报 告 人：Yan Catherine
报告题目： Multivariate Goncarov Polynomials and Integer Sequences
报告时间：2022年12月12日（周一）上午10：00
报告地点： Zoom Meeting Meeting ID: 998 4017 5110 Passcode: 240018
主办单位：数学与统计学院、科学技术研究院
报告人简介：
Catherine Yan is a Professor in the Department of Mathematics at Texas A&M University. Her mathematical interest lies in Algebraic and Enumerative Combinatorics. She received a Bachelor degree at Peking University and a Phd in Mathematics at MIT under the supervision of Gian-Carlo Rota. She was a Sloan Research Fellow and a Fellow of American Mathematics Society, and serves on the editorial boards of several research journals, including being a co-Editor-in-Chief for Advances in Applied Mathematics.
报告摘要：
Univariate delta Gonˇcarov polynomials arise when the classical Gonˇcarov interpolation problem in numerical analysis is modifified by replacing derivatives with delta operators. When the delta operator under consideration is the backward difffference operator, we acquire the univariate difffference Gonˇcarov polynomials, which have a combinatorial relation to lattice paths in the plane with a given right boundary. In this talk, we extend several algebraic and analytic properties of univariate Gonˇcarov polynomials to the multivariate case with both the derivative and backward difffference operators. We then establish a combinatorial interpretation of multivariate Gonˇcarov polynomials in terms of certain constraints on d-tuples of integer sequences. This motivates a connection between multivariate Gonˇcarov polynomials and a higher-dimensional generalized parking function, the U-parking function, from which we derive several enumerative results based on the theory of delta operators. Time allows, we will also discuss the relation between U-parking functions and the (p, q)-parking functions of Cori and Poulalhon.
This talk is based on joint work with Ayo Adeniran and Lauren Snider.
