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Bio
Bio
I am a postdoctoral fellow at the University of Toronto working in analysis and geometry. I am particularly interested in microlocal/semiclassical analysis, dynamical systems and inverse problems arising in mathematical physics. From 2020-2025, I was a Postdoctoral Assistant Professor at the University of Michigan, with visiting stints at McGill University and IST Austria working with the Kaloshin Group. I completed my PhD in mathematics in 2020 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.
A tribute to the late Steve Zelditch (1953-2022) in the SIAM Orthogonal Polynomials and Special Functions newsletter.
Spectral rigidity of Liouville tori (joint with Joscha Henheik, Vadim Kaloshin, and Yunzhe Li), arXiv-pdf 2025
Deformational Spectral Rigidity of Axially Symmetric Symplectic Billiards (joint with Corentin Fierobe and Alfonso Sorrentino), arXiv-pdf 2024, Nonlinearity 2025
Silent Orbits and Cancellations in the Wave Trace (joint with Illya Koval) arXiv-pdf 2024, undergoing revisions.
Balian-Bloch-Zelditch Wave Inavriants for Nearly Degenerate Orbits (joint with Vadim Kaloshin and Illya Koval) arXiv-pdf 2024, to appear in AMS Contemporary Mathematics, Volume in Honor of Steve Zelditch.
Amir Vig. Compactness of Marked Length Isospectral Sets of Birkhoff Billiard Tables, arxiv-pdf 2023, undergoing revisions.
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.
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