学术报告（于飞 2026.9.18）

摘要：Strata of differentials exhibit rich interactions between algebraic geometry, topology, and dynamics. In this talk, I will discuss several recent developments from these different perspectives.

I will first describe how degenerations of differentials naturally give rise to Gorenstein singularities, and how the geometry of the differential controls the resulting singularities and their deformation theory. I will also discuss applications of this correspondence to the Hassett--Keel program for the moduli space of curves.

I will then turn to the global topology of strata. We prove that many strata are not orbifold \(K(\pi,1)\)'s, and, beyond non-asphericity, detect explicit nontrivial higher homotopy groups. This gives infinitely many counterexamples to a conjecture of Kontsevich, as well as to a folklore conjecture concerning the contractibility of spaces of Bridgeland stability conditions.

Finally, I will discuss a Hodge-theoretic approach relating Lyapunov exponents, Harder--Narasimhan filtrations, and monodromy, and explain how these structures can be used to distinguish arithmetic and thin monodromy groups.

The first part is joint work with Dawei Chen; the second is joint work with Dawei Chen, Jingyin Huang, and Yu Qiu; and the last is joint work with Dawei Chen and Junming Zhang. The latter two projects were developed with AI assistance.