学术报告会：Basic hypergeometric series associated to the root systems and Mock Theta Functions

报告题目：Basic hypergeometric series associated to the root systems and Mock Theta Functions

报告人：张之正（洛阳师范学院 教授/博导）

报告时间：2021年4月29日下午15：00—16：30

报告地点：S3-409

个人简介：

张之正，博士，二级教授，南开大学与南京大学双站博士后，现任洛阳师范学院数学科学学院院长。河南省优秀专家，河南省学术技术带头人，河南省高校创新人才，河南省五一劳动奖章获得者，河南省教师教育专家，先后主持国家自然科学基金项目6项，在国内外发表论文100余篇，SCI收录论文70余篇，主要研究组合数学、特殊函数论； 中国工业与应用数学学会全国竞赛工作委员会委员与图论组合及应用专业委员会副主任，中国运筹学会理事兼图论组合分会常务理事，中国数学会组合数学与图论专业委员会委员，河南省数学会常务理事，河南省高校数学教学指导委员会委员。

Abstract

The theory of basic hypergeometric series consists of many known summation and transformation formulas. These basic hypergeometric series identities frequently appear in combinatorics and in related area such as number theory, physics, and representation theory of Lie algebras. Multiple basic hypergeometric series associated to the unitary group An (or U(n + 1)), Cn and Dn have been investigated by various authors. Many different types of such series exist in the literature. In this talk, we give

lU(n + 1) analogue of AAB Bailey lattice (Agarwal, Andrews and Bressoud) and its applications;

lU(n + 1), Cn and elliptic generalizations of WP-Bailey pairs and their applications,

lA WP-Bailey lattices and its U(n + 1) analogue.

lSeveral Mock theta functions