Cluster structures on braid varieties
We show the existence of cluster $\mathcal {A} $-structures and cluster Poisson structures
on any braid variety, for any simple Lie group. The construction is achieved via weave …
on any braid variety, for any simple Lie group. The construction is achieved via weave …
Positive configuration space
N Arkani-Hamed, T Lam, M Spradlin - Communications in Mathematical …, 2021 - Springer
We define and study the totally nonnegative part of the Chow quotient of the Grassmannian,
or more simply the nonnegative configuration space. This space has a natural stratification …
or more simply the nonnegative configuration space. This space has a natural stratification …
An invitation to positive geometries
T Lam - Open Problems in Algebraic Combinatorics, 2024 - books.google.com
An invitation to positive geometries Page 168 Proceedings of Symposia in Pure Mathematics
Volume 110 , 2024 https://doi. org/10.1090/pspum/110/02013 An invitation to positive …
Volume 110 , 2024 https://doi. org/10.1090/pspum/110/02013 An invitation to positive …
[PDF][PDF] Relative cluster categories and Higgs categories with infinite-dimensional morphism spaces
Cluster algebras with coefficients are important since they appear in nature as coordinate
algebras of varieties like Grassmannians, double Bruhat cells, unipotent cells,···. The …
algebras of varieties like Grassmannians, double Bruhat cells, unipotent cells,···. 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 …
Braid variety cluster structures, I: 3D plabic graphs
P Galashin, T Lam, M Sherman-Bennett… - arXiv preprint arXiv …, 2022 - arxiv.org
We introduce $3 $-dimensional generalizations of Postnikov's plabic graphs and use them
to establish cluster structures for type $ A $ braid varieties. Our results include known cluster …
to establish cluster structures for type $ A $ braid varieties. Our results include known cluster …
Quasi-coincidence of cluster structures on positroid varieties
M Pressland - arXiv preprint arXiv:2307.13369, 2023 - arxiv.org
By work of a number of authors, beginning with Scott and culminating with Galashin and
Lam, the coordinate rings of positroid varieties in the Grassmannian carry cluster algebra …
Lam, the coordinate rings of positroid varieties in the Grassmannian carry cluster algebra …
[PDF][PDF] Braid variety cluster structures, II: general type
P Galashin, T Lam, M Sherman-Bennett - arXiv preprint arXiv:2301.07268, 2023 - arxiv.org
arXiv:2301.07268v2 [math.AG] 7 Feb 2023 Page 1 BRAID VARIETY CLUSTER STRUCTURES,
II: GENERAL TYPE PAVEL GALASHIN, THOMAS LAM, AND MELISSA SHERMAN-BENNETT …
II: GENERAL TYPE PAVEL GALASHIN, THOMAS LAM, AND MELISSA SHERMAN-BENNETT …
Symmetries of stochastic colored vertex models
P Galashin - The Annals of Probability, 2021 - projecteuclid.org
We discover a new property of the stochastic colored six-vertex model called flip-invariance.
We use it to show that for a given collection of observables of the model, any transformation …
We use it to show that for a given collection of observables of the model, any transformation …
Polypositroids
T Lam, A Postnikov - Forum of Mathematics, Sigma, 2024 - cambridge.org
We initiate the study of a class of polytopes, which we coin polypositroids, defined to be
those polytopes that are simultaneously generalized permutohedra (or polymatroids) and …
those polytopes that are simultaneously generalized permutohedra (or polymatroids) and …