报告题目：The modified Macdonald polynomials and Mahonian statistics

报告人：靳宇教授

报告地点：数理楼235教室

报告时间：2025年2月20日（周四） 上午10:00-11:30

报告摘要：The modified Macdonald polynomials indexed by partitions are the basis of the symmetric functions in infinitely many variables with coefficients in the field of rational functions of two variables. The combinatorial investigation of modified Macdonald polynomials has been greatly promoted by the celebrated breakthrough on the connections between them and Mahonian statistics on fillings of Young diagrams due to Haglund, Haiman and Loehr (2005).

Recently, Corteel, Haglund, Mandelshtam, Mason and Williams (2019, 2021) discovered a compact formula for the modified Macdonald polynomials and made a conjecture on an equivalent form of them. This was subsequently affirmed by Ayyer, Mandelshtam and Martin (2022) and they proposed a stronger conjecture on a refined equivalence. Our main result confirms their conjecture. That is, we establish the equidistribution between the pairs (inv, maj) and (quinv, maj) on any row-equivalency class of a given filling of a Young diagram. In particular if the Young diagram is rectangular, the triples (inv, quinv, maj) and (quinv, inv, maj) have the same distribution over the row-equivalence class. This talk is based on joint work with Xiaowei Lin.

报告人简介：靳宇，厦门大学数学科学学院教授，博士生导师。主要研究方向是组合数学。2005年西南大学本科毕业，2010年南开大学组合数学中心博士毕业，之后在德国Kaiserslautern大学，奥地利维也纳科技大学和维也纳大学做博士后研究。2021年回国入职厦门大学。已经在J. Combin. Theory Ser. A和Random Struct. Algor.等重要学术期刊发表多篇文章。先后获得过美国生物数学协会的Lee Segel奖学金，德国洪堡博士后奖学金，主持过德国国家基金委DFG的个人项目，奥地利国家基金委Elise-Richter项目。