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Deformation Theory of $\mathbb{E}_n$-Monoidal Categories

组织者

斯拉瓦·皮缅诺夫 , 安吉尔·托莱多

演讲者

Yining Chen

时间

2026年04月20日 16:00 至 17:00

地点

A3-1-301

线上

Zoom 559 700 6085 (BIMSA)

摘要

Fix a field $k$ of characteristic $0$. It is well known that the deformation theory of a (plain) $k$-linear category $\mathcal{C}$ is controlled by its Hochschild cohomology i.e. $\mathrm{End}_{\mathrm{End}(\mathcal{C})}(1)$, which is an $\mathbb{E}_2$-algebra. In this talk, I will describe which (non-unital) $\mathbb{E}_{n+2}$-algebra controls the deformation theory of $\mathbb{E}_n$-monoidal categories and its applications to deformation quantization with respect to shifted Poisson structures. Then I will consider the example of $\mathbf{Rep}(G)$. If time permits, I will also talk about the relation of factorization homology and deformations. An example of it is that as proved by Ben-Zvi-Brochier-Jordan, the factorization homology of $\mathbf{Rep}_{\hbar}(G)$ gives a formal deformation of the category of sheaves on the character variety.