In the afternoon of October 25th, Professor Li Liu-Lan of Hengyang Normal University was invited to give an academic report entitled: Coefficient estimates for some classes of functions for the teachers and students of the college. The presentation was hosted by Mr. Fu Xi.

Introduction: Dr. Liu-Lan Li is a professor of Hengyang Normal University, a master's supervisor, and a director of Hunan Provincial Mathematical Society. He is mainly engaged in the research of geometric function theory such as Klein groups and harmonic maps. He has published more than 30 scientific papers in Proc. Amer. Math. Soc., J. Math. Anal. Appl., Nonlinear Anal. and Isr. J. Math. He has presided over and completed the projects of National Natural Science Foundation of China (NSFC), Hunan Outstanding Youth Foundation, Provincial Natural Science Youth Foundation, Provincial Excellent Youth Foundation of Education Department, and Provincial Key Project of Education Department, etc. In 2020, his scientific research achievement Research on Some Problems Associated with the Theory of Tone and Mapping won the third prize of the Provincial Natural Science Prize (ranked the second).

In this presentation, Prof. Li firstly introduced two famous coefficient conjectures in classical single-leaf analytic functions: Bieberbach's conjecture and Zalcman's conjecture. Based on these two conjectures, there have been a series of research results about the coefficients of single-leaf analytic functions. Then, Ms. Li reported the coefficient estimation results of a special class of single-leaf functions on the unit disk. Different from the traditional research methods, they skillfully obtain the exact coefficient estimation with the help of the properties of a class of continuous convex generalized functions to obtain the specific expression form of the function. Finally, Ms. Li also introduced some unsolved problems in the study of coefficient estimation.

Through Prof. Li's report, we deeply understood the importance of coefficient estimation in single-lobe analytic functions. Some teachers and students also had in-depth exchanges and discussions with Prof. Li after the presentation.