
## 5. Fukaya category of Hitchin fibration

1. #### Problem 5.1.

Compute the Fukaya category of the total space of the Hitchin fibration, and compare with representations of the double affine Hecke algebra (DAHA).
Physicists believe that the Fukaya category should be (in some sense) equivalent to the derived category of representations of a DAHA. References?
•     The above problem is fairly ambitious: so what would be a first step? The next problem would give some situations where we could perform calculations of the Fukaya category.

#### Problem 5.2.

Characterize situation where the central fibre of the Hitchin fibration has known, smooth components, intersecting transversely.
I think the rank 2 parabolic case was mentioned as a situation where this occurs?

Cite this as: AimPL: Singular geometry and Higgs bundles in string theory, available at http://aimpl.org/singularhiggs.