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We introduce the notion of analytic stability data on the Lie algebra of vector fields on a torus. We prove that the subspace of analytic stability data is open and closed in the topological space of all stability data. We formulate a general conjecture which explains how analytic stability data give rise to resurgent series. This conjecture is checked in several examples.
We study Quot schemes of 0-dimensional quotients of sheaves on 3-folds $X$. When the sheaf $mathcal{R}$ is rank 2 and reflexive, we prove that the generating function of Euler characteristics of these Quot schemes is a power of the MacMahon function
We introduce moduli spaces of stable perverse coherent systems on small crepant resolutions of Calabi-Yau 3-folds and consider their Donaldson-Thomas type counting invariants. The stability depends on the choice of a component (= a chamber) in the co
In this paper, we explore the wall crossing phenomenon for K-stability, and apply it to explain the wall crossing for K-moduli stacks and K-moduli spaces.
Tropical geometry and the theory of Newton-Okounkov bodies are two methods which produce toric degenerations of an irreducible complex projective variety. Kaveh-Manon showed that the two are related. We give geometric maps between the Newton-Okounkov
We study motivic Donaldson-Thomas invariants in the sense of Behrend-Bryan-Szendroi. A wall-crossing formula under a mutation is proved for a certain class of quivers with potentials.