Families of Automorphic Forms and the Trace Formula

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.

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 Includes supplementary material: sn.pub/extras

Autorentext
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.

Inhalt
Germ expansions for real groups (J. Arthur).- Slopes of modular forms (K. Buzzard, T. Gee).- Transfer principles for bounds of motivic exponential functions (R. Cluckers, J. Gordon I. Halupczok).- Growth of Hecke fields along a p-adic analytic family of modular forms (H. Hida).- The trace formula and prehomogeneous vector spaces (W. Hoffmann).- The local Langlands conjectures for non-quasi-split groups (T. Kaletha).- Asymptotics and local constancy of characters of p-adic groups (J.-L. Kim, S.-W. Shin, N. Templier).- Endoscopy and cohomology of a quasi-split U(4) (S. Marshall).- Distribution of Hecke Eigenvalues for GL(n) (J. Matz).- Zeta functions for the adjoint action of GL(n) and density of residues of Dedekind zeta functions (J. Matz).- Some results in the theory of low-lying zeros of families of L-functions (B. Mackall, S. Miller, C. Rapti, C. Turnage-Butterbaugh, K. Winsor).- Asymptotics of automorphic spectra and the trace formula (W. Müller).- Families of L-functions and theirsymmetry (P. Sarnak, S.-W. Shin, N. Templier).