John Turnage

I am a PhD candidate in mathematics at the University of Utah, advised by Akil Narayan and affiliated with the Scientific Computing and Imaging Institute. I expect to complete my PhD in May 2027.

My research lies in approximation theory and probability on function spaces, with applications to operator learning, numerical integration, and uncertainty quantification. Much of my current work concerns recovering operators between function spaces from observations of their inputs and outputs, including PDE solution operators. I study how the choice of approximation space and sampling measure affects the stability and accuracy of least-squares recovery, and how Gaussian measures on spaces of residual operators can describe the uncertainty remaining in a finite approximation. Related interests include reduced-order modeling, inverse problems, and measure transport.