Math 693 FALL 2016

Lecture Notes

  • Lectures 1 and 2- Conormal Distributions

  • Lecture 3- Conormal Distributions, symbols and oscillatory integrals

  • Lecture 4- Conormal Distributions, symbols and oscillatory integrals-continuation

  • Lecture 5- (REVISED) Conormal Distributions, symbols and oscillatory integrals-continuation

  • Lecture 6- C-infinity manifolds, distributions on manifolds

  • Lecture 7- Vector bundles and distributions

  • Lecture 8- Vector bundles and distributions-- Continuation

  • Lecture 9- Vector bundles and distributions-- Continuation

  • Lecture 10-- The cotangent bundle

  • Lecture 11 - Vector Fields; the Lie derivative

  • Lecture 12- Lie derivative of differential forms

  • Lecture 13- Symplectic manifolds

  • Lecture 14- Symplectic manifolds-Continuation

  • Lecture 15- Hamilton Jacobi Theory

  • Lecture 16- Parametrizations of Lagrangian submanifolds

  • Lecture 17- Parametrizations of Lagrangian submanifolds-Continuation

  • Lecture 18- Review of Pseudodifferential operators- Lagrangian Distributions

  • Lecture 19- Lagrangian Distributions, continuation

  • Lecture 20- Stationary Phase

  • Lecture 21- Phase functions and oscillatory Integrals

  • Lecture 22- Lagrangian Distributions, continuation

  • Lecture 23- Lagrangian Distributions, continuation

  • Lecture 24- The Calculus of FIOs

  • Lecture 25- Transversality, composion of canonical relations

  • Lecture 26- The Calculus of FIOs-- Continuation