Explore the intricate world of arithmetic automorphic periods on unitary groups in this advanced mathematics lecture. Delve into the definition of arithmetic automorphic periods as Petersson inner products of deRham rational forms, derived from the cohomology of Shimura varieties. Examine the relationship between these periods and special values of L-functions, particularly for holomorphic forms. Investigate a proposed conjecture concerning relations among general arithmetic periods of representations within the same L-packet. Follow along as the speaker, Jie Lin from Universität Duisburg-Essen, presents a conditional proof for this conjecture, offering insights into this complex area of mathematical research.