© 2016

Families of Automorphic Forms and the Trace Formula

  • Werner Müller
  • Sug Woo Shin
  • Nicolas Templier


  • Develops analytic, p-adic and geometric perspectives on families of automorphic forms in relation to the trace formula

  • Focuses on recent developments and conjectures at the frontier of current knowledge based on in-depth exchanges between symposium participants

  • Provides researchers in the field and aspiring students with an appraisal of the feasibility of a range of approaches to open problems, as well as the subject's key difficulties

Conference proceedings

Part of the Simons Symposia book series (SISY)

Table of contents

  1. Front Matter
    Pages i-xii
  2. James Arthur
    Pages 1-91
  3. Kevin Buzzard, Toby Gee
    Pages 93-109
  4. Raf Cluckers, Julia Gordon, Immanuel Halupczok
    Pages 111-127
  5. Ju-Lee Kim, Sug Woo Shin, Nicolas Templier
    Pages 259-295
  6. Simon Marshall
    Pages 297-325
  7. Blake Mackall, Steven J. Miller, Christina Rapti, Caroline Turnage-Butterbaugh, Karl Winsor
    Pages 435-476
  8. Peter Sarnak, Sug Woo Shin, Nicolas Templier
    Pages 531-578

About these proceedings


Featuring the work of twenty-three internationally-recognized experts, this volume explores the trace formula, spectra of locally symmetric spaces, p-adic families, and other recent techniques from harmonic analysis and representation theory. 

Each peer-reviewed submission in this volume, based on the Simons Foundation symposium on families of automorphic forms and the trace formula held in Puerto Rico in January-February 2014, is the product of intensive research collaboration by the participants over the course of the seven-day workshop. The goal of each session in the symposium was to bring together researchers with diverse specialties in order to identify key difficulties as well as fruitful approaches being explored in the field. The respective themes were counting cohomological forms, p-adic trace formulas, Hecke fields, slopes of modular forms, and orbital integrals.


L-functions and symmetry automorphic forms trace formula families of automorphic representations of higher rank groups spectra of locally symmetric spaces p-adic families harmonic analysis and representation theory counting cohomological forms p-adic trace formulas Hecke fields slopes of modular forms orbital integrals

Editors and affiliations

  • Werner Müller
    • 1
  • Sug Woo Shin
    • 2
  • Nicolas Templier
    • 3
  1. 1.Mathematical InstituteUniversity of BonnBonnGermany
  2. 2.Department of MathematicsUniversity of California, BerkeleyBerkeleyUSA
  3. 3.Department of MathematicsCornell UniversityIthacaUSA

About the editors

Werner Müller is Professor Emeritus at the Mathematical Institute of the University of Bonn. He is the author of over fifty publications, including articles in Inventiones Mathematicae, Geometric and Functional Analysis, and Communications in Mathematical Physics. His research interests include geometric analysis, scattering theory, analytic theory of automorphic forms, and harmonic analysis on locally symmetric spaces.

Sug Woo Shin is Associate Professor of Mathematics at the University of California at Berkeley. His research is centered on number theory, Shimura varieties, Langlands functoriality, trace formula, and automorphic forms. His work has appeared in many journals, including Inventiones Mathematicae, Mathematische Annalen, and the Israel Journal of Mathematics.

Nicolas Templier is Associate Professor of Mathematics at Cornell University. His work focuses on number theory, automorphic forms, arithmetic geometry, ergodic theory, and mathematical physics. His list of publications include articles in Inventiones Mathematicae, the Ramanujan Journal, and the Israel Journal of Mathematics.

Bibliographic information