Combinatorics and Algebra Seminar-Square root crystals and Grothendieck positivity

Speaker: Eric Marberg, HKUST
Date and time: Tuesday, April 1, 4–5 pm
Place: Phillips 730

Title: Square root crystals and Grothendieck positivity

Abstract: Schur polynomials arise geometrically as cohomology representatives of Schubert varieties in the type A Grassmannian. When one studies K-theory instead of cohomology, these representatives are upgraded to functions known as symmetric Grothendieck polynomials. Many generating functions in combinatorics have nontrivial yet positive decompositions into Schur polynomials. The classical theory of type A crystals provides a graphical framework for proving this kind of Schur positivity. This talk will discuss a new category of "square root crystals" that can be used to establish stronger Grothendieck positivity properties. This is joint work with Kam Hung Tong and Tianyi Yu.