报告题目：An elliptic extension of the multinomial theorem

报告人：Michael Schlosser教授  奥地利维也纳大学

报告时间：2023年9月27日下午3：00—4：00

报告地点：雁山校区理四501报告厅

报告摘要：We present a multinomial theorem for elliptic commuting variables. This result extends the speaker's previously obtained elliptic binomial theorem to higher rank. Two essential ingredients are a simple elliptic star-triangle relation, ensuring the uniqueness of the normal form coefficients, and, for the recursion of the closed form elliptic multinomial coefficients, the Weierstra{\ss} type $\mathsf A$ elliptic partial fraction decomposition. From our elliptic multinomial theorem we obtain, by convolution, an identity that is equivalent to Rosengren's type $\mathsf A$ extension of the Frenkel--Turaev ${}_{10}V_9$ summation, which in the trigonometric or basic limiting case reduces to Milne's type $\mathsf A$ extension of the Jackson ${}_8\phi_7$ summation. Interpreted in terms of a weighted counting of lattice paths in the integer lattice $\mathbb Z^r$, our derivation of the $\mathsf A_r$ Frenkel--Turaev summation constitutes the first combinatorial proof of that fundamental identity, and, at the same time, of important special cases including the $\mathsf A_r$ Jackson summation.

For full details, see the preprint \texttt{https://arxiv.org/abs/ 2307.12921}.

报告人简介：Michael Schlosser教授师从维也纳大学的Christian Krattenthaler院士，研究领域主要涵盖组合数学和q-级数。目前，他担任JMAA、Ramanujan J、J Algebraic Combin和Contrib. Discrete Math等多个SCI杂志的编辑委员，曾担任2016年和2017年SASTRA Ramanujan奖评委。Michael Schlosser教授是国际上研究多变量q-超几何级数的顶级专家之一，他在Adv. Math.、Compos. Math.、Trans. Amer. Math. Soc.、Selecta Math. (N.S.)等著名数学期刊上发表了80多篇学术论文，他的研究工作极大地推动了多变量q-超几何级数的发展。