Lectures
Mon 11:00AM - 12:00PM
Wed 11:00AM - 1:00PM
Office Hours
Wed 1:00PM – 2:00PM
Important information · zoom
link
Due to the
December 2021 Covid
Omicron surge, classes will be online
until (at least) January 31 2022. Lectures will be
delivered by Zoom; please join this
zoom
link.
Should you have any questions,
please
send
me an email message.
Quercus
There is a Quercus page set up for
this course; if you plan to attend this course without
enrolling
please
send
me an email and I can add you to Quercus. It will
make my life easier to distribute announcements and
other important information. I will keep the material
available in this page
for reference.
Syllabus
The syllabus can be downloaded here
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Schedule
January 10
General information, Course Introduction
January 12
Trace Formulas Preliminaries
January 12
Trace Formulas Preliminaries
January 17
The Poisson's summation formula
January 19
Heat trace on tori
January 24
Wave trace on tori
February 2
Trace formulas and oscillatory integrals
February 7
Wave trace, wrapping up
February 9
Anosov flows and closing lemma
February 14
Closing Lemma, Livšic's Theorem
February 16
Cone Hyperbolic flows, Jacobi fields
February 28
Hyperbolicity of Geodesic flow in negative curvature
March 2
Transitivity of Geodesic flows in negative curvature I
March 7
Transitivity of Geodesic flows in negative curvature II
March 9
Transitivity of Geodesic flows in negative curvature III
March 14
Proof of Guillemin–Kazhdan I
March 16
Proof of Guillemin–Kazhdan II
March 23
Proof of Otal's Theorem I
March 28
Proof of Otal's Theorem II
March 30
Proof of Otal's Theorem III
April 4
Sunada Construction I
April 6
Sunada Construction II
List of reading items
A. Uribe –
Trace Formulae
J. Chazarain -
Formule de Poisson pour les variétés riemanniennes
Amie Wilkinson –
Lectures on Otal's Theorem
J.-P. Otal –
The length spectrum of negatively curved manifolds (in French)
V. Guillemin, D. Kazhdan –
Some inverse spectral results for negatively curved 2-manifolds
T. Sunada (砂田 利一) –
Riemannian coverings and isospectral manifolds
R. Brooks -
The Sunada Method
S. Zelditch -
Inverse spectral problem for analytic domains II. ℤ₂–symmetric domains
S. Zelditch -
Spectral determination of analytic bi-axisymmetric plane domains
C. Guillarmou, T. Lefeuvre -
The marked length spectrum of Anosov manifolds
—, V. Kaloshin, Qiaoling Wei -
Dynamical spectral rigidity among ℤ₂–symmetric strictly convex domains close to a circle