【学术报告】Λ-invariant and tropical invariant in cluster theory

报告人：曹培根（中国科学技术大学）

时 间：2025年11月29日16:00

地 点：海韵园实验楼S106

内容摘要:

The Λ-invariant and d-invariant are introduced by Kang-Kashiwara-Kim-Oh and by Kashiwara-Kim-Oh-Park in the study of monoidal cluster categorification using finite-dimensional modules over quiver Hecke algebras and quantum affine algebras. It is known that many interesting cluster algebras carry a natural compatible Poisson structure. Such cluster algebras are called Λ-cluster algebras. The Λ-invariant can be viewed as the monoidal categorification of the compatible Poisson structure but it contains much more information.

The tropical invariant and F-invariant for a pair of good elements (e.g., cluster monomials) in a Λ-cluster algebra are introduced in my paper. It is proved that the Λ-invariant coincides with the tropical invariant on cluster monomials and hence the twice d-invariant coincides with the F-invariant.

个人简介：

曹培根，中国科学技术大学特任教授，主要从事代数表示论，丛理论以及两者的交叉研究。学术成果发表在Adv. Math., Compos. Math., Math. Ann., IMRN 等学术期刊。

联系人：阮诗佺