695 citations · 2k across the 49 of their papers we have counts for
51 papers
Welschinger invariants and the Conway polynomial
Vivek Shende, Wennan Zhang
Welschinger showed that counts of connected holomorphic disks with Lagrangian boundary in symplectic 6-manifolds, meeting at least one boundary constraint, can be made invariant by…
Skein traces from curve counting
Tobias Ekholm, Pietro Longhi, Sunghyuk Park +1
Given a 3-manifold , and a branched cover arising from the projection of a Lagrangian 3-manifold in the cotangent bundle of to the zero-section, we define a map from the…
The skein valued mirror of the topological vertex
Tobias Ekholm, Pietro Longhi, Vivek Shende
We count holomorphic curves in complex 3-space with boundaries on three special Lagrangian solid tori. The count is valued in the HOMFLYPT skein module of the union of the tori. Us…
Counting bare curves
Tobias Ekholm, Vivek Shende
We construct a class of perturbations of the Cauchy-Riemann equations for maps from curves to a Calabi-Yau threefold. Our perturbations vanish on components of zero symplectic area…
Skein valued cluster transformation in enumerative geometry of Legendrian mutation
Matthias Scharitzer, Vivek Shende
Under certain hypotheses, we show that Legendrian surfaces related by disk surgery will have q-deformed augmentation spaces that are related by q-deformed cluster transformation. T…
Quantum mirrors of cubic planar graph Legendrians
Matthias Scharitzer, Vivek Shende
For a certain class of Legendrian surfaces in the five-sphere, associated to cubic planar graphs, we show that the all-genus skein-valued holomorphic curve invariants of any fillin…