报告时间：2025年11月1日，15：30-16：30
报告地点：苏州大学本部精正楼103
报告人：Michael J. Schlosser（University of Vienna)
摘要：
We present a multinomial theorem for elliptic commuting variables in a certain "elliptic" quadratic algebra. This result represents a generalization of the (speaker's) elliptic binomial theorem to higher rank. Two essential ingredients are an elliptic scalar version of the dynamical Yang-Baxter equation (as a consistency relation, ensuring the uniqueness of the normal form coefficients), and, for the recursion of the closed form elliptic multinomial coefficients, the Weierstrass type A elliptic partial fraction decomposition. From our elliptic multinomial theorem we obtain, by convolution, an identity that is equivalent to Rosengren's type A extension of the Frenkel-Turaev $10V9$ summation (which in the trigonometric or basic limiting case reduces to Milne's type A extension of the Jackson 8phi7 summation). Interpreted in terms of a weighted counting of lattice paths in the integer lattice $Z^r$, our derivation of the $A_r$ Frenkel-Turaev-Rosengren summation constitutes the first combinatorial proof of that fundamental identity, and, at the same time, of important special cases including the $A_r$ Jackson-Milne summation.For more details, see //www.emis.de/journals/SIGMA/2025/052/
报告人简介：
Michael J. Schlosser is currently an Associate Professor in Mathematics at the University of Vienna. He did his PhD in Vienna under the supervision of Christian Krattenthaler and has held positions at the Ohio State University, inColumbus, Ohio, USA, and at Northwestern University in Evanston, Illinois, USA, before returning to Vienna. The work of Michael J. Schlosser is centered in combinatorics, special functions and number theory. He is a leading expert in multivariate basic and elliptic hypergeometric series and their connections to combinatorics. He has written almost 100 papers, his publications have appeared in various respected journals among which are Advances in Mathematics, Compositio Mahematica, Transactions of the American Mathematical Socienty, etc. He is also an editor at the Journal of Mathematical Analysis and Applications, The Ramanujan Journal, Journal of Algebraic Combinatorics, and others. He has further served the community by being a member in various review panels and committees, such as twice in the Sastra Ramanujan Prize Committee.
邀请人：马欣荣