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Abstract: We will discuss ongoing work with Alexandra Florea, Matilde Lalín, and Amita Malik on the shifted convolution problem for divisor functions in function fields. This involves studying the average value of $d(f) d(f+h)$ where $h$ is a fixed polynomial (having possibly large degree $m$) in $mathbb{F}_q[T]$ and $f$ runs over all monic polynomials in $mathbb{F}_q[T]$ of degree $n$, where $n$ goes to infinity. Our techniques mirror the classical approach of Estermann in the integer setting. The main new ingredient is a functional equation for the Estermann function (equivalently, a Voronoi summation formula for the divisor function) that seems be to novel for this setting. If time permits, we will discuss a related result involving the shifted convolution of the norm-counting functions of quadratic extensions. The talk should be accessible to those unfamiliar with function fields.