Time：14:00-15:00, Tuesday, June 2 2026
Venue：E14-301
Speaker：Fei Yu, Zhejiang University
Title：Gorenstein Singularities, Moduli of Differentials, and the K(\pi,1) Conjecture
Abstract：I will discuss joint work with Dawei Chen on a construction that associates to a holomorphic differential a Gorenstein curve singularity with a \mathbb{G}_m-action. This construction identifies strata of differentials with smooth loci in negatively graded deformation spaces of the associated singularities. I will then describe applications to the Hassett–Keel program, to K. Saito's K(\pi,1) conjecture on the smooth deformation space of an isolated complete intersection singularity, and to Kontsevich's \(K(\pi,1)\) conjecture on strata of abelian differentials.
Finally, I will briefly mention ongoing joint work with Dawei Chen, Jingyin Huang, and Yu Qiu, where AI-assisted exploration led us to show that when the number of zeros or poles is at least four, every connected component of the strata of differentials in genus one with prescribed zero and pole orders is not a K(\pi,1). For quadratic differentials, this provides infinitely many counterexamples to a conjecture attributed to Kontsevich and to an expected K(\pi,1) property of stability condition spaces through the work of Bridgeland and Smith.
