Aidan Backus

I am Aidan Backus, a-fifth year Ph.D. candidate at Brown University, where I am a member of the geometric analysis group and a student of Georgios Daskalopolous. Previously, I was at UC Berkeley. I am on the job market for a postdoc.I can be reached at [email protected]. See also my CV and research statement.

• Research
• Travel
• Miscellany

Research

I work in geometric measure theory, the study of geometric structures which are too singular to study using differential calculus. I have used GMT to study calculus of variations in L^∞ and BV and the fractal uncertainty principle.Classically the calculus of variations has studied partial differential equations which arise as solutions of optimization problems in L², or more generally a reflexive Banach space. The analysis becomes much trickier in L^∞ and BV, but in these spaces the problems have much clearer geometric interpretations (for example, the prototypical BV problem is concerned with finding area-minimizing hypersurfaces) and my research attempts to use geometric and convex duality-based techniques to make progress.The fractal uncertainty principle asserts, informally, that we cannot know that a quantized particle's position and momentum both lie inside a fractal. This is frequently of interest in quantum chaos, since chaotic dynamical systems tend to attract to Cantor sets.

Research preprints

Expository / undergraduate preprints

Travel

Miscellany