Seminar

Pipe dreams are tiling models originally introduced to study objects related to the Schubert calculus and K-theory of the Grassmannian. They can also be viewed as ensembles of random lattice walks with various interaction constraints. In our quest to understand what the maximal and typical algebraic objects look like, we revealed some interesting permutons. The proofs use the theory of the Totally Asymmetric Simple Exclusion Process (TASEP). Deeper connections with free fermion 6 vertex models and domino tilings of the Aztec diamond and Alternating Sign Matrices allow us to describe the extreme cases of the original algebraic problem. This is based on joint work with A. H. Morales, L. Petrov, D. Yeliussizov.