41 citations · 153 across the 15 of their papers we have counts for
4 papers · 1 filter
Stability conditions, cluster varieties, and Riemann-Hilbert problems from surfaces
Dylan G. L. Allegretti
We consider two interesting spaces associated to a quiver with potential: a space of stability conditions and a cluster variety. In the case where the quiver with potential arises…
Stability conditions and cluster varieties from quivers of type
Dylan G. L. Allegretti
We describe the relationship between two spaces associated to a quiver with potential. The first is a complex manifold parametrizing Bridgeland stability conditions on a triangulat…
The geometry of cluster varieties from surfaces
Dylan G. L. Allegretti
Cluster varieties are geometric objects that have recently found applications in several areas of mathematics and mathematical physics. This thesis studies the geometry of a large…
The cluster symplectic double and moduli spaces of local systems
Dylan G. L. Allegretti
We prove a conjecture of Fock and Goncharov which provides a birational equivalence of a cluster variety called the cluster symplectic double and a certain moduli space of local sy…