Automorphic Forms and Related Geometry: Assessing the Legacy of I.I. Piatetski-Shapiro
About this Title
James W. Cogdell, Ohio State University, Columbus, OH, Freydoon Shahidi, Purdue University, West Lafayette, IN and David Soudry, Tel Aviv University, Tel Aviv, Israel, Editors
Publication: Contemporary Mathematics
Publication Year 2014: Volume 614
ISBNs: 978-0-8218-9394-4 (print); 978-1-4704-1658-4 (online)
This volume contains the proceedings of the conference Automorphic Forms and Related Geometry: Assessing the Legacy of I.I. Piatetski-Shapiro, held from April 23–27, 2012, at Yale University, New Haven, CT.
Ilya I. Piatetski-Shapiro, who passed away on 21 February 2009, was a leading figure in the theory of automorphic forms. The conference attempted both to summarize and consolidate the progress that was made during Piatetski-Shapiro's lifetime by him and a substantial group of his co-workers, and to promote future work by identifying fruitful directions of further investigation. It was organized around several themes that reflected Piatetski-Shapiro's main foci of work and that have promise for future development: functoriality and converse theorems; local and global $L$-functions and their periods; $p$-adic $L$-functions and arithmetic geometry; complex geometry; and analytic number theory. In each area, there were talks to review the current state of affairs with special attention to Piatetski-Shapiro's contributions, and other talks to report on current work and to outline promising avenues for continued progress.
The contents of this volume reflect most of the talks that were presented at the conference as well as a few additional contributions. They all represent various aspects of the legacy of Piatetski-Shapiro.
Graduate students and research mathematicians interested in automorphic forms, number theory, representation theory, and geometry.
Table of Contents
- James Arthur – On parameters for the group
- J. W. Cogdell – Piatetski-Shapiro's Work on Converse Theorems
- Stephen Gelbart, Stephen D. Miller, Alexei Panchishkin and Freydoon Shahidi – A -adic integral for the reciprocal of -functions
- Simon Gindikin – Harmonic analysis on symmetric spaces as complex analysis
- Michael Harris – Testing rationality of coherent cohomology of Shimura varieties
- Haruzo Hida – Hecke fields of Hilbert modular analytic families
- Roger Howe and Soo Teck Lee – Structure of holomorphic unitary representations: the case of
- Hervé Jacquet – Mellin Transform of Whittaker functions
- Dihua Jiang – Automorphic Integral Transforms for Classical Groups I: Endoscopy Correspondences
- Ju-Lee Kim – An inductive formula for -factors
- Erez Lapid and Zhengyu Mao – On a new functional equation for local integrals
- Colette Mœglin – Paquets stables des séries discrètes accessibles par endoscopie tordue; leur paramètre de Langlands
- Ngô Bao Châu – On a certain sum of automorphic -functions
- Alexei Panchishkin – Analytic constructions of -adic -functions and Eisenstein series
- J. W. Cogdell, F. Shahidi and T.-L. Tsai – On stability of root numbers
- Christopher Skinner – CAP forms, Eisenstein series, and some arithmetic applications
- David Soudry – Automorphic descent: an outgrowth from Piatetski-Shapiro's vision
- Michael Friedman and Mina Teicher – On the singularities of branch curves of surfaces and applications