**Abstract:**

The Schensted correspondence is a bijection between permutations in \$S_n\$ and pairs of standard Young tableaux \$(P,Q)\$ with \$n\$ boxes which have the same shape. This bijection has remarkable properties in algebraic and enumerative combinatorics. Motivated by a problem in cryptography, we study a graded quotient \$R_n\$ of the polynomial ring in \$n \times n\$ variables whose standard monomial theory encodes Viennot's shadow line formulation of the Schensted correspondence. The quotient ring \$R_n\$ may be understood as coming from the locus of permutation matrices via the machine of orbit harmonics. I will report on work of my student Moxuan Liu who has extended this theory to colored permutation groups.

**Note: This talk begins with a pre-seminar (aimed at graduate students) at 3:30–4:00. The main talk starts at 4:10.**

**Join Zoom Meeting: https://washington.zoom.us/j/ 91547335974Meeting ID: 915 4733 5974**