Combinatorial models of polynomials from Schubert Calculus

Polynomials are powerful tools in many fields, for example, representation theory, geometry, and topology. In algebraic combinatorics, studying polynomials through combinatorial methods often yields deeper insights into these areas. I will talk about several families of polynomials arising from Schubert calculus, which originated in enumerative geometry.  We will look at various combinatorial models, including diagrams (representing cells in a plane) and tableaux (arrangements of numbers in boxes), with many examples. These discrete objects, along with operations defined on them, exhibit rich combinatorial properties. They can be used to simplify computations, extract algebraic and geometric information, and uncover hidden symmetries within these polynomials.