E-mail me to max@maxlein.com and visit my blog.
My research spans the gamut from theoretical physics to rather abstract mathematics. I am open to supervising students of physics and mathematics, have a look at my (non-exhaustive) list of topics.
Most of the problems I am interested in take inspiration from physics, including condensed matter physics, propagation of classical waves in periodic media, systems with magnetic fields, semiclassical limits and topological phenomena. Mathematically, I employ tools from functional analysis, (magnetic) pseudodifferential theory and work at the intersection of (functional) analysis and (operator) algebras.
I see several advantages of a more mathematical approach to physics: mathematics is the language of physics, and I have access to a broader array of tools. Secondly, I can build new tools that are tailored to a specific problem such as magnetic pseudodifferential operators. And thirdly, it furthers conceptual clarity. Making assumptions explicit and understanding when they are used helps one understand the mechanism behind physical phenomena.
Currently, my research centers around several topics (more details can be found here and theses topics here):
