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Graduate Thesis Defenses 2021

Christian Gaetz

Title: New combinatorics of the weak and strong Bruhat orders
Date: Tuesday, February 23, 2021 | 11:00am | Room: Remote
Zoom Meeting ID: 985 7133 9903 Committee: Alexander Postnikov (advisor), Richard Stanley, David Speyer

Abstract

This thesis describes a line of work, much of it joint with Yibo Gao, which began with our proof of Stanley’s conjecture that the weak order on the symmetric group is Sperner. Further developments—either directly related or related in our thinking at the time—involve weighted path enumeration in the weak and strong Bruhat orders, specializations of Schubert polynomials, separable elements in finite Weyl groups, and inequalities for linear extensions of finite posets.