Enumerating Smooth-Like Permutations Via the Geometry of Schubert Varieties

Explore a mathematical lecture on the enumeration of smooth-like permutations through the geometric lens of Schubert varieties. In this one-hour talk from the Connections to Schubert Calculus Learning Seminar at the Institute for Advanced Study, Edward Richmond from Oklahoma State University delves into how various families of smooth-like permutations can be enumerated using methods similar to those applied to smooth permutations. Learn about Ryan's 1984 discovery that smooth Schubert varieties in type A form iterated fiber-bundles of Grassmannian varieties, and how Haiman later calculated the generating function for counting smooth permutations using this structure. Discover how pattern avoidance characterizes these smooth-like permutation families, featuring insights from Richmond's joint work with W. Slofstra and F. Azam. The lecture takes place on May 07, 2025, at 3:30pm in Simonyi 101.