Jacopo Stoppa

Relative K-stability of extremal metrics

We show that if a polarised manifold admits an extremal metric then it is Kpolystable relative to a maximal torus of automorphisms.

Joyce–Song wall crossing as an asymptotic expansion

We conjecture that the Joyce-Song wall-crossing formula for Donaldson-Thomas invariants arises naturally from an asymptotic expansion in the field theoretic work of Gaiotto, Moore and Neitzke. This would also give a new perspective on how the formulae of Joyce-Song and Kontsevich-Soibelman are related. We check the conjecture in many examples.

TBA type equations and tropical curves

The Joyce integrable system and the corresponding Bridgeland–Toledano-Laredo connections are fundamental objects associated with suitable abelian categories or, more generally, with a class of continuous families of stability data. We offer an overview of some of our work, mostly joint with M. Garcia Fernandez, focusing on equations of TBA type as a useful tool in the analysis of these objects and their deformations, and as a means to establish a connection with tropical geometry.