Postdoctoral Fellow at the University of Toronto (2025-)
Postdoctoral Assistant Professor at the University of Michigan (2020-2025)
Teaching assistant at the University of California, Irvine (2014-2020)
Postdoctoral Fellow at Institute of Science and Technology, Austria (2022)
Postdoctoral Researcher at McGill University (2021)
Program Associate at MSRI (2019)
amir "dot" vig "at" utoronto "dot" ca
University of Toronto
Department of Mathematics
St George office: SF-2302A
Mississauga office: DH-3097D
University of California, Irvine
PhD in Mathematics (June 2020)
Dissertation Title: The Inverse Spectral Problem for Convex Planar Domains
Advisor: Hamid Hezari
MS in Mathematics (March 2016)
University of North Carolina at Chapel Hill
BS in Mathematics with Distinction (May 2014)
Honored Instructor Award (University of Michigan, 2025)
AMS-Simons Travel Grant (American Mathematical Society and Simons Foundation, 2024)
Von Neumann Award for Outstanding Performance (University of California Irvine, 2019)
Faculty Mentorship Fellowship, honorable mention (University of California Irvine, 2017)
GAANN Fellowship (US Department of Education, 2014-2015)
Semiclassical and microlocal analysis, dynamical systems, billiards, inverse problems, spectral theory, partial differential equations, Riemannian and symplectic geometry, mathematical physics
Spectral rigidity of Liouville tori (joint with Joscha Henheik, Vadim Kaloshin, and Yunzhe Li)
Deformational Spectral Rigidity of Axially Symmetric Symplectic Billiards (joint with Corentin Fierobe and Alfonso Sorrentino)
Silent Orbits and Cancellations in the Wave Trace (joint with Illya Koval)
Submitted (2024)
Balian-Bloch-Zelditch Wave Inavriants for Nearly Degenerate Orbits (joint with Vadim Kaloshin and Illya Koval)
AMS Volume in Honor of Steve Zelditch (Accepted)
Amir Vig. Compactness of Marked Length Isospectral Sets of Birkhoff Billiard Tables
Submitted, undergoing revisions
Amir Vig. The Wave Trace and Birkhoff Billiards
Robin Spectral Rigidity of the Ellipse
The Inverse Spectral Problem for Convex Planar Domains, (PhD thesis)
Spectral rigidity of Liouville tori, Inverse Problems Seminar, UC Irvine (2026)
Spectral rigidity of Liouville tori, Dynamics Seminar, University of Toronto, Canada (2025)
On the inverse spectral problem for convex planar domains, Seminario di Sistemi Dinamici, Universita di Roma Tor Vergata, Italy (2025)
Spectral theory of convex planar domains, Laboratoire de Mathématiques Jean Leray, Nantes Université, France (2025)
Cancellations in the wave trace, Hamiltonian Dynamics at Maryland, University of Maryland (2025)
Birkhoff billiards and the marked length spectrum, Dynamics Seminar, University of Chicago (2025)
Spectral theory of convex planar domains, Spectral and Scattering Theory Seminar, Purdue Universitie, West Lafayette IN (2025)
Marked length spectral invariants of Birkhoff billiard tables and compactness of isospectral sets, Harmonic Analysis Seminar, UC Irvine (2024)
Marked length spectral invariants and compactness of isospectral sets, Spectral Geometry in the Clouds, virtual (2024)
Silent geodesics and cancellations In the wave trace, AMS Special Session: Harmonic Analysis, Partial Differential Equations, and Spectral Theory, UC Riverside (2024)
Potential Theory and Feynman Diagrams in Spectral Theory, Geometry Seminar at North Carolina State University, Raleigh (2024)
On the marked length spectrum of Birkhoff billiard tables, Summer School: Geometric Inverse Problems and Inverse Problems for Elliptic Equations, UC Santa Cruz (2024)
Potential theory and Feynman diagrams in inverse problems, Differential Equations Seminar, University of Michigan, Ann Arbor (2024)
Silent geodesics and cancellations In the wave trace, CDSNS Colloquium, Georgia Institute of Technology, Atlanta (2024)
Geometry of billiards, University of Michigan Math Club, Ann Arbor, Michigan (2024)
Compactness of the marked length isospectral set, Simons Center for Geometry and Physics, Stony Brook NY (2023)
Cancellations in the wave trace, Spectral Theory and Relativity thematic program, Erwin Schrödinger Institute, Vienna, Austria (2023)
Cancellations in the wave trace, Midwestern Microlocal Meetings, Northwestern University, Evanston, Illinois (2023)
The wave trace and Birkhoff billiards, DynamIST Seminar, Institute of Science and Technology Austria, Klosterneuburg (2022)
Spectral Invariants and Birkhoff Billiards: Analysis Zoom Seminar, CRM, Montréal Québec (2021)
Wave invariants and inverse spectral theory, Geometry and Analysis Zoominar, University of California Santa Cruz (2020)
Wave invariants and inverse spectral theory, MSRI Graduate Seminar, Mathematical Sciences Resesarch Institute (MSRI) (2019)
Wave invariants and inverse spectral theory, Harmonic Analysis and Differential Equations Seminar, University of California Berkeley (2019)
Small scale quantum ergodicity in rational polygons, MSRI Graduate Seminar, Mathematical Sciences Resesarch Institute (MSRI) (2019)
The wave trace and Birkhoff billiards, Gradute Student Topology and Geometry Conference, University of Illinois Urbana-Champaign (2019)
Spectral theory of the ellipse, Geometry and topology seminar, Esch-sur-Alzette, Université du Luxembourg (2018)
Spectral theory of the ellipse, Microlocal methods in global analysis, University of Göttingen, Germany (2018)
Spectral theory of the ellipse, Analytic study of flows, Peyresq, France (2018)
Summer 2024: TA for Spectral Geometry, Microlocal Analysis and Quantum Dynamics (MAQD), Northwestern University, Evanston (2024)
Summer 2021: TA for Microlocal Analysis, Séminaire de Mathématiques Supérieures Summer School on Microlocal Analysis: Theory and Applications (virtual)
Summer 2019: TA for Quantum Mechanics, Graduate Minischool (SNAP) (Northwestern University)
Symplectic Dynamics and Topology, CIME, Cetraro Italy (2025)
Stockholm Master Class in Dynamical Systems, KTH, Sweden (2025)
Hamiltonian Dynamics at Maryland, University of Maryland (2025)
AMS Special Session: Harmonic Analysis, Partial Differential Equations, and Spectral Theory, Riverside CA (2024)
Summer School: Geometric Inverse Problems and Inverse Problems for Elliptic Equations, UC Santa Cruz (2024)
Microlocal Analysis and Quantum Dynamics, Northwestern University, Evanston IL (2024)
Workshop: Mathematical Billiards: At the Crossroads of Dynamics, Geometry, Analysis, and Mathematical Physics, Stony Brook NY (2023)
Spectral Theory and Mathematical Relativity, Universität Wien, Erwin Schrödinger Institute, Vienna, Austria (2023)
Microlocal and probabilistic methods in geometry and dynamics, Campus Universitaire de Jussieu, Paris, France (2023)
Midwestern microlocal meetings, Northwestern University, Evanston, Illinois (2023)
Global Analysis: A Conference in Honor of Steve Zelditch, virtual (2022)
Analytic and geometric aspects of spectral theory, Casa Matemática Oaxaca, Mexico (2022)
Séminaire de mathématiques supérieures summer school on microlocal analysis: Theory and Applications, virtual (2021)
Virtual mini-workshop in geometric analysis (2020)
Semester on microlocal analysis, Mathematical Sciences Research Institute, Berkeley CA (2019)
Summer Northwestern analysis program on semiclassical analysis, Northwestern University, Evanston IL (2019)
Microlocal analysis and applications, Shanghai Center for Mathematical Sciences, Fudan University, Shanghai China (2019)
Probing the earth and the universe with microlocal analysis, Banff International Research Station, Canada (2019)
Gradute student topology and geometry conference, University of Illinois Urbana-Champaign (2019)
Microlocal analysis, inverse problems and resonances: a conference in honor of Plamen Stefanov, Purdue University, Lafayette, Indiana (2019)
Geometric singular analysis and mathematical physics, University of Oldenburg, Germany (2018)
Geometry and topology seminar, Université du Luxembourg, Esch-sur-Alzette Luxembourg (2018).
Inverse and spectral problems for nonlocal operators, Max-Plank Institute, Leipzig, Germany (2018)
Microlocal methods in global analysis, University of Göttingen, Germany (2018)
Journées de physique mathématique de Lyon: Quantum chaos, Laboratoire de Physique de l’ENS Lyon, France (2018)
Analytic study of flows, Peyresq, France (2018)
Summer Northwestern analysis program, Northwestern University, Evanston, IL (2017)
Third symposium on scattering and spectral theory, Universidad Federal de Santa Caterina, Florianópolis, Brazil (2017)
Analytical aspects of hyperbolic flows, Université de Nantes, France (2017)
Microlocal analysis and its applications, University of Cardiff, UK (2017)
Elliptic equations and harmonic analysis on rough sets, MSRI, Berkeley, CA (2016)
Houston summer school on dynamical systems, University of Houston, TX (2016)
Joint mathematics meetings, global harmonic analysis, Seattle, WA (2016)
Second Chicago summer school in analysis, University of Chicago, IL (2015)
UNC-CH PDE mini-school, University of North Carolina, Chapel Hill, NC (2014)
University of Toronto
Winter 2026: Math 102, Introduction to Mathematical Proofs
Fall 2025: Math 224H5, Linear Algebra II
University of Michigan
Winter 2025: Math 525, Graduate Probability Theory
Winter 2025: Math 425, Introduction to Probability
Fall 2024: Math 215-030, Multivariable Calculus
Fall 2024: Math 215-040, Multivariable Calculus
Winter 2024: Math 215-040, Multivariable Calculus
Winter 2024: Math 215-020, Multivariable Calculus
Fall 2023: Math 215-080, Multivariable Calculus
Fall 2023: Math 215-090, Multivariable Calculus
Winter 2023: Math/Stats 425-006, Introduction to Probability
Winter 2023: Math/Stats 425-008, Introduction to Probability
Fall 2022: Math/Stats 425-003, Introduction to Probability
Fall 2022: Math/Stats 425-006, Introduction to Probability
Winter 2022: Math/Stats 425-002: Introduction to Probability
Fall 2021: Math/Stats 425-005, Introduction to Probability
Fall 2021: Math/Stats 425-009, Introduction to Probability
Fall 2020: Math 116-042, Calculus 2
Fall 2020: Math 116-052, Calculus 2
McGill University
Spring 2021: Math 263
University of California Irvine
Summer Session 1 2020: Math 2B, Calculus II (2B)
Spring 2020: Department Fellowship
Winter 2020: Math 210B, Graduate Real Analysis (210B)
Fall 2019: On Leave, MSRI Semester on Microlocal Analysis
Spring 2019: Math 205C/H140C, Intro Graduate Analysis III
Winter 2019: Math 205B/H140B, Intro Graduate Analysis II
Fall 2018: Math 205A/H140A, Intro Graduate Analysis I
Spring 2018: Math 210C, Graduate Real Analysis III
Winter 2018: Math 210B, Graduate Real Analysis
Fall 2017: Math 210A, Graduate Real Analysis I
Spring 2017: Math 205C/H140C, Intro Graduate Analysis III
Winter 2017: Math 3A, Linear Algebra
Winter 2017: Math 175, Combinatorics
Fall 2016: Math 112, Partial Differential Equations
Fall 2016: Math 118, Theory of Differential Equations
Spring 2016: Math 141, Topology
Spring 2016: Math 140C, Analysis in Several Variables
Winter 2015: Math 140B, Elementary Analysis II (5 pm section)
Winter 2015: Math 140B, Elementary Analysis II (8 am section)
Fall 2015: Math 140A, Elementary Analysis I (1 pm section)
Fall 2015: Math 140A, Elementary Analysis I (10 am section)
Spring 2015: Math 3A, Linear Algebra (12 pm section)
Spring 2015: Math 3A, Linear Algebra (8 am section)
Ergodic theory, complex variables and geometry, topics in differential geometry, differential geometry, microlocal analysis, partial differential equations, functional analysis, introduction to manifolds and geometry, real analysis, complex analysis, algebra, various research seminars
Fluent in English, Pashto and Farsi, proficient in Hindi/Urdu and Spanish, elementary French
AMS Volume In Honor of Steve Zelditch
Communications in Mathematical Physics
Journal of Differential Equations
Journal of Geometric Analysis
Nonlinear Analysis
Regular and Chaotic Dynamical Systems
Speaker at Math Club, University of Michigan (2024)
Refugee mentor and tutor for Jewish Family Services of Washtenaw County (2023)
Speaker at Math Teachers' Circle, University of Michigan (2023)
President of the UCI Chapter of the American Mathematical Society (2017-2020)
Volunteer with Helping Hand Relief for the Poor (2018-2019)
Volunteer with International Orphan Care (2018)
STEM Panelist at the Afghan American Conferences: Berkeley, California and Washington, D.C. (2015, 2017)
Volunteer with Tiyya Foundation (2017)
Speaker for a Support Network Among URM, Low-Income, and First Generation Students from the School of Physical Sciences, University of California, Irvine -- together with A. Pantano (2017)
Colead Math Circle, University of California Irvine (2017)
President of UCI Afghan Students Union (2015-2017)
Volunteer with Islamic Relief (2015, 2016)
Intern at International Consortium for Law and Development in Islamabad, Pakistan (2012)
Intern at the Embassy of Afghanistan in Washington D.C. (2011)