报告题目：Presentation of cluster braid groups of marked surfaces with punctures and orbifold points

报 告 人：黄敏 副教授（中山大学（珠海））

报告时间：2026年9月3日（星期四）10:00—11:00

报告地点：数学科学学院111-A

校内联系人：王起 副教授 联系方式：84708351-8501

报告摘要：We study the braid groups arising from marked surfaces with punctures and orbifold points, within the framework of noncommutative cluster algebras. For any triangulation of such a surface, we define the braid group \(Br_\Delta\) as the automorphism group of the triangulation in a suitable groupoid of tagged triangulations. In the unpunctured case, these groups recover the twisted braid groups of decorated surfaces, which were studied by Qiu in the context of proving the simply-connectedness of stability condition spaces in 3-Calabi--Yau categories associated to marked surfaces. We provide a complete finite presentation of \(Br_\Delta\) by nine families of relations determined entirely by the local combinatorial data of the triangulation. This presentation unifies and generalizes all classical Artin braid groups of finite and affine types arising from surfaces, including types \(A\), \(B\), \(C\), \(D\), \(\tilde{A}\), and \(\tilde{D}\). We further introduce triangle groups \(\mathbb{T}_\Delta\) as noncommutative clusters, and show that they admit a faithful action of the braid group in most cases. Based on joint work with Arkady Berenstein and Vladimir Retakh.

报告人简介：黄敏，中山大学数学学院（珠海）副教授。2017年于浙江大学获得博士学位，先后在加拿大谢布克大学、香港大学从事博士后研究。主要从事丛代数及相关领域的研究工作，在《Advances in Mathematics》《Transactions of the American Mathematical Society》《Nagoya Mathematical Journal》《Science China Mathematics》等国际数学期刊发表多篇论文。