Amir Vig CV

Research Interests

Inverse problems, spectral theory, billiards, dynamical systems, semiclassical and microlocal analysis, differential geometry, quantum chaos, harmonic analysis, mathematical physics

Publications and Preprints

1. Balian-Bloch Wave Inavriants for Nearly Degenerate Orbits (https://arxiv.org/abs/2404.02381) (joint with Vadim Kaloshin and Illya Koval)

2. Amir Vig. Compactness of the Length Isospectral Set for Birkhoff Billiards (arxiv-pdf 2023)

3.  Amir Vig. The Wave Trace and Birkhoff Billiards (arXiv-pdf 2019, Journal of Spectral Theory 2022)

4. Robin Spectral Rigidity of the Ellipse (arXiv-pdf 2018, Journal of Geometric Analysis 2020)

5. Wave Trace Cancellations for Hyperbolic Orbits in Convex Billiard Tables (joint with Vadim Kaloshin and Illya Koval (Slides from Erwin Schroödinger Institute)

6. The Inverse Spectral Problem for Convex Planar Domains, (PhD thesis)

Conference Talks

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, Georgia Tech, 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, Klosterneuburg, Austria (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)

An inverse spectral problem for the ellipse, Spectral and Scattering Theory Seminar, Purdue University (canceled due to covid)

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)

Invited Conferences

Workshop: Mathematical Billiards: At the Crossroads of Dynamics, Geometry, Analysis, and Mathematical Physics, Stony Brook NY. (2023)

Microlocal Analysis and Quantum Dynamics, Northwestern University, Evanston (2024)

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)

Teaching

University of Michigan

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, Probability Theory

Winter 2023: Math/Stats 425-008, Probability Theory

Fall 2022: Math/Stats 425-003, Probability Theory

Fall 2022: Math/Stats 425-006, Probability Theory

Winter 2022: Math/Stats 425-002: Probability Theory

Fall 2021: Math/Stats 425-005, Probability Theory

Fall 2021: Math/Stats 425-009, Probability Theory

Fall 2020: Math 116-042, Calculus 2

Fall 2020: Math 116-052, Calculus 2

McGill University

Spring 2021: Math 263

Institute of Science and Technology Austria

Spring 2022:

University of California Irvine

Summer Session 1 2020: Calculus 2

Spring 2020: Department Fellowship

Winter 2020: Graduate Real Analysis

Fall 2019: On Leave, MSRI Semester on Microlocal Analysis

Summer 2019: Quantum Mechanics, Graduate Minischool (SNAP)

Spring 2019: Intro Graduate Analysis

Winter 2019: Intro Graduate Analysis

Fall 2018: Intro Graduate Analysis

Spring 2018: Graduate Real Analysis

Winter 2018: Graduate Real Analysis

Fall 2017: Graduate Real Analysis

Spring 2017: Intro Graduate Analysis

Winter 2017: Linear Algebra

Winter 2017: Combinatorics

Fall 2016: Partial Differential Equations

Fall 2016: Theory of Differential Equations

Spring 2016: Topology

Spring 2016: Real Analysis III, Several Variables

Winter 2015: Real Analysis II (5 pm section)

Winter 2015: Real Analysis II (8 am section)

Fall 2015: Real Analysis I (1 pm section)

Fall 2015: Real Analysis I (10 am section)

Spring 2015: Linear Algebra (12 pm section)

Spring 2015: Linear Algebra (8 am section)

Winter 2015: No teaching, GAANN Fellowship

Fall 2014: No teaching, GAANN Fellowship

Graduate Coursework

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

Languages

Fluent in English, Pashto and Farsi, proficient in Hindi/Urdu and Spanish, elementary French, Python, Matlab, and Mathematica.

Service

Refugee mentor and tutor, Jewish Family Services of Washtenaw County (2023)

Pashto and Farsi translator, Jewish Family Services of Washtenaw County (2023)

Math Teachers' Circle, University of Michigan (2022-2023)

Referee for Nonlinear Analysis, Elsevier (2021)

President of American Mathematical Society, UCI Chapter (2017-2020)

STEM Panelist at the Afghan American Conferences: UC Berkeley, UCLA and George Washington Univiersity (2015-2017)

Volunteer with Helping Hand Relief for the Poor (2018-2019)

Volunteer with Islamic Relief (2015-2018)

Volunteer with Tiyya Foundation (2017)

President of UCI Afghan Students Union (2015-2017)

President of Afghan Students in Hope for a New Afghanistan (2011)

Intern at International Consortium for Law and Development in Islamabad, Pakistan (2012)

Intern at the Embassy of Afghanistan in Washington D.C. (2011)

References

Hamid Hezari, Associate Professor of Mathematics, University of California Irvine

hezari "at" math "dot" uci "dot" edu

Gunther Uhlmann, Walker Family Endowed Professor in Mathematics, University of Washington

gunther "at" math "dot" washington "dot" edu

Steven Zelditch, Professor of Mathematics, Northwestern University

s-zelditch "at" northwestern "dot" edu

Colin Guillarmou, Professor of Mathematics

Laboratoire de Mathématiques d’Orsay

Faculté des Sciences d’Orsay Universitè Paris-Sud (France)

cguillar "at" math "dot" cnrs "dot" fr

Katya Krupchyk, Professor of Mathematics, University of California Irvine

katya "dot" krupchyk "at" uci "dot" edu

Nathan Kaplan, Associate Professor of Mathematics, University of California Irvine

nckaplan "at" math "dot" uci "dot" edu