19 citations · 75 across the 13 of their papers we have counts for
14 papers
Combinatorics of Mirković-Vilonen cycles in twisted affine Grassmannians
Jiuzu Hong, Linhui Shen, Daping Weng
We investigate the explicit geometric and combinatorial structure of Mirković-Vilonen (MV) cycles in twisted affine Grassmannians associated with special parahoric group schemes. U…
Weighted Cycles on Weaves
Daping Weng
We introduce weighted cycles on weaves of general Dynkin types and define a skew-symmetrizable intersection pairing between weighted cycles. We prove that weighted cycles on a weav…
Intersections of Dual -Webs
Linhui Shen, Zhe Sun, Daping Weng
We introduce a topological intersection number for an ordered pair of -webs on a decorated surface. Using this intersection pairing between reduced $(\operator…
Augmentations, Fillings, and Clusters for 2-Bridge Links
Orsola Capovilla-Searle, James Hughes, Daping Weng
We produce the first examples relating non-orientable exact Lagrangian fillings of Legendrian links to cluster theory, showing that the ungraded augmentation variety of certain max…
Demazure weaves for reduced plabic graphs (with a proof that Muller-Speyer twist is Donaldson-Thomas)
Roger Casals, Ian Le, Melissa Sherman-Bennett +1
First, this article develops the theory of weaves and their cluster structures for the affine cones of positroid varieties. In particular, we explain how to construct a weave from…
F-Polynomials of Donaldson-Thomas Transformations
Daping Weng
-polynomials are integer coefficient polynomials encoding the mutations of cluster variables inside a cluster algebra. In this article, we study the -polynomials associated w…
Microlocal Theory of Legendrian Links and Cluster Algebras
Roger Casals, Daping Weng
We show the existence of quasi-cluster -structures and cluster Poisson structures on moduli stacks of sheaves with singular support in the alternating strand diagram o…
Positive Braid Links with Infinitely Many Fillings
Honghao Gao, Linhui Shen, Daping Weng
We prove that any positive braid Legendrian link not isotopic to a standard finite type link admits infinitely many exact Lagrangian fillings.
Augmentations, Fillings, and Clusters
Honghao Gao, Linhui Shen, Daping Weng
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 Lagran…
Cluster Structures on Double Bott-Samelson Cells
Linhui Shen, Daping Weng
Let be a symmetrizable generalized Cartan matrix. We introduce four different versions of double Bott-Samelson cells for every pair of positive braids in the generalized braid…
Cyclic Sieving and Cluster Duality of Grassmannian
Linhui Shen, Daping Weng
We introduce a decorated configuration space with a potential function . We prove the cluster duality conjecture of Fock-Goncharov…
Donaldson-Thomas Transformation of Double Bruhat Cells in Semisimple Lie Groups
Daping Weng
Double Bruhat cells were studied by Fomin and Zelevinsky. They provide important examples of cluster algebras and cluster Poisson varieties. Cluster varieties produce exa…
Donaldson-Thomas Transformation of Double Bruhat Cells in General Linear Groups
Daping Weng
Kontsevich and Soibelman defined the Donaldson-Thomas invariants of a 3d Calabi-Yau category with a stability condition. Any cluster variety can produce an example of such a catego…
Donaldson-Thomas Transformation of Grassmannian
Daping Weng
Kontsevich and Soibelman defined the notion of Donaldson-Thomas invariants of a 3d Calabi-Yau category with a stability condition. A family of examples of such categories can be co…