In this talk, we introduce the Deferred Cyclotomic Representation (DCR) of the q-hypergeometric series, an algebraic framework that resolves these computational bottlenecks. By mapping the multiplicative structure of q-factorials onto a free abelian group generated by irreducible cyclotomic polynomials, the DCR framework translates algebraic multiplication and division into exact sparse integer vector additions. This isolates the combinatorial skeleton of the series from the target evaluation field. We shall demonstrate how DCR enables the extraction of common polynomial divisors, intrinsically resolves root-of-unity poles, and allows the evaluation of generic tensor category identities in exact cyclotomic fields. QRecoupling.jl open-source package is developed for further research and applications.

This talk presents a stratified quantization recipe for the half density, or half-form bundle, over the moduli space which incorporates these singular strata independently into the defining integral. By isolating the treatment of the singularities we more closely harmonize the geometrically derived invariants with the expected WRT invariants from QFT.

In this work, we derive B-model String Theory dual data for a wide family of matrix-valued chiral algebras. Amongst the dual String Theory backgrounds, one finds novel non-commutative geometries. Using techniques from Homological Algebra, we extract universal properties of the conjectural worldsheet theories dual to these chiral algebras, in the form of $A_\infty$ categories and modules. We believe some of the techniques developed in this work may find use in broader examples of Holography.