International Conference on
Spectral Geometry

July 19-23, 2010
Dartmouth College

Maass fade

Pre-conference minicourse schedule and slides

We offer three minicourses (download schedule or see below), totaling eight lectures over the two-day period, with the following themes and speakers:
  1. Background on Hamiltonian and quantum mechanics, and the semiclassical limit (Alejandro Uribe). The main goal of this minicourse is to explain the connection between the spectral decomposition of the Laplacian and geodesic flow. It will cover the technical notions of phase space, pseudodifferential operators and microlocalization. This material is needed to understand the QUE problem, as well as some aspects of the inverse spectral problem.

    Alejandro has said that a LATeX version of his notes may be written up in conjunction with Zuoqin Wang. Meanwhile some of Alejandro's notes are covered in his trace formulae review, and the local Weyl Law and Quantum Ergodicity Theorem in Zelditch's CDM quantum chaos review, finally the Zworksi-Evans lecture notes on semiclassical analysis.

  2. Spectral theory on hyperbolic surfaces with emphasis on the arithmetic case (David Borthwick). The spectral theory of the Laplacian on arithmetic surfaces has some very special features that are generally unknown by people working on inverse problems. This minicourse will start with basic results arising from the uniformization theorem for hyperbolic surfaces and then specialize to the arithmetic case. Hecke operators will be discussed, as well as some of the main spectral results in this area.

    Here are the complete slides from David's lectures, and extra notes and references that accompany them.

  3. Orbifolds and their spectral theory (Carolyn Gordon). Riemannian orbifolds are not yet as well-known as Riemannian manifolds, and this minicourse is planned to cover that gap. Topics will include orbifold singularities, the spectrum of the Laplacian on compact orbifolds, existence of the heat trace expansion, and a survey of inverse spectral results on orbifolds.

    Here are the slides from Carolyn's first lecture; notes covering both lectures will be posted shortly.

    References include: Ch. 13 of Thurston's notes, Geometry of Free Manifolds.

Friday July 16

Morning talks in 007 Kemeny
8 - 8:50 amBreakfast in 007 Kemeny
9 - 10 amAlejandro Uribe I
10:15 - 11:15 amCarolyn Gordon I
11:30 - 12:30 pmAlejandro Uribe II
12:30 - 2 pm(lunch break)
Afternoon talks in 008 Kemeny
2 - 3:30 pmDavid Borthwick I
4 - 5 pmQ&A session
5 - 6 pmWine & cheese reception
in 300 Kemeny

Saturday July 17

All talks in 008 Kemeny
8 - 8:50 amBreakfast in 008 Kemeny
9 - 10 amDavid Borthwick II
10:15 - 11:15 amCarolyn Gordon II
11:30 - 12:30 pmDavid Borthwick III
12:30 - 2 pm(lunch break)
2 - 3:30 pmAlejandro Uribe III
4 - 5 pmQ&A session

Main workshop schedule and slides

Here are the titles and abstracts of the talks (PDF format).

Here is the main schedule from Monday morning July 19 to lunchtime on Friday July 23 (PDF format).

Slides from talks at the conference (mostly in PDF format). They are in alphabetical order by speaker (see above for schedule):

Poster session

The poster session is Tuesday 4 - 5pm, with refreshments. Here are some of the posters themselves: