Around Langlands Correspondences

Around Langlands Correspondences
Author: Farrell Brumley
Publisher: American Mathematical Soc.
Total Pages: 394
Release: 2017
Genre: Mathematics
ISBN: 147043573X

Presents, through a mix of research and expository articles, some of the fascinating new directions in number theory and representation theory arising from recent developments in the Langlands program. Special emphasis is placed on nonclassical versions of the conjectural Langlands correspondences, where the underlying field is no longer the complex numbers.

Langlands Correspondence for Loop Groups

Langlands Correspondence for Loop Groups
Author: Edward Frenkel
Publisher: Cambridge University Press
Total Pages: 5
Release: 2007-06-28
Genre: Mathematics
ISBN: 0521854431

The first account of local geometric Langlands Correspondence, a new area of mathematical physics developed by the author.

The Local Langlands Conjecture for GL(2)

The Local Langlands Conjecture for GL(2)
Author: Colin J. Bushnell
Publisher: Springer Science & Business Media
Total Pages: 352
Release: 2006-08-29
Genre: Mathematics
ISBN: 354031511X

The Local Langlands Conjecture for GL(2) contributes an unprecedented text to the so-called Langlands theory. It is an ambitious research program of already 40 years and gives a complete and self-contained proof of the Langlands conjecture in the case n=2. It is aimed at graduate students and at researchers in related fields. It presupposes no special knowledge beyond the beginnings of the representation theory of finite groups and the structure theory of local fields.

Motives

Motives
Author:
Publisher: American Mathematical Soc.
Total Pages: 694
Release: 1994-02-28
Genre: Mathematics
ISBN: 0821827987

'Motives' were introduced in the mid-1960s by Grothendieck to explain the analogies among the various cohomology theories for algebraic varieties, and to play the role of the missing rational cohomology. This work contains the texts of the lectures presented at the AMS-IMS-SIAM Joint Summer Research Conference on Motives, held in Seattle, in 1991.

Representations of Reductive p-adic Groups

Representations of Reductive p-adic Groups
Author: Anne-Marie Aubert
Publisher: Springer
Total Pages: 297
Release: 2019-04-16
Genre: Mathematics
ISBN: 9811366284

This book consists of survey articles and original research papers in the representation theory of reductive p-adic groups. In particular, it includes a survey by Anne-Marie Aubert on the enormously influential local Langlands conjectures. The survey gives a precise and accessible formulation of many aspects of the conjectures, highlighting recent refinements, due to the author and her collaborators, and their current status. It also features an extensive account by Colin Bushnell of his work with Henniart on the fine structure of the local Langlands correspondence for general linear groups, beginning with a clear overview of Bushnell–Kutzko’s construction of cuspidal types for such groups. The remaining papers touch on a range of topics in this active area of modern mathematics: group actions on root data, explicit character formulas, classification of discrete series representations, unicity of types, local converse theorems, completions of Hecke algebras, p-adic symmetric spaces. All meet a high level of exposition. The book should be a valuable resource to graduate students and experienced researchers alike.

Love and Math

Love and Math
Author: Edward Frenkel
Publisher: Basic Books
Total Pages: 314
Release: 2013-10-01
Genre: Mathematics
ISBN: 0465069959

An awesome, globe-spanning, and New York Times bestselling journey through the beauty and power of mathematics What if you had to take an art class in which you were only taught how to paint a fence? What if you were never shown the paintings of van Gogh and Picasso, weren't even told they existed? Alas, this is how math is taught, and so for most of us it becomes the intellectual equivalent of watching paint dry. In Love and Math, renowned mathematician Edward Frenkel reveals a side of math we've never seen, suffused with all the beauty and elegance of a work of art. In this heartfelt and passionate book, Frenkel shows that mathematics, far from occupying a specialist niche, goes to the heart of all matter, uniting us across cultures, time, and space. Love and Math tells two intertwined stories: of the wonders of mathematics and of one young man's journey learning and living it. Having braved a discriminatory educational system to become one of the twenty-first century's leading mathematicians, Frenkel now works on one of the biggest ideas to come out of math in the last 50 years: the Langlands Program. Considered by many to be a Grand Unified Theory of mathematics, the Langlands Program enables researchers to translate findings from one field to another so that they can solve problems, such as Fermat's last theorem, that had seemed intractable before. At its core, Love and Math is a story about accessing a new way of thinking, which can enrich our lives and empower us to better understand the world and our place in it. It is an invitation to discover the magic hidden universe of mathematics.

The Langlands Classification and Irreducible Characters for Real Reductive Groups

The Langlands Classification and Irreducible Characters for Real Reductive Groups
Author: J. Adams
Publisher: Springer Science & Business Media
Total Pages: 331
Release: 2012-12-06
Genre: Mathematics
ISBN: 146120383X

This monograph explores the geometry of the local Langlands conjecture. The conjecture predicts a parametrizations of the irreducible representations of a reductive algebraic group over a local field in terms of the complex dual group and the Weil-Deligne group. For p-adic fields, this conjecture has not been proved; but it has been refined to a detailed collection of (conjectural) relationships between p-adic representation theory and geometry on the space of p-adic representation theory and geometry on the space of p-adic Langlands parameters. This book provides and introduction to some modern geometric methods in representation theory. It is addressed to graduate students and research workers in representation theory and in automorphic forms.

Representation Theory and Complex Analysis

Representation Theory and Complex Analysis
Author: Michael Cowling
Publisher: Springer Science & Business Media
Total Pages: 400
Release: 2008-02-27
Genre: Mathematics
ISBN: 3540768912

Six leading experts lecture on a wide spectrum of recent results on the subject of the title. They present a survey of various interactions between representation theory and harmonic analysis on semisimple groups and symmetric spaces, and recall the concept of amenability. They further illustrate how representation theory is related to quantum computing; and much more. Taken together, this volume provides both a solid reference and deep insights on current research activity.