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BIMSA Lecture
Coproducts on critical cohomological Hall algebras - what structure is there on module categories of affine quantum groups?
Coproducts on critical cohomological Hall algebras - what structure is there on module categories of affine quantum groups?
组织者
演讲者
时间
2025年06月13日 11:00 至 12:00
地点
A3-3-301
线上
Zoom 482 240 1589
(BIMSA)
摘要
Many of the algebraic objects which launched the study of geometric representation theory in the 80s and 90s, like Drinfeld's Yangians and quantum groups, it turns out are the cohomologies of certain 3-Calabi-Yau moduli stacks (cohomological Hall algebras). Physically, categories C of CoHA-modules are line operators for string theory on a 3CY manifold. We will review the (limited) extent to which this has been made rigorous, and what structures on C this predicts.
The bulk of the talk is about constructing the physics-predicted algebraic structures on C, or equivalently on the CoHA. We construct a coproduct on the CoHA locally in the 3CY moduli stack M, and discuss how it patches. This coproduct is coloured by cohomology generators of M, which we show induces a vertex coproduct, which we show recovers Drinfeld's original coproduct. We give a conceptual definition of extending general CoHAs.
(Joint with S. Kaubrys and S. Jindal)
The bulk of the talk is about constructing the physics-predicted algebraic structures on C, or equivalently on the CoHA. We construct a coproduct on the CoHA locally in the 3CY moduli stack M, and discuss how it patches. This coproduct is coloured by cohomology generators of M, which we show induces a vertex coproduct, which we show recovers Drinfeld's original coproduct. We give a conceptual definition of extending general CoHAs.
(Joint with S. Kaubrys and S. Jindal)
演讲者介绍
阿列克谢·拉滕采夫，是一位专注于代数几何、几何表示论和枚举不变量的青年数学家。他于剑桥大学三一学院获得数学学士（一等荣誉）和硕士（优秀）学位，师从伊恩·格罗诺夫斯基。随后在牛津大学基督堂学院获得数学博士学位。他拥有丰富的教学与学术组织经验，曾在牛津大学、南丹麦大学等机构讲授多门课程，并是多个研讨会和阅读小组（如牛津物理与几何研讨会、分解代数在线研讨会等）的创始人或组织者。