**Abstract:**

The \$q\$-Whittaker symmetric function associated to an integer partition is a \$q\$-analogue of the Schur symmetric function. We give a new formula for the \$q\$-Whittaker function in terms of partial flags compatible with a nilpotent endomorphism over the finite field of size \$1/q\$. We show that considering pairs of partial flags and taking Jordan forms leads to a probabilistic bijection between nonnegative-integer matrices and pairs of semistandard tableaux of the same shape, which we call the \$q\$-Burge correspondence. In the \$q \to 0\$ limit, we recover a known description of the classical Burge correspondence (also called column RSK). This is joint work with Hugh Thomas.

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

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