MATH 693: Reading course: Analysis on Manifolds. Fall 2014.


INSTRUCTOR:
D. Jakobson
Office: BH1220
Office Hours: Tuesday 11:30-12:30 and Wednesday, 9:20-10:20
Tel: 398-3828
E-mail: jakobson@math.mcgill.ca
Web Page: www.math.mcgill.ca/jakobson
Course page: http://www.math.mcgill.ca/jakobson/courses/math693.html
MEETINGS:
  • Tuesday, 13:00-14:00, Burnside 1205; Thursday, 9:00-10:00, Burnside 1205
  • There will be no meeting on Tuesday, September 16

  • COURSE DESCRIPTION:
    We shall discuss selected chapters from Y. Canzani's lecture notes, Analysis on manifolds via the Laplace operator
    Presentations, Grading
    Students registered for the course will be expected to give one or two oral presentations (around 30 minutes) on a topic suggested by the instructor. The grade will be based on those presentations and on short reports written by students.


    Previous related courses at McGill
  • Spectral theory of Automorphic forms
  • Winter 2013: Seminar on Hyperbolic Geometry and Automorphic Forms. This web page has links to some results in geometry and dynamical systems that are only sketched in H. Iwaniec's book.
  • to be continued...

  • Possible themes for Presentation
  • to be announced

  • Links

  • Course Dynamics and Quantum Chaos on hyperbolic surfaces by Alex Gorodnik at Bristol.
  • A book by Peter Buser (in Google books): Geometry and Spectra of Compact Riemann Surfaces
  • Shlomo Sternberg: Lecture notes in Real Analysis

  • Introduction to Riemannian Geometry
  • Sigmundur Gudmundsson's lectures notes, especially chapters 6, 7, 8, 9.
  • Laplacian, heat kernel etc

  • Lectures on semiclassical analysis by M. Zworski.
  • A future book by Victor Ivrii (large file!)
  • There are many lectures notes on the home page of Robert Brooks
  • Notes on heat kernel asymptotics by D. Grieser
  • Lecture Notes by Melrose
  • P. Gilkey: Invariance theory, the heat equation, and the Atiyah-Singer index theorem: EMIS server and pdf file
  • P. Gilkey, J. Leahy and J. Park: Spinors, spectral geometry, and Riemannian submersions: EMIS server
  • Lecture Notes by Melrose
  • to be continued
  • Introductory Links in Differential Geometry, Spectral Geometry etc

  • some cool graphics: GANG; Plane curves
  • Lecture notes in DG on the net: Nigel Hitchin; Gabriel Lugo; Balazs Csikos; C.T.J. Dodson
  • Differential Geometry pages at wikipedia and at mathworld
  • Survey papers from Alan Weinstein's course at Berkeley: page 1 and page 2
  • Survey papers from a course by Tamas Hausel at UTexas; in particular Eigenvalues and the Heat Kernel by A. Young; Curvature and fundamental group by S. Kang.
  • UChicago warmup page

  • NOTICE: McGill University values academic integrity. Therefore, all students must understand the meaning and consequences of cheating, plagiarism and other academic offences under the Code of Student Conduct and Disciplinary Procedures (see McGill web page on Academic Integrity for more information).
    NOTICE: In accord with McGill University's Charter of Student Rights, students in this course have the right to submit in English or in French any work that is to be graded.
    NOTICE: In the event of extraordinary circumstances beyond the University's control, the content and/or evaluation scheme in this course is subject to change.