# 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

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 L

^{2}, 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

TBD: The canonical lamination calibrated by a cohomology class

2 April 2024: An ∞-Laplacian for differential forms, and calibrated laminations

12 March 2024, joint with Ng Ze-An: The Lipschitz extension problem with prescribed local Lipschitz constants and eikonal mappings

2 November 2023: Minimal laminations and level sets of 1-harmonic functions. To appear in

*Journal of Geometric Analysis*.23 February 2023, joint with James Leng and Zhongkai Tao: The fractal uncertainty principle via Dolgopyat's method in higher dimensions. To appear in

*Analysis and Partial Differential Equations*.

### Expository / undergraduate preprints

19 June 2023: Regularity of sets of least perimeter in Riemannian manifolds

28 April 2020: The Breit-Wigner series for noncompactly supported potentials on the line

10 December 2019, joint with Peter Connick and Joshua Lin: An algorithm for computing root multiplicities in Kac-Moody algebras

## Travel

May 2024, Des Moines: Algorithmic Fractal Dimensions

January 2024, San Francisco: Joint Mathematics Meetings

November 2023, Storrs: University of Connecticut PDE and Differential Geometry Seminar

July 2023, Madison: Summer School on the Fractal Uncertainty Principle

April 2023, Princeton: Geometry Festival

March 2023, Providence: Geometric Analysis Workshop

January 2023, Boston: Joint Mathematics Meetings

November 2022, Storrs: Northeast Workshop in Geometric Analysis

October 2022, Amherst: Fall Eastern AMS Sectional Meeting

September 2022, Princeton: A Celebration of Karen Uhlenbeck's 80th Birthday

## Miscellany

My bachelor's thesis: The Breit-Wigner series and resonances of potentials

Another undergraduate project on analysis and logic: Formalizations of analysis

Some notes on logic and analysis from when I was an undergraduate