Speaker: Harshit Yadav
Date: January 19, 2026
Affiliation: University of Alberta, Canada

Abstract: Modular tensor categories (MTCs) that are finite and semisimple sit at a crossroads of several areas: they produce $3$-manifold invariants via $3$d topological field theory, they give representations of $\mathrm{SL}_2(\mathbb{Z})$, and they arise from sources such as quantum groups and rational vertex operator algebras (VOAs). A broader goal, motivated for instance by non-rational (or logarithmic) conformal field theory, is to understand and construct MTCs without finiteness and semisimplicity assumptions, where questions like the existence of dual objects (rigidity), needed to construct manifold invariants, become more subtle. This talk describes a strategy to construct such non-semisimple and non-finite MTCs. Inspired by VOA extensions, it uses the category of local modules over a commutative algebra object in a braided tensor category. Time permitting, applications to module categories of non-rational VOAs will also be discussed.