I am a Postdoctoral Assistant Professor at the University of Michigan working in analysis and geometry. I am particularly interested in microlocal/semiclassical analysis, dynamical systems and inverse problems arising in mathematical physics. In the spring and summer of 2021, I was a visiting postdoctoral researcher at McGill University. In the spring and summer of 2022, I was a postdoctoral researcher at IST Austria working with the Kaloshin Group. I completed my PhD in mathematics at the University of California, Irvine under the direction of Hamid Hezari. In the fall of 2019, I was also a program associate at the Mathematical Sciences Research Institute for the Semester on Microlocal Analysis. When not doing math, you can find me baking pastries, roasting coffee, gardening, playing saxophone or cycling whenever it's sunny outside!
A tribute to the late Steve Zelditch (1953-2022) in the SIAM Orthogonal Polynomials and Special Functions newsletter.
Deformational Spectral Rigidity of Axially Symmetric Symplectic Billiards (joint with Corentin Fierobe and Alfonso Sorrentino) arXiv-pdf 2024, submitted.
Silent Orbits and Cancellations in the Wave Trace (joint with Illya Koval) arXiv-pdf 2024, submitted.
Balian-Bloch-Zelditch Wave Inavriants for Nearly Degenerate Orbits (joint with Vadim Kaloshin and Illya Koval) arXiv-pdf 2024, AMS Volume in Honor of Steve Zelditch, accepted.
Amir Vig. Compactness of Marked Length Isospectral Sets of Birkhoff Billiard Tables, arxiv-pdf 2023, submitted.
Amir Vig. The Wave Trace and Birkhoff Billiards (arXiv-pdf 2019, Journal of Spectral Theory 2022)
Robin Spectral Rigidity of the Ellipse (arXiv-pdf 2018, Journal of Geometric Analysis 2020)
The Inverse Spectral Problem for Convex Planar Domains, (PhD thesis)
I support Federico Ardila's axioms:
Axiom 1: Mathematical potential is distributed equally amongst different groups, irrespective of geographic, demographic, and economic boundaries.
Axiom 2: Everyone can have joyful, meaningful, and empowering mathematical experiences.
Axiom 3: Mathematics is a powerful, malleable tool that can be shaped and used differently by various communities to serve their needs.
Axiom 4: Every student deserves to be treated with dignity and respect.