Geometric and Spectral Analysis
About this Title
Pierre Albin, University of Illinois at Urbana-Champaign, Urbana, IL, Dmitry Jakobson, McGill University, Montreal, Quebec, Canada and Frédéric Rochon, Université du Québec à Montréal, Montréal, Québec, Canada, Editors
Publication: Contemporary Mathematics
Publication Year 2014: Volume 630
ISBNs: 978-1-4704-1043-8 (print); 978-1-4704-2059-8 (online)
In 2012, the Centre de Recherches Mathématiques was at the center of many interesting developments in geometric and spectral analysis, with a thematic program on Geometric Analysis and Spectral Theory followed by a thematic year on Moduli Spaces, Extremality and Global Invariants.
This volume contains original contributions as well as useful survey articles of recent developments by participants from three of the workshops organized during these programs: Geometry of Eigenvalues and Eigenfunctions, held from June 4–8, 2012; Manifolds of Metrics and Probabilistic Methods in Geometry and Analysis, held from July 2–6, 2012; and Spectral Invariants on Non-compact and Singular Spaces, held from July 23–27, 2012.
The topics covered in this volume include Fourier integral operators, eigenfunctions, probability and analysis on singular spaces, complex geometry, Kähler-Einstein metrics, analytic torsion, and Strichartz estimates.
Graduate students and research mathematicians interested in geometric analysis and spectral geometry.
Table of Contents
- Maxim Braverman and Boris Vertman – A New Proof of a Bismut-Zhang Formula for Some Class of Representations
- Robert J. Berman – Tunneling, the Quillen Metric and Analytic Torsion for High Powers of a Holomorphic Line Bundle
- Victor Guillemin, Eveline Legendre and Rosa Sena-Dias – Simple Spectrum and Rayleigh Quotients
- Yanir A. Rubinstein – Smooth and Singular Kähler–Einstein Metrics
- Gerardo A. Mendoza – Complex $b$-Manifolds
- Bert-Wolfgang Schulze – Iterative Structures on Singular Manifolds
- Zhiqin Lu and Julie Rowlett – The Fundamental Gap and One-Dimensional Collapse
- Raphaël Ponge – The Logarithmic Singularities of the Green Functions of the Conformal Powers of the Laplacian
- Yuri Safarov – A Symbolic Calculus for Fourier Integral Operators
- Dean Baskin, Jeremy L. Marzuola and Jared Wunsch – Strichartz Estimates on Exterior Polygonal Domains
- Nicolas Burq and Gilles Lebeau – Probabilistic Sobolev Embeddings, Applications to Eigenfunctions Estimates
- Liviu I. Nicolaescu – Random Smooth Functions on Compact Riemannian Manifolds
- Binh T. Nguyen, Denis S. Grebenkov and Andrey L. Delytsin – On the Exponential Decay of Laplacian Eigenfunctions in Planar Domains with Branches
- Guillaume Poliquin – Bounds on the Principal Frequency of the $p$-Laplacian