Graduate course MAT 1063 HF
Microlocal Analysis and Applications I
Professor Victor Ivrii
Time-Table
Monday 2:10–3:00, Wednesday 1:10–2:00, Friday 2:10–3:00
HU 1028
My office: 215 Huron, Room 1008
My time-Table
Course Description
My phone: 416-978-4031
Our Wiki
My email:
ivrii@math.toronto.edu
Description
It will be theory and applications.
Content
Fourier Integral Operators:
Oscillatory solutions, relation to classical dynamics.
Elements of classical dynamics.
Lagrangian distributions, phase functions and amplitudes, Lagrangian manifolds.
Canonical graphs and Fourier Integral Operators.
Metaplectic operators.
Oscillatory solutions near and beyond caustics.
Maslov Canonical Operator.
Propagation of singularities.
Fourier Integral Operators Approach.
Heisenberg approach.
Coherent States approach.
Energy estimates approach.
Propagation near boundary (survey)
Applications to Spectral Asymptotics.
Tauberian Approach.
Poisson Relations, Spectrum and Length Spectrum.
Sharp spectral asymptotics.
Dependencies
(They are not listed as pre-requisites)
MAT1063 Microlocal Analysis and Applications I
(as of Fall 2007); while not official pre-requisite but one needs to know material;
Real Analysis (graduate or undergraduate);
Complex Analysis (graduate or undergraduate, or even non-specialist);
Analysis on Manifold (elements)s;
Ordinary Differential Equations (graduate or undergraduate);
Partial Differential Equations (graduate or undergraduate).
© 2007 by Victor Ivrii
