BPS spectra and 3-manifold invariants
We provide a physical definition of new homological invariants ℋ a (M 3) of 3-manifolds
(possibly, with knots) labeled by abelian flat connections. The physical system in question …
(possibly, with knots) labeled by abelian flat connections. The physical system in question …
Microlocal Morse theory of wrapped Fukaya categories
S Ganatra, J Pardon, V Shende - arXiv preprint arXiv:1809.08807, 2018 - arxiv.org
The Nadler--Zaslow correspondence famously identifies the finite-dimensional Floer
homology groups between Lagrangians in cotangent bundles with the finite-dimensional …
homology groups between Lagrangians in cotangent bundles with the finite-dimensional …
Cluster varieties from Legendrian knots
V Shende, D Treumann, H Williams, E Zaslow - 2019 - projecteuclid.org
Many interesting spaces—including all positroid strata and wild character varieties—are
moduli of constructible sheaves on a surface with microsupport in a Legendrian link. We …
moduli of constructible sheaves on a surface with microsupport in a Legendrian link. We …
Sheaf quantization in Weinstein symplectic manifolds
D Nadler, V Shende - arXiv preprint arXiv:2007.10154, 2020 - arxiv.org
arXiv:2007.10154v3 [math.SG] 31 Dec 2022 Page 1 arXiv:2007.10154v3 [math.SG] 31 Dec
2022 SHEAF QUANTIZATION IN WEINSTEIN SYMPLECTIC MANIFOLDS DAVID NADLER …
2022 SHEAF QUANTIZATION IN WEINSTEIN SYMPLECTIC MANIFOLDS DAVID NADLER …
Torus knots and the rational DAHA
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 …
knot from the unique finite-dimensional simple representation of the rational DAHA of type A …
Infinitely many Lagrangian fillings
R Casals, H Gao - Annals of Mathematics, 2022 - projecteuclid.org
We prove that all maximal-tb positive Legendrian torus links (n,m) in the standard contact 3-
sphere, except for (2,m), (3,3), (3,4) and (3,5), admit infinitely many Lagrangian fillings in the …
sphere, except for (2,m), (3,3), (3,4) and (3,5), admit infinitely many Lagrangian fillings in the …
Legendrian weaves: N–graph calculus, flag moduli and applications
R Casals, E Zaslow - Geometry & Topology, 2023 - msp.org
We study a class of Legendrian surfaces in contact five-folds by encoding their wavefronts
via planar combinatorial structures. We refer to these surfaces as Legendrian weaves, and …
via planar combinatorial structures. We refer to these surfaces as Legendrian weaves, and …
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" …
certain class of dualizable abelian fibrations. Multiplicativity of the perverse filtration and the" …
Positroids, knots, and -Catalan numbers
P Galashin, T Lam - Duke Mathematical Journal, 2024 - projecteuclid.org
We relate the mixed Hodge structure on the cohomology of open positroid varieties (in
particular, their Betti numbers over C and point counts over F q) to Khovanov–Rozansky …
particular, their Betti numbers over C and point counts over F q) to Khovanov–Rozansky …
Algebraic weaves and braid varieties
In this manuscript we study braid varieties, a class of affine algebraic varieties associated to
positive braids. Several geometric constructions are presented, including certain torus …
positive braids. Several geometric constructions are presented, including certain torus …