报告题目：Orthogonal polynomials and Rogers-Ramanujan type identities

报告人：孙慧教授

报告时间：2022/03/25 15:00-16:30

报告地点：腾讯会议 278-204-267

报告摘要：In Ramanujan's Lost Notebooks and the famous Slater's list, there are numerous identities of Rogers–Ramanujan type. It is known that q-orthogonal polynomials are closely related to these identities via their generating functions, the three-term recurrence relations and other properties. Recently, G.E. Andrews found a surprising phenomenon that the classical orthogonal polynomials also could enter naturally into the world of q. More precisely, by constructing Bailey pairs related to Bailey's Lemma, Andrews applied Chebyshev polynomials of the third and the fourth kinds to study Dyson's “favorite” identity of Rogers–Ramanujan type. In this talk, we will extend Andrews' way to find further applications of Chebyshev polynomials of the third kind in the study of Rogers–Ramanujan type identities. As consequences, we obtain a companion identity to Dyson's favourite identity. We also derive the related identities as Hecke–type double series involving indefinite quadratic forms.

报告人简介：孙慧，2004年毕业于山东大学，2009年毕业于南开大学组合数学中心获得博士学位，现为南开大学组合数学中心教授，博士生导师。主要研究方向为代数组合学，q-级数和特殊函数，在相关领域发表多篇重要成果，论文发表在Adv. Appl. Math., SIAM J. Discrete Math., J. Number Theory等组合数学领域的重要国际期刊上。曾主持国家自然科学基金项目数学天元项目、青年项目各一项，一项天津市青年项目，现主持一项国家自然科学基金面上项目。