Aidan Backus
I am Aidan Backus. As of summer 2025, I am a postdoc at the University of Toronto. My mentors are Bob Jerrard, Robert McCann, and Adrian Nachman. Previously, I was at Brown University, where I was mentored by George Daskalopoulos.I can be reached at [email protected]. See also my CV and research statement.I'm proud to have been raised in the California public school system, from kindergarten to undergrad, and am saddened by federal attempts to undermine it.
Research
I work in geometric measure theory, the study of geometric structures which are too singular to study using differential calculus. I'm particularly interested in calculus of variations in L∞ and BV, and its applications to geometry. 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.
Research publications
To appear, Journal of Mathematical Analysis and Applications, joint with Ze-An Ng: The Lipschitz extension problem with prescribed local Lipschitz constants and eikonal mappings (arXiv)
13 June 2025, Analysis and Partial Differential Equations, joint with James Leng and Zhongkai Tao: The fractal uncertainty principle via Dolgopyat's method in higher dimensions
8 August 2024, Journal of Geometric Analysis: Minimal laminations and level sets of 1-harmonic functions (arXiv)
Research preprints
10 March 2025: Reconstructing currents from their projections
1 January 2025: The max flow/min cut theorem and the topological least gradient problem
29 November 2024: The canonical lamination calibrated by a cohomology class
Preprints, not intended for publication
2 April 2024: An ∞-Laplacian for differential forms, and calibrated laminations
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
Informal Notes
Some interesting open problems: A list of problems that I've thought about at least a little bit. If you know how to make progress on them, let's talk about it!
Functions of least gradient and area-minimizing laminations: A guide to my work on functions of least gradient and the laminations produced from their level sets, plus some motivation from the Daskalopoulos--Uhlenbeck theory of geodesic laminations.
The Fenchel-Rockafellar theorem: A short self-contained proof of the Fenchel-Rockafellar convex duality theorem.
Travel
June 2025, Providence: Geometric Analysis Workshop
April 2025, Hartford: Spring Eastern AMS Sectional Meeting
February 2025, Chicago: University of Chicago Geometric Analysis Seminar
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