16:00
地点：理科楼A304
报告摘要：An algebraic variety is a set of zeros of polynomials, and it has a naturally defined coordinate ring. Hilbert's syzygy theorem then asserts that there exists a finite length minimal graded free resolution of the coordinate ring. The information from the resolution can be expressed by a Betti diagram. It has been drawn great attention to understand algebraic and geometric properties encoded in the syzygies of the variety. One important invariant derived from syzygies is the Castelnuovo-Mumford regularity of the variety. It can be traced back to Castelnuovo's study in 1893 on the linear system of algebraic curves. The other one is the Betti numbers, which can be understood through Koszul groups developed by M. Green. In this talk, we review recent progress in the study of syzygies along the line of bounding Castelnuovo-Mumford regularity and syzygies of algebraic curves and their secant varieties.
报告人简介：牛文博，美国阿肯色大学副教授。主要研究方向是代数几何，包括syzygy理论，linkage理论，singularities, fundamental forms, 和multiplier ideals 等。
邀请人：左怀青
