D-finite power series are solutions of homogeneous linear differential equations with rational function coefficients. This is an important class of special functions since it appears ubiquitously in algebra, combinatorics, and number theory. In this talk, we will focus on the arithmetic aspect of D-finite power series and present many rationality theorems on these series.

Brief Introduction:

Shaoshi Chen is an associate professor of Academy of Mathematics and Systems Science, Chinese Academy of Sciences, whose research interests include Symbolic Computation, Algorithmic Combinatorics and Arithmetic Theory of Power Series. Together with his collaborators, he developed the fourth generation of creative telescoping algorithms for automatic proofs of combinatorial identities and proved the Wilf-Zeilberger conjecture on mixed hypergeometric functions. Currently, he is focusing on developing the arithmetic theory of power series in several variables. He is now the secretary of ACM SIGSAM and serving in the editorial boards of Annals of Combinatorics, Journal of Difference Equations and Applications, Journal of Systems Science and Complexity. He was awarded the second Wen-Tsun Wu Youth Research Award for Computer Mathematics in 2019 and the Distinguished Paper Award of the 46th International Symposium on Symbolic and Algebraic Computation in 2021.