杭州师范大学 郭军伟教授、杭州师范大学 曹健教授、温州大学 刘纪彩教授 学术报告

报告题目1：A new family of $q$-hypergeometric congruences from Andrews' multi-series transformation

报告人：郭军伟教授，杭州师范大学

报告时间：2024年9月13日（周五）9:00-12:00

报告地点：20-306

报告摘要：We deduce a new family of $q$-hypergeometric congruences modulo the fourth power of a cyclotomic polynomial from George Andrews' multi-series extension of the Watson transformation. A Karlsson--Minton type summation for very-well-poised basic hypergeometric series due to George Gasper also plays an important role in our proof. We put forward two relevant conjectures on supercongruences and $q$-supercongruences for further study.

报告人简介：郭军伟，1977年出生于浙江东阳，南开大学博士，法国里昂第一大学博士后。杭州师范大学教授、薛定谔国际数学物理研究所访问学者，曾任华东师范大学数学系教授，博士生导师。主要从事组合数学、q-级数和数论的研究，共发表SCI论文150余篇。他利用单位根来证明q-同余式的创新方法，在国际权威期刊《Advances in Mathematics》上发表。先后主持三项国家自然科学基金，以及上海市教育发展基金会晨光计划、上海市科委青年科技启明星计划、江苏省自然科学基金等项目，并入选江苏省教育厅“青蓝工程”中青年学术带头人等。

报告题目2：Expansions of q-operational equations and applications to the q-Hardy-Hille type formulas and the generalized Askey--Wilson polynomials

报告人：曹健教授，杭州师范大学

报告时间：2024年9月13日（周五）9:00-12:00

报告地点：20-306

报告摘要：The mission of this talk is to find two general q-operational equations together with the expansion issue of the bivariate q-Laguerre polynomials from the perspective of q-partial differential equations. We also give some applications including some q-Hardy--Hille type formulas and the generalized Askey--Wilson polynomials. In addition, we present the Rogers-type formulas and the U(n+1)-type generating functions for the bivariate q-Laguerre polynomials by the technique based upon q-operational equations. Moreover, we derive a new generalized Andrews--Askey integral and a new transformation identity involving the bivariate q-Laguerre polynomials by applying q-operational equations. Finally, we find q-operational equations and q-partial differential equations for the generalized Askey--Wilson polynomials and give some applications.

报告人简介：曹健，杭州师范大学教授，硕士生导师，从事组合数学与特殊函数领域的研究，主持国家及浙江省基金等多项，已在《Fractional Calculus and Applied Analysis》、《Studies in Applied Mathematics》、《Advances in Applied Mathematics》等国际重要期刊发表论文40余篇，入选杭州市属高校中青年学术带头人、杭州市“131”人才等，多次在全国组合数学与图论、海峡两岸图论与组合数学、英国肯特大学及伦敦大学学院等国内外学术会议上作报告。

报告题目3：A combinatorial approach to Berkovich type identities

报告人：刘纪彩教授，温州大学

报告时间：2024年9月13日（周五）9:00-12:00

报告地点：20-306

报告摘要：Recently, Berkovich established nine $q$-binomial identities involving the Legendre symbol $(\frac{d}{3})$. In this talk, we investigate Berkovich type identities and establish a unified form of $q$-binomial identities of this type through a combinatorial approach. This unified form includes Berkovich's nine identities as special cases. Many new such identities can be also deduced from this unified form.

报告人简介：刘纪彩，温州大学瓯江特聘教授，硕士生导师。主要从事组合数学与数论研究，迄今在《Proc. Amer. Math. Soc.》、《Advances in Applied Mathematics》、《Journal of Number Theory》等期刊上发表学术论文50余篇，主持国家自然科学基金青年项目与面上项目各一项。