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Graded cluster algebras arising from marked surfaces with puncture
时间:2021年07月13日 14:25 点击数:

报告人:唐孝敏

报告地点:腾讯会议ID:316 765 972

报告时间:2021年7月15日星期四9:00-10:00

邀请人:陈良云

报告摘要:

Cluster algebras were conceived by Fomin and Zelevinsky in 2000 as a tool for studying dual canonical bases and total positivity in semisimple Lie groups and their quantum analogs. However, the theory of cluster algebras has since taken on a life of its own, as connections and applications have been discovered in diverse areas of mathematics, including representation theory of quivers and finite dimensional algebras, Poisson geometry, string theory, discrete dynamical systems and integrability, and combinatorics. Gradings for cluster algebras have been introduced in various ways by a number of authors and for a number of purposes. Recently, Booker-Price T in [J. Algebra, 2020, 560: 89-113] study the gradings arising from triangulations of marked bordered 2-dimensional surfaces without puncture. In this paper, we mainly study the degree of triangulation of marked bordered 2-dimensional surfaces with puncture. We give a valuation functions on such a surface by using the methods of [Acta Math., 2008, 21:83-146] and [J. Algebr. Comb., 2015, 42: 1111-1134]. We give two examples to illustrate the theory and show that each homogeneous space has finitely many variables. This work is jont with Dr. Yongyue Zhong.

会议ID:0715

主讲人简介:

唐孝敏, 黑龙江大学数学科学学院院长,教授、博士生导师,黑龙江省数学会副理事长。主要研究李理论及相关方向,主持及参加国家自然科学基金、黑龙江省自然科学基金、黑龙江省教育厅项目等各类科研项目10余项, 在《Math. Nachr.》、《Taiwanese J. Math》、《Linear Algebra Appl.》、《Linear Multilinear Algebra》等SCI收录期刊发表学术论文30多篇,并出版专著、教材2部。

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