A sequence P_n(x) of polynomials in x is holonomic (or P-recursive) if it satisfies a linear recurrence with polynomial coefficients in both x and n. Many polynomial sequences from combinatorics, representation theory and number theory  are shown to be holonomic. In this talk, we will first initiate some natural and fundamental problems on holonomic polynomial sequences. After this, we will answer the first problem which is about the classification of the degree growth of such sequences and show two applications related to combinatorial identities  and exponential sums over finite fields respectively. This is a joint work with Jason P. Bell, Daqing Wan and Hang Yin.

陈绍示, 现为中国科学院数学与系统科学研究院研究员。主要研究符号计算、机器证明与组合理论。在数学期刊 Foundations of Computational Mathematics, Algebra and Number Theory, Selecta Mathematica等发表论文40余篇。目前担任中国数学会计算机数学专业委员会主任与国际符号与代数计算年会（ISSAC）指导委员会委员. 曾获得第二届 “吴文俊计算机数学青年学者奖”(2019)，第46届国际符号与代数计算年会(ISSAC2021)“杰出论文奖”，与国际计算机代数应用大会(ACA2022)“青年学者奖”。