Legendrian knots and constructible sheaves

V Shende, D Treumann, E Zaslow - Inventiones mathematicae, 2017 - Springer
We study the unwrapped Fukaya category of Lagrangian branes ending on a Legendrian
knot. Our knots live at contact infinity in the cotangent bundle of a surface, the Fukaya …

Torus knots and mirror symmetry

A Brini, M Mariño, B Eynard - Annales Henri Poincaré, 2012 - Springer
We propose a spectral curve describing torus knots and links in the B-model. In particular,
the application of the topological recursion to this curve generates all their colored HOMFLY …

Torus knots and the rational DAHA

E Gorsky, A Oblomkov, J Rasmussen, V Shende - 2014 - projecteuclid.org
We conjecturally extract the triply graded Khovanov–Rozansky homology of the (m, n) torus
knot from the unique finite-dimensional simple representation of the rational DAHA of type A …

The Hilbert scheme of a plane curve singularity and the HOMFLY homology of its link

A Oblomkov, J Rasmussen, V Shende - Geometry & Topology, 2018 - msp.org
We conjecture an expression for the dimensions of the Khovanov–Rozansky HOMFLY
homology groups of the link of a plane curve singularity in terms of the weight polynomials of …

Perverse filtrations and Fourier transforms

D Maulik, J Shen, Q Yin - arXiv preprint arXiv:2308.13160, 2023 - arxiv.org
We study the interaction between Fourier-Mukai transforms and perverse filtrations for a
certain class of dualizable abelian fibrations. Multiplicativity of the perverse filtration and the" …

A closed formula for the evaluation of foams

LH Robert, E Wagner - Quantum Topology, 2020 - ems.press
A closed formula for the evaluation of foams Page 1 Quantum Topol. 11 (2020), 411–487 DOI
10.4171/QT/139 Quantum Topology © European Mathematical Society A closed formula for …

Quadruply-graded colored homology of knots

E Gorsky, S Gukov, M Stosic - arXiv preprint arXiv:1304.3481, 2013 - arxiv.org
We conjecture the existence of four independent gradings in the colored HOMFLY
homology. We describe these gradings explicitly for the rectangular colored homology of …

Compactified Jacobians and q, t-Catalan numbers, I

E Gorsky, M Mazin - Journal of Combinatorial Theory, Series A, 2013 - Elsevier
Compactified Jacobians and q,t-Catalan numbers, I Page 1 Journal of Combinatorial Theory,
Series A 120 (2013) 49–63 Contents lists available at SciVerse ScienceDirect Journal of …

The HOMFLYPT skein algebra of the torus and the elliptic Hall algebra

H Morton, P Samuelson - 2017 - projecteuclid.org
We give a generators and relations presentation of the HOMFLYPT skein algebra H of the
torus T 2, and we give an explicit description of the module corresponding to the solid torus …

Refined curve counting on complex surfaces

L Göttsche, V Shende - Geometry & Topology, 2014 - msp.org
We define refined invariants which “count” nodal curves in sufficiently ample linear systems
on surfaces, conjecture that their generating function is multiplicative, and conjecture explicit …