6 papers · 1 filter
Mirror symmetry for the Painlevé character varieties
Joël Beimler, Mingyuan Hu, William Olsen +1
We establish a homological mirror theorem for the 4-manifolds arising as moduli of (irregular) rank two local systems on the projective line. Specifically, we prove that the Fukaya…
A topological classification of generating functions
Sylvain Courte, Vivek Shende
From a generating function for a Legendrian in a -jet bundle, we may extract the following topological information: (1) a trivialization of the stable Gauss map, (2) the sheaf o…
Topological algebra of symplectic geometry of symmetric powers
Vivek Shende, Peng Zhou
To a noncompact orientable surface with no closed boundary, we associate the sum of Fukaya categories of (Liouville sectors associated to) its symmetric powers. We construct sector…
Aganagic's invariant is Khovanov homology
Elise LePage, Vivek Shende
On the Coulomb branch of a quiver gauge theory, there is a family of functions parameterized by choices of points in the punctured plane. Aganagic has predicted that Khovanov homol…
Quiver Hecke algebras from Floer homology in Couloumb branches
Mina Aganagic, Ivan Danilenko, Yixuan Li +2
Homology theories categorifying quantum group link invariants are known to be governed by the representation theory of quiver Hecke algebras, also called KLRW algebras. Here we sho…
The Hamiltonian reduction of hypertoric mirror symmetry
Michael McBreen, Vivek Shende, Peng Zhou
We give a `Fukaya category commutes with reduction' theorem for the Hamiltonian torus action on a multiplicative hypertoric variety.