Donaldson-Thomas invariants for 3d CY categories assigned to the moduli spaces of local systems on surfaces
Posted in
Speaker:
A. Goncharov
Affiliation:
Yale/MPIM
Date:
Tue, 21/06/2016 - 15:00 - 16:00
Location:
MPIM Lecture Hall
Parent event:
Seminar on Algebra, Geometry and Physics - This is a joint work with Linhui Shen (Northwestern University) Kontsevich and Soibelman
defined Donaldson-Thomas invariants of a 3d Calabi-Yau category equipped with a stability
condition. Any cluster variety gives rise to a family of such categories. Their DT invariants are
encapsulated in a single formal automorphism of the cluster variety, the DT-transformation. - Let S be an oriented surface with punctures, and a finite number of special boundary points
considered modulo isotopy. It give rise to a moduli space X(m, S), closely related to the moduli
space of PGL(m)-local systems on S. This space carries a canonical cluster Poisson variety structure. - We calculate the DT-transformation of the moduli space X(m,S), with few exceptions.
- This, combined with the work of Gross, Hacking, Keel and Kontsevich, gives rise to a canonical
basis in the space of regular functions on the cluster variety X(m,S), conjectured by V. Fock and
the speaker.
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