勷勤数学•专家报告

题      目：On simplicial complexes with maximal total Betti number and total bigraded Betti number

报  告  人： 于立 教授  (邀请人：范飞飞)

                                       南京大学

时      间： 11月8日  10：00-11:00

地     点：数科院西楼111

报告人简介:

        于立，南京大学数学学院教授，博士生导师，研究方向为代数拓扑、变换群理论等。研究工作发表在《Adv. Math.》，《Int. Math. Res. Not.》，《Sci. China Math.》，《Algebr. Geom. Topol. 》，《Forum Math.》等国际著名期刊上。

摘      要：

       The total Betti number (i.e. the sum of all the Betti numbers) of a space measures the topological complexity of the space and plays important roles in many theories in mathematics. In this talk, we first classify those simplicial complexes with a given number of vertices that have the maximal total Betti number. Then we study similar problems for the sum of bigraded Betti numbers. It is known that the sum of bigraded Betti numbers of a simplicial complex K with m vertices is bounded from below by 2^{m-dim K-1}. We discuss the classification of all the simplicial complexes with m vertices that have the maximal or the minimal sum of bigraded Betti numbers, respectively.

        欢迎老师、同学们参加、交流！