As a mathematician, I am interested in physical problems and geometry. In my mind, the linkage between these two components is through partial differential equations (PDEs). PDEs are typically studied in an analytical sense with boundary value problems posed on subregions in n-dimensional Eucliean space. However, the coordinate free perspective granted by Riemannian geometry may provide new insights or techniques to make progress in both old and new problems.
Aishah Albarakati, Marko Budišić, Rose Crocker, Juniper Glass-Klaiber, Sarah Iams, John Maclean, Noah Marshall, Colin Roberts, Erik S. Van Vleck, Model and data reduction for data assimilation: Particle filters employing projected forecasts and data with application to a shallow water model , Computers & Mathematics with Applications, 2021, ISSN 0898-1221.
Brooks Adams, Henry Adams, and Colin Roberts, Sweeping Costs of Planar Domains , In Erin W Chambers, Brittany T Fasy, and Lori S Ziegelmeier, eds., Research in Computational Topology, pages 71-92, AWM Springer series, volume 13, 2018.
Jonathan Gilbert, Colin Roberts, and Jacob Roberts, Near-Resonant Light Propagation in an Absorptive Spatially Anisotropic Ultracold Gas , Journal of the Optical Society of America B, pages 718723, volume 25, number 4, 2018.