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Author: Clay Mathematics Institute. Summer School Publisher: American Mathematical Soc. ISBN: 9780821838440 Category : Mathematics Languages : en Pages : 708
Book Description
Langlands program proposes fundamental relations that tie arithmetic information from number theory and algebraic geometry with analytic information from harmonic analysis and group representations. This title intends to provide an entry point into this exciting and challenging field.
Author: Clay Mathematics Institute. Summer School Publisher: American Mathematical Soc. ISBN: 9780821838440 Category : Mathematics Languages : en Pages : 708
Book Description
Langlands program proposes fundamental relations that tie arithmetic information from number theory and algebraic geometry with analytic information from harmonic analysis and group representations. This title intends to provide an entry point into this exciting and challenging field.
Author: Werner Müller Publisher: Springer ISBN: 3319948334 Category : Mathematics Languages : en Pages : 461
Book Description
The second of three volumes devoted to the study of the trace formula, these proceedings focus on automorphic representations of higher rank groups. Based on research presented at the 2016 Simons Symposium on Geometric Aspects of the Trace Formula that took place in Schloss Elmau, Germany, the volume contains both original research articles and articles that synthesize current knowledge and future directions in the field. The articles discuss topics such as the classification problem of representations of reductive groups, the structure of Langlands and Arthur packets, interactions with geometric representation theory, and conjectures on the global automorphic spectrum. Suitable for both graduate students and researchers, this volume presents the latest research in the field. Readers of the first volume Families of Automorphic Forms and the Trace Formula will find this a natural continuation of the study of the trace formula.
Author: Publisher: World Scientific ISBN: Category : Languages : en Pages : 1001
Author: Werner Müller Publisher: Springer ISBN: 3319414240 Category : Mathematics Languages : en Pages : 581
Book Description
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.
Author: Andrew Knightly Publisher: American Mathematical Soc. ISBN: 0821837397 Category : Mathematics Languages : en Pages : 392
Book Description
The Fourier coefficients of modular forms are of widespread interest as an important source of arithmetic information. In many cases, these coefficients can be recovered from explicit knowledge of the traces of Hecke operators. The original trace formula for Hecke operators was given by Selberg in 1956. Many improvements were made in subsequent years, notably by Eichler and Hijikata. This book provides a comprehensive modern treatment of the Eichler-Selberg/Hijikata trace formulafor the traces of Hecke operators on spaces of holomorphic cusp forms of weight $\mathtt{k >2$ for congruence subgroups of $\operatorname{SL 2(\mathbf{Z )$. The first half of the text brings together the background from number theory and representation theory required for the computation. Thisincludes detailed discussions of modular forms, Hecke operators, adeles and ideles, structure theory for $\operatorname{GL 2(\mathbf{A )$, strong approximation, integration on locally compact groups, the Poisson summation formula, adelic zeta functions, basic representation theory for locally compact groups, the unitary representations of $\operatorname{GL 2(\mathbf{R )$, and the connection between classical cusp forms and their adelic counterparts on $\operatorname{GL 2(\mathbf{A )$. Thesecond half begins with a full development of the geometric side of the Arthur-Selberg trace formula for the group $\operatorname{GL 2(\mathbf{A )$. This leads to an expression for the trace of a Hecke operator, which is then computed explicitly. The exposition is virtually self-contained, withcomplete references for the occasional use of auxiliary results. The book concludes with several applications of the final formula.
Author: Rajendra Bhatia Publisher: World Scientific ISBN: 9814462934 Category : Mathematics Languages : en Pages : 4137
Book Description
ICM 2010 proceedings comprises a four-volume set containing articles based on plenary lectures and invited section lectures, the Abel and Noether lectures, as well as contributions based on lectures delivered by the recipients of the Fields Medal, the Nevanlinna, and Chern Prizes. The first volume will also contain the speeches at the opening and closing ceremonies and other highlights of the Congress.
Author: Jonathan Pila Publisher: Cambridge University Press ISBN: 1009170325 Category : Mathematics Languages : en Pages : 267
Book Description
Explores the recent spectacular applications of point-counting in o-minimal structures to functional transcendence and diophantine geometry.
Author: Wee Teck Gan Publisher: World Scientific ISBN: 9811285837 Category : Mathematics Languages : en Pages : 449
Book Description
This is a collection of lecture notes from the minicourses in the December 2018 Langlands Workshop: Endoscopy and Beyond. The volume combines seven introductory chapters on trace formulas, local Arthur packets, and beyond endoscopy. It aims to introduce the endoscopy classification via a basic example of the trace formula for SL(2), explore the more refined questions on the structure of Arthur packets, and look beyond endoscopy following the suggestions of Langlands, Braverman-Kazhdan, Ngo, and Altuğ. The book is a helpful reference for undergraduates, postgraduates, and researchers.
Author: Paul Mezo Publisher: American Mathematical Soc. ISBN: 0821875655 Category : Mathematics Languages : en Pages : 106
Book Description
Suppose $G$ is a real reductive algebraic group, $\theta$ is an automorphism of $G$, and $\omega$ is a quasicharacter of the group of real points $G(\mathbf{R})$. Under some additional assumptions, the theory of twisted endoscopy associates to this triple real reductive groups $H$. The Local Langlands Correspondence partitions the admissible representations of $H(\mathbf{R})$ and $G(\mathbf{R})$ into $L$-packets. The author proves twisted character identities between $L$-packets of $H(\mathbf{R})$ and $G(\mathbf{R})$ comprised of essential discrete series or limits of discrete series.
Author: Clay Mathematics Institute. Summer School
Author: Clay Mathematics Institute. Summer School
Author: Werner Müller
Author: 
Author: Werner Müller
Author: Andrew Knightly
Author: Rajendra Bhatia
Author: 
Author: Jonathan Pila
Author: Wee Teck Gan
Author: Paul Mezo