报告人：陈绍示 副研究员
报告题目：A Gessel way to the diagonal theorem on D-finite power series
报告时间：2022年5月31日（周二）上午9：30
报告地点：腾讯会议 189-759-085
主办单位：数学与统计学院、科学技术研究院
报告人简介：
陈绍示, 中国科学院数学与系统科学研究院副研究员, 博士生导师。主要研究符号计算，计算微分代数与组合数学。中国科学院与法国巴黎综合理工学校联合培养博士毕业，曾先后在奥地利 Linz 大学符号计算研究所、美国北卡罗来纳州立大学、加拿大菲尔兹数学研究所与滑铁卢符号计算研究组从事博士后工作。在符号计算领域旗舰会议 ISSAC 发表论文16篇，以及 Algebra and Number Theory, Journal of Symbolic Computation，和 Journal of Combinatorial theory, Series A 等期刊发表论文 10 余篇。目前担任 Annals of Combinatorics, ACM Communications in Computer Algebra, Maple Transactions, Journal of Systems Science and Complexity, 和《系统科学与数学》等杂志编委。现任国际符号与代数计算年会 ISSAC 指导委员会主席, 2021年开始担任 ACM SIGSAM (ACM 符号与代数计算专业委员会) 秘书长与中国数学会计算机数学专业委员会秘书长.曾获得第二届 “吴文俊计算机数学青年学者奖”与第46届国际符号与代数计算年会ISSAC2021 “杰出论文奖”。入选中国科学院第七届“陈景润未来之星”人才计划和中国科学院2018年度青年创新促进会会员.
报告摘要：
Special functions that satisfy linear differential equations with polynomial coefficients appear ubiquitously in combinatorics and mathematical physics. Such kind of special functions are called D-finite functions by Stanley. In the early 1980's, many combinatorists, such as Gessel, Stanley, Zeilberger etc., conjectured that the diagonal of rational power series in several variables is D-finite. Gessel and Zeilberger proved this conjecture in their papers, respectively. Later, Lipshitz pointed out that their proofs are not complete and he gave a proof by basing on a different idea. Zeilberger completed his proof with the theory of holonomic D-modules. In this talk, we follow the spirit of Gessel's proof strategy and fix the gap in his proof. The key ingredients we used are some basic properties of the diagonal operation. This is a joint work with Pingchuan Ma and Chaochao Zhu.