Cluster structures on coordinate rings
Cluster structures on coordinate rings
This started as a learning seminar on cluster structures on coordinate rings of various algebraic varieties, before mutating into a research seminar on cluster algebras, braids, and link invariants. Here we will be uploading the notes and material for the seminar.
When? Mondays 9:00-10:30am Pacific = 11:00am-12:30pm CDMX = 12:00pm-1:30pm Eastern = 6:00-7:30pm Central Europe
Where? Online. Contact the organizers for the Zoom link and password.
References: Please find links to references for the learning part of the seminar in the preliminary plan.
Organized by Mikhail Gorsky and José Simental.
Date
Feb. 21
Feb. 28
Mar. 7
Mar. 14 - Apr. 4
Apr. 11
Cohomology of braid varieties
Cluster algebras and Legendrian links
Infinitely many Lagrangian fillings
No meetings
Cluster structures associated to open Richardson varieties: simply-laced types
Apr. 18
Apr. 25
May 2
May 9
Total positivity in the Gröbner fan and cluster algebras
Knot theory and Cluster algebras
DGA Representations, Ruling Polynomials, and the Colored HOMFLY-PT Polynomial
May 23
May 30
June 6
June 27
Infinitely many planar exact Lagrangian fillings and symplectic Milnor fibers
Deformation theory for finite cluster complexes
Categorification for positroid varieties
Cluster structures for braid varieties
Date
June 24
July 1
July 8
July 22
July 29
August 5
August 12
August 19
August 26
Sept. 2
Sept. 9
Sept. 16
Oct. 7
Oct.15(Friday!)
Oct. 21
Nov. 4
Nov. 15
Nov. 29
Dec. 6
Overview and organizational meeting
Cluster algebras: basic definitions and examples
Cluster structure on Gr(k,n)
Cohomology of cluster varieties
Positroid varieties: definitions and main properties
Cluster structures on positroid varieties
Cluster structures on Richardson varieties
Braid varieties
Algebraic weaves
Double Bott-Samelson cells I
Double Bott-Samelson cells II
Positroids, knots and q,t-Catalan numbers
Homotopy equivalences of varieties built from braids
Braiding and twisting open positroid varieties
Legendrian weave calculus and clusters
Lagrangian fillings for Legendrian links of finite or affine type
Recap of previous talks
Knots and Jacobian algebras
Examples of cluster structures on Coulomb branches
Speaker
This seminar takes place within the AiM Research Community on Link Homology.