Amir Vig
Bio
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 at an Afghan mehmani (get together), baking pastries, roasting coffee, playing saxophone or cycling whenever it's sunny outside!
A tribute to the late Steve Zelditch (1953-2022).
Balian-Bloch Wave Inavriants for Nearly Degenerate Orbits (https://arxiv.org/abs/2404.02381) (joint with Vadim Kaloshin and Illya Koval)
Compactness of Marked Length Isospectral Sets of Birkhoff Billiard Tables (arxiv-pdf 2023)
Wave Trace Cancellations for Hyperbolic Orbits in Convex Billiard Tables (joint with Vadim Kaloshin and Illya Koval (Slides from Erwin Schroödinger Institute)
The Wave Trace and Birkhoff Billiards (arXiv-pdf, Journal of Spectral Theory 2022)
Robin Spectral Rigidity of the Ellipse (arXiv-pdf, 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.