BPS spectra and 3-manifold invariants

S Gukov, D Pei, P Putrov, C Vafa - Journal of Knot Theory and Its …, 2020 - World Scientific
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 …

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 …

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 …

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 …

Integrability as duality: the gauge/YBE correspondence

M Yamazaki - Physics Reports, 2020 - Elsevier
The Gauge/YBE correspondence states a surprising connection between solutions to the
Yang–Baxter equation with spectral parameters and partition functions of supersymmetric …

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 …

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 …

Augmentations, fillings, and clusters

H Gao, L Shen, D Weng - arXiv preprint arXiv:2008.10793, 2020 - arxiv.org
We investigate positive braid Legendrian links via a Floer-theoretic approach and prove that
their augmentation varieties are cluster K2 (aka. A-) varieties. Using the exact Lagrangian …

Betti geometric langlands

D Ben-Zvi, D Nadler - Algebraic geometry: Salt Lake City 2015, 2018 - books.google.com
We introduce and survey a Betti form of the geometric Langlands conjecture, parallel to the
de Rham form developed by Beilinson-Drinfeld and Arinkin-Gaitsgory, and the Dolbeault …

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 …