13:00
Protected sectors of four-dimensional N=2 superconformal field theories connect their operator spectra to algebraic geometry and vertex operator algebras. I will introduce a proposal to encode the Higgs branch and the Schur and Macdonald indices in a single (filtered graded) affine scheme. Its reduced structure recovers the Higgs branch, while its nonreduced structure and filtration captures additional protected information through its arc space. I will explain how these schemes can be constructed from OPE decoupling relations, with their defining relations constrained by "syzygy maximization", and discuss the proposed relation of their coordinate rings to Zhu’s C2-algebras. Argyres–Douglas theories provide concrete examples. Furthermore, Higgs branch RG flows admit an algebraic description through restriction of a defining potential to Slodowy slices. I will conclude with recent progress towards a uniform construction for broad families of Argyres--Douglas theories, Dp(G, O), via Jacobian ideals related to so-called polynomial twisted periods.