Pre-conference minicourse schedule and slides

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.

Main workshop schedule and slides

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):

• Stephen Fulling: Index theorems for quantum graphs
• Andrew Hassell: Estimates on Neumann eigenfunctions at the boundary, and the "Method of Particular Solutions" for computing them
• Luc Hillairet: Generic simplicity using asymptotic separation of variables
• Dima Jakobson: Gauss curvature of random metrics (preprint)
• Peter Kuchment: Parseval frames of exponentially decaying Wannier functions
• Michael Levitin: Fourier transform, null varieties, and Laplacian's eigenvalues
• Jeremy Marzuola: Eigenfunction concentration and Strichartz estimates for planar polygonal domains
• Peter Sarnak: The distribution of mass and zeros for high frequency eigenfunctions on the modular surface
• Vladimir Sharafutdinov: Local audibility of a hyperbolic metric
• Dorothee Schueth: Local symmetry of harmonic spaces as determined by the spectra of small geodesic spheres (preprint)
• Melissa Tacy: Eigenfunction L^p estimates on manifolds of constant negative curvature
• Steve Zelditch: Quantum ergodic restriction theorems (preprint for case with boundary)

Poster session

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

• Tayeb Aissiou: Semiclassical limits of eigenfunctions of the Laplacian on Tⁿ
• Teresa Arias-Marco: On inaudible curvature properties of closed Riemannian manifolds: left, center, right
• Semen Dyatlov: Quasi-Normal modes for Kerr-de Sitter black holes: left, center, right
• Ori Parzanchevsky: Isospectrality and representations of finite groups