报 告 人： 杨立波教授
报告题目：Brenti's conjecture on q-Eulerian polynomials
报告时间：2014年9月15日（周一）下午4:00
报告地点：静远楼1506学术报告厅
主办单位：数学与统计学院、科技处
报告摘要：We use the method of mutual interlacing to prove Brenti's conjecture on $q$-Eulerian polynomials for Weyl groups of type $D$. Explicitly, we obtain a refinement of Brenti's $q$-Eulerian polynomials of type $D$, and then show that these refined Eulerian polynomials satisfy certain recurrence relation. By using the Routh--Hurwitz theory and the recurrence relation, we prove that these polynomials form a mutually interlacing sequence for any positive $q$, and hence prove Brenti's conjecture. For $q=1$, our result reduces to the real-rootedness of the Eulerian polynomials of type $D$, which were originally conjectured by Brenti and recently proved by Savage and Visontai.
杨立波教授简介：
博士，南开大学教授，博士生导师，教育部新世纪优秀人才。现任南开大学组合数学中心副主任，天津市工业与应用数学学会副秘书长。主要从事代数组合学方面的研究，在对称函数理论和单峰型理论方面做出多项重要成果，现已在《Transactions of the AMS》、《Journal of Combinatorial Theory, Series A》、《Advances in Applied Mathematics》、《Journal of Algebraic Combinatorics》等权威数学期刊发表论文20篇。主持完成了国家自然科学基金青年基金项目1项，面上项目1项，参与完成了973项目子课题1项，现参与国家自然科学基金重点项目1项。