Abstract: I will discuss joint work with Dawei Chen on a construction which associates to a holomorphic differential a Gorenstein curve singularity with Gm-action. It identifies strata of differentials with smooth loci in negatively graded deformation spaces of the associated singularities, and gives a framework for studying their boundary, birational geometry, topology, and categorical invariants.

I will then describe applications to the Hassett--Keel program, K(\pi,1)-questions, and graded Cohen--Macaulay categories. Finally, I will briefly mention ongoing joint work with Dawei Chen, Jingyin Huang, and Yu Qiu, where AI-assisted exploration led to new counterexamples to the expected K(\pi,1)-property for strata of differentials.