报告题目 (Title)：Frobenius algebra structure of statistical manifold
报告人 (Speaker)：刘克峰 教授（University of California, Los Angeles）
报告时间 (Time)：2022年10月13日(周四) 10:00-11:00
报告地点 (Place)：腾讯会议（716-8675-1741）
邀请人(Inviter)：席东盟、李晋、张德凯
主办部门：理学院数学系
报告摘要：In information geometry, a statistical manifold is a Riemannian manifold (M,g) equipped with a totally symmetric (0,3)-tensor. We show that the tangent bundle of a statistical manifold has a Frobenius algebra structure if and only if the sectional K-curvature vanishes. This gives a statistical-geometric curvature interpretation for WDVV equation. We study natural statistical structures on the tangent bundle of a statistical manifold and gave a new proof of Alekseevsky-Cortes’ geometric construction of r-maps that associates a special real manifold to a special Kahler manifold. The application of information geometry in data science will be briefly indicated. This is joint work with Hao Xu and Yanhui Zhi.
