Tutte Colloquium -Oliver Pechenik-Dynamics of Increasing Tableaux

Abstract: Standard tableaux are certain grids of numbers that lead a double life in algebraic combinatorics, with distinct roles in geometry and in representation theory. Extending the geometry to K-theory led to a corresponding extension of the combinatorics to a theory of increasing tableaux. I will discuss a long and ongoing program to explicate the combinatorial dynamics of these tableaux, which seems to be revealing that they also have a mysterious second life in representation theory. Despite the algebraic connections, the core problem is fundamentally combinatorial: to give a sufficiently good bijection between tableaux and a set of planar diagrams.