## NDSU Mathematics

### Fall 2022 Mathematics Colloquium

###### Time and Location:

Minard 112 at 3:00 PM (Refreshments at 2:30 in Minard 404)

Special Colloquia or Tri-College Colloquia venues and times may vary, please consult the individual listing.

#### Tuesday, October 11             Oliver Pechenik (University of Waterloo)

##### Cell decompositions and rings-with-bases

Abstract: When I first saw linear algebra, every vector space was $\mathbb{R}^n$, it came with a "standard coordinate basis", and linear transforms were the same as matrices. Later, I learned I was supposed to treat abstract vector spaces abstractly without specifying an arbitrarily-chosen basis or working in coordinates. Even later, I learned that sometimes there is a "canonical" basis and it's powerful to work in those coordinates after all. In this talk, we'll look at the cohomology and K-theory of some moduli spaces of flags and loops and see that they have canonical bases, with applications to the combinatorics of symmetric and quasisymmetric functions.

#### Thursday, October 13             Joshua Swanson (University of Southern California)

##### "Spinny pictures": connecting Catalan combinatorics, alternating sign matrices, and plabic graphs

Abstract: "Rotating" trees is a key step in balancing data structures like B-trees and AVL-trees. Modern databases and digital life are built upon this surprisingly crucial operation. Mathematically, a particularly beautiful instance of tree rotation arises by bijectively encoding complete binary trees as non-crossing matchings on a circle and literally spinning the circular matching. Certain non-obvious properties on the tree level become obvious when translated to the context of such a "spinny picture".

Far from being an isolated curiosity, we will show that such "spinny pictures" serve as a bridge between a remarkably diverse array of topics spanning enumerative combinatorics, representation theory, and algebraic geometry. We will in particular discuss our recent resolution of a nearly 30-year-old problem related to work of Kuperberg and Khovanov involving promotion on 4-row rectangular tableaux. The background assumed will be low, and pictures will be plentiful.

Joint work with Christian Gaetz, Oliver Pechenik, Stephan Pfannerer, and Jessica Striker.

Abstract:  TBD

Abstract:  TBD

#### Tuesday, December 6             Hongyan Hou (MSUM)

##### TBD

Abstract: TBD

Student Focused. Land Grant. Research University.