Melanie Rupflin

Prof. Melanie Rupflin is a Professor of Mathematics at the University of Oxford's Mathematical Institute, based in the Andrew Wiles Building. Her research focuses on nonlinear partial differential equations (PDEs) and geometric variational problems, particularly harmonic maps and geometric flows such as the Teichmüller harmonic map flow. She develops quantitative theories to analyze singularity formation, energy concentration, and gradient flow dynamics.

Her work emphasizes precise control over geometric evolution processes and their asymptotic behavior. She collaborates extensively with Peter Topping and others, producing influential papers on topics like bubble tree convergence, Lojasiewicz inequalities, and geometric PDEs on surfaces. Rupflin also teaches advanced courses such as Part A Differential Equations and Part B Functional Analysis 2, with lecture materials available via the Oxford Mathematics YouTube channel.

Her research addresses fundamental questions in geometric analysis, including the existence and uniqueness of weak solutions, energy quantization, and the interplay between topology and PDE dynamics. Current projects explore refined asymptotics of geometric flows and boundary value problems in hyperbolic geometry.