报告题目 (Title)：Constructing mathematical invariants by counting beyond numbers（用超数计数构造数学不变量）
报告人 (Speaker)：林宗柱 教授（美国Kansas州立大学）
报告时间 (Time)：2023年6月15日(周四) 10:00
报告地点 (Place)：校本部F309
邀请人(Inviter)：张红莲 教授
主办部门：理学院数学系
报告摘要：In modern mathematics, there are so many sophisticated theories, such as homology/cohomology theory in topology, K-theory, Riemann Zeta functions in number theory, Hall algebras in representation theory, and Gromov-Witten theory in enumerative algebraic geometry. To an undergraduate student, one must be wondering why mathematicians are creating so many abstract and hard to understand theories. This talk is aimed to undergraduate math majors and to give a rough motivation on these types of mathematical theories from the viewpoint of counting. We will start from counting in preschool using fingers (even toes) to college using set theory, integration theory in calculus, and measure theory in analysis, Then we try to count the "number" of all quadratic curves on the plane, which requires new counting tools, and gives the motivation to motivic counting. At the end, we will see that roughly all the theories mentioned above are nothing but counting some interesting geometric objects. If time permits, I will also mention how Weil conjecture links counting the number of rational points over finite fields to the cohomology of the topological space over complex numbers for an algebraic variety which can be defined over integers, such as those defined by Fermat equations.
