报告地点：腾讯会议 837-529-571 (密码：221117)
报告时间：2022年11月17日9:00-12:00
主持人：陈智奇
1、报告题目： Applications of spherical twist functors to Lie algebras associated to root categories of preprojective algebras
报告人：徐帆副教授（清华大学）
报告时间：2022年11月17日9:00-10:00
报告摘要：Let Λ_{Q} be the preprojective algebra of a finite acyclic quiver Q of non-Dynkin type and D^{b}(rep^{n}Λ_{Q}) be the bounded derived category of finite dimensional nilpotent Λ_{Q}-modules. We define spherical twist functors over the root category R_{Λ_{Q}} of D^{b}(rep^{n}Λ_{Q}) and then realize the Weyl group associated to Q as certain subquotient of the automorphism group of the Ringel-Hall Lie algebra g(R_{Λ_{Q}}) of R_{Λ_{Q}} induced by spherical twist functors. We also present a conjectural relation between certain Lie subalgebras of g(R_{Λ_{Q}}) and g(R_{Q}), where g(R_{Q}) is the Ringe-Hall Lie algebra associated to the root category R_{Q} of Q. This talk is based on joint work with Fang Yang.
专家简介：徐帆，清华大学数学科学系副教授、博士生导师，研究领域为代数表示论。与合作者在三角范畴上Hall代数与（量子）丛理论等领域取得一系列结果，在Duke Math. J.、Trans. Amer. Math. Soc.、Math. Z.等国际学术期刊发表高水平论文二十余篇。
2、报告题目： From (derived) Hall algebras to acyclic quantum cluster algebras
报告人：Xueqing Chen教授（美国威斯康星大学白水分校）
报告时间：2022年11月17日10:00-11:00
报告摘要：Inspired by Caldero-Keller’s discovery of the similarity between the multiplication formulas in a cluster algebra and that in a (dual) Hall algebra, we firstly discuss an algebra homomorphism from the dual Hall algebra associated to Rep(Q) (category of representations of an acyclic quiver Q) to the corresponding quantum cluster algebra. Then we address the connection from two certain quotients of subalgebras of the derived Hall algebras of Rep(Q) to acyclic quantum cluster algebra. Finally, we give cluster multiplication formulas via the above derived Hall algebras. This talk is based on the joint works with Ming Ding and Fan Xu, and with Ming Ding and Haicheng Zhang respectively.
专家简介：陈学庆，美国威斯康星大学白水分校教授。研究领域为有限维代数（箭图）的表示、Hall代数与量子群、Cluster代数与量子Cluster代数。2002年博士毕业于加拿大卡尔顿大学，先后在加拿大渥太华大学及加拿大温莎大学从事科研工作。在Compositio Math., Contem. Math., J. Algebra等国际学术期刊上发表高水平论文30余篇。
3、报告题目：Atomic bases of quantum cluster algebras of type A_{2n−1,1}
报告人：丁明教授（广州大学）
报告时间：2022年11月17日11:00-12:00
报告摘要：Let Q be the affine quiver of type A_{2n−1,1} and A_{q}(Q) be the quantum cluster algebra associated to the valued quiver (Q, (2, 2, . . . , 2)). We prove some cluster multiplication formulas and deduce that the cluster variables associated with vertices of Q satisfy a quantum analogue of the constant coefficient linear relations. We then construct two bar-invariant integral bases B and S of A_{q}(Q) consisting of positive elements, and prove that B is an atomic basis.
This talk is based on the joint works with Xueqing Chen and Fan Xu.
专家简介：丁明，广州大学数学与信息科学学院教授，研究领域为代数表示论，2009年博士毕业于清华大学。在Math. Z.、J. Algebra、Algebr. Represent. Theory等国际学术期刊发表论文十几篇，主持完成国家自然科学基金面上项目、青年项目和教育部博士点基金项目各一项。
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