Derived traces of Soergel categories

The Soergel category and the redotted Webster algebra

We describe a collection of graded rings which surject onto Webster rings for sl(2) and which should be related to certain categories of singular Soergel bimodules. In the first non-trivial case, we construct a categorical braid group action which categorifies the Burau representation.

Serre对偶与Whitehead链环

Serre Duality and the Whitehead Link

本文证明了二面体Soergel双模同伦范畴中全扭转作为Serre函子，并利用部分迹函子的可表示性计算了Whitehead链环的三重分次链环同调。

Traces on ideals in pivotal categories

We extend the notion of an ambidextrous trace on an ideal (developed by the first two authors) to the setting of a pivotal category. We show that under some conditions, these traces lead to invariants of colored spherical graphs (and so to modified 6j-symbols).

Relative (pre)-modular categories from special linear Lie superalgebras

We examine two different m-traces in the category of representations over the quantum Lie superalgebra associated to $\mathfrak{sl}(m|n)$ at root of unity. The first m-trace is on the ideal of projective modules and leads to new Extended Topological Quantum Field Theories. The second m-trace is on the ideal of perturbative typical modules. We consider the quotient with respect to negligible morphisms coming from this m-trace and show that in the case of $\mathfrak{sl}(2|1)$ this quotient leads to 3-manifolds invariants. We conjecture that the quotient category of perturbatives over quantum $\m…

Hecke范畴、幂等元与交换栈

Hecke categories, idempotents, and commuting stacks

本研究建立了仿射Hecke范畴水平迹的幂等完备化这一拓扑范畴，与半幂零交换栈的等变导出范畴这一几何范畴间的联系，完善了此前的相关研究提案。

基于球面融合范畴的带缺陷态和模型

State sum models with defects based on spherical fusion categories

该研究定义了带三类缺陷的三角化3-流形的Turaev-Viro-Barrett-Westbury态和模型，证明其三角剖分独立性，验证缺陷曲面态和的亏格检测与嵌入敏感性，并得到球面融合范畴中心的带状不变量。