Stability conditions and cluster varieties from surfaces
Student No.:40
Time:Tue & Thu, 13:30-15:05
Instructor:Dylan Allegretti  
Place:Tue, Conference Room 3/ Thu, Conference Room 2, Jin Chun Yuan West Bldg.
Starting Date:2018-4-3
Ending Date:2018-4-26

Description:This lecture series will focus on the relationship between two spaces associated to a quiver with potential. The first is a complex manifold parametrizing Bridgeland stability conditions on a triangulated category, and the second is a cluster variety with a natural Poisson structure. Work by the physicists Gaiotto, Moore, and Neitzke suggests that these spaces are related in a highly nontrivial way involving Donaldson-Thomas invariants and the Kontsevich-Soibelman wall-crossing formula. I will report on ongoing joint work with Tom Bridgeland, which aims to develop a rigorous mathematical understanding of this relationship in the case where the quiver with potential arises from a triangulation of a marked bordered surface.


Prerequisite:Some familiarity with derived and triangulated categories is helpful but not necessary.


[1] Bridgeland, T. and Smith, I. Quadratic differentials as stability conditions. arXiv:1302.7030 [math.AG].

[2] Bridgeland, T. Riemann-Hilbert problems from Donaldson-Thomas theory. arXiv:1611.03697 [math.AG].

[3] Allegretti, D.G.L. Stability conditions and cluster varieties from quivers of type A. arXiv:1710.06505 [math.AG].


[4] Allegretti, D.G.L. and Bridgeland, T. The monodromy of meromorphic projective structures. arXiv:1802.02505 [math.GT].

[5] Allegretti, D.G.L. Voros symbols as cluster coordinates. arXiv:1802.05479 [math.CA].