Diagonals and Hadamard Products of D-finite Power Series

D-finite power series appear ubiquitously in combinatorics, number theory, and mathematical physics. They satisfy systems of linear partial differential equations whose solution spaces are finite-dimensional, which makes them enjoy a lot of nice closure properties. In particular, the diagonals and Hadamard products of D-finite power series are still D-finite. The first part of this talk will present a proof of the diagonal theorem following an idea of Gessel and also provide a single exponential bound on the degree and order of the defining differential equation satisfied by the diagonal (based on a joint work with Frederic Chyzak, Pingchuan Ma and Chaochao Zhu). The second part of this talk is about the arithmetic properties of Hadamard products of D-finite power series (based on a joint work with Ruyong Feng, Manuel Kauers, Michael Singer and Umberto Zannier).

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。在符号计算旗舰会议 ISSAC 与数学期刊 Foundations of Computational Mathematics、Algebra and Number Theory、Selecta Mathematica 等发表论文40余篇。目前担任 Journal of Symbolic Computation、Annals of Combinatorics、Journal of Difference Equations and Applications、Journal of Systems Science and Complexity 等杂志编委，还担任中国数学会计算机数学专业委员会主任。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（ISSAC 2021）“杰出论文奖”，与国际计算机代数应用大会（ACA 2022）“青年学者奖”。