学术报告1
时间：2021.1.17（周日），16:00-17:00
腾讯会议：404959984
https://meeting.tencent.com/s/s45hI3bme8D0
报告题目：Some algebraic structures on rooted trees
摘要：In this talk, we first recall some classical Hopf algebras on rooted trees, including Connes-Kreimer Hopf algebra and Loday-Ronco Hopf algebra. Then we give a combinatorial description of the coproduct of the Loday-Ronco Hopf algebra, and construct an infinitesimal version of the Connes-Kreimer Hopf algebra. Finally, a dendriform-Nijenhuis bialgebra is built on top of decorated planar rooted trees.
报告人：高兴教授 兰州大学
报告人简介：高兴，兰州大学教授、博士生导师。于2010年7月在兰州大学数学与统计学院获得博士学位，留校工作至今。在2015年8月至2016年8月间，在美国Rutgers大学交流访问，师从Rota-Baxter代数的国际领军人物郭锂教授。主要从事Rota-Baxter代数和代数组合等领域的研究，在Journal of Algebra、Journal of Pure and Applied Algebra、J. Algebraic Combin.等国际期刊上发表SCI学术论文四十余篇。主持数学天元基金、青年科学基金、国家自然科学基金面上项目和甘肃省自然科学基金项目,获甘肃省自然科学奖二等奖，出版专著一本。
学术报告2
时间：2021.1.17（周日），17:00-18:00
腾讯会议：404959984
https://meeting.tencent.com/s/s45hI3bme8D0
报告题目：Grassmannian cluster categories
摘要：Jensen, King, and Su in 2013 associated a Kac-Moody root systemJk,nto a Grassmannian cluster categoryCM(Bk,n)and showed that in the finite types, rigid indecomposable modules correspond to roots. In general, the link between the categoryCM(Bk,n)and the root systemJk,nremains mysterious and it is an open question whether indecomposable modules always give roots. In this talk, I will talk about recent work with Karin Baur, Dusko Bogdanic, and Ana Garcia Elsener, on Grassmannian cluster categories. We show that every indecomposable rank 2 module corresponds to a root of the associated root system. We also show that indecomposable rank 3 modules inCM(Bk,n)all give rise to roots ofJk,n. For the rank 3 modules inCM(Bk,n)corresponding to real roots, we show that their underlying profiles are cyclic permutations of a certain canonical one. We also characterize the rank 3 modules inCM(B3,n)corresponding to imaginary roots. By proving that there are exactly 225 profiles of rigid indecomposable rank 3 modules inCM(B3,9)we confirm the link between the Grassmannian cluster category and the associated root system in this case. We conjecture that the profile of any rigid indecomposable module inCM(Bk,n)corresponding to a real root is a cyclic permutation of a canonical profile.
报告人：李建荣博士 兰州大学/奥地利格拉茨大学
报告人简介：李建荣，2012年博士毕业于兰州大学数学与统计学院并留校工作，现为奥地利格拉茨大学博士后研究员，主要从事量子群，表示论，丛代数等的研究。完成国家自然科学基金青年基金项目一项，并与合作者在Mathematische Zeitschrift, Int. Math. Res. Notices, J. Algebra, Algeb. Rep. Theory, J. Algebraic Comb., J. Lie theory等国际SCI期刊上发表学术论文20余篇。
