Georgia Institute of Technology School of Mathematics | Georgia Institute of Technology | Atlanta, GA

I will discuss two projects concerning Mallows permutations, with Ander Holroyd, Tom Hutchcroft and Avi Levy.  First, we relate the Mallows permutation to stable matchings, and percolation on bipartite graphs. Second, we study the scaling limit of the cycles in the Mallows permutation, and relate it to diffusions and continuous trees.