- Scholarship in 2023 at Massachusetts Institute of Technology
About Michael Law’s work
Michael Law is a mathematician working in the field of geometric analysis whose current research spans several subfields, including harmonic maps, general relativity and spin geometry.
The subject of harmonic maps unifies various mathematical and scientific problems. Law’s research proposes to study the space of harmonic maps between two manifolds using harmonic map heat flow (HMHF), which is a more widely applicable approach than existing methods, which rely on tools from complex geometry. Law aims to deepen our understanding of HMHF by generalising recent results in mean curvature flow following the work of Colding and Minicozzi.
Law also studies the mathematics behind Einstein’s theory of general relativity. In general relativity, the notion of mass is subtle and is one of which no universally accepted mathematical formulation exists. As such, there are many open mathematical problems about mass which originate from physical intuition. Law aims to extend existing results on the positivity of mass, building on seminal contributions of Schoen, Yau and Witten. A common theme in this line of work is the use of spinors, which are themselves of geometric interest due to their connections to the scalar curvature of a manifold.
Biography
Michael Law graduated with a BSc in Mathematics and Statistics from the University of Melbourne in 2020 and with a first-class degree in Mathematical Sciences from the Australian National University in 2021. At the University of Melbourne, he was awarded both the Dixson Prize in Pure Mathematics and the Maurice H. Belz Prize in Statistics. In 2022, he was granted a Presidential Fellowship at MIT. He is currently pursuing his PhD research and studies at the same institution.