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学术报告:Polynomials and polytopes

发布日期:2020年07月16日 09:53 作者: 访问量:


报告题目:Polynomials and polytopes

报告人:郭龙 (南开大学副教授)

报告时间:2020728(周二)上午9:00

报告地点:腾讯会议ID157 635 296

联系人:林丽双 副教授

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报告摘要: Polynomials and polytopes are central objects in algebraic combinatorics. In this talk, we shall discuss the Newton polytopes of several important families of polynomials in algebraic combinatorics, including for example Schubert polynomials, Grothendieck polynomials, key polynomials. We develop a combinatorial algorithm to determine the vertices of the Newton polytopes of Schubert and key polynomials. As an application, we prove that the vertices of the Newton polytope of a key polynomial can be generated by permutations in a Bruhat order interval,settling a conjecture proposed by Cara Monical, Neriman Tokcan and Alex Yong. This is joint work with Neil J.Y. Fan.

 

报告人简介:郭龙,南开大学组合数学中心副教授。研究方向是代数组合学,在Schubert计数演算、对称函数、多面体、Kazhdan-Lusztig理论等课题取得研究成果。例如,与合作者解决了国际数学家大会邀请报告人Igor PakGunter Ziegler等人提出的猜想和公开问题;得到了邵逸夫数学奖获得者David KazhdanGeorge Lusztig建立的著名的R-多项式反演公式的组合证明。部分工作被Igor Pak在其个人主页介绍,并被国际数学家大会邀请报告人、传奇青年数学家June Huh引用。

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