Research

My research interests lie in the intersection of differential geometry, mathematical physics and partial differential equations. I am particularly interested in the analytical and geometric aspects of solutions to heat equations arising from geometric variational problems such as the harmonic map, mean curvature, Ricci and Yang-Mills flows.

The following is a list of my preprints and publications:

• Heat ball formulæ for k-forms on evolving manifolds. Advances in Calculus of Variations, to appear. (published version)
• Local energy inequalities for mean curvature flow into evolving ambient spaces. manuscripta mathematica, to appear. (published version)
• Local regularity for the harmonic map and Yang-Mills heat flows. Submitted, August 2018.
• Energy identities and monotonicity for evolving k-forms on moving Riemannian spaces. Journal of Evolution Equations, 18(2):549–560, Jun 2018. (published version)
• Local monotonicity for the Yang-Mills-Higgs flow. Calc. Var. Partial Differential Equations, 55(1):1–14, February 2016. (published version)
• Monotonicity for p-harmonic vector bundle-valued k-forms. arXiv preprints, June 2015.

My Ph.D. thesis may be found here.