The Langlands Program is among the most important mathematical frameworks of our time. A Langlands Program for Covering Groups? Wee Teck Gan Abstract.

The book is divided on the studied aspects in integral geometry and that are of interest in field theory, at least, to the solution or obtaining of integrals to the field equations corresponding to the moduli stacks planted. It is a way of organizing number theoretic data in terms of analytic objects. Give it a shot. The geometric Langlands correspondence for complex algebraic curves, the way it is currently understood, differs from the original Langlands correspondence for number fields in that it is formulated in terms of sheaves rather than functions in the intermediate case of curves over finite fields, both formulations are possible.

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Geometric Langlands program tries to achieve a similar conceptual uni cation in the case of function elds. The Langlands program has to do with number theory. The Langlands program is the name generally given to a highly influential vision unifying two different areas of mathematics, referring to a set of ideas first brought to light by Robert Langlands at the end of the s. He has also published a number of surveys aimed at mathematicians. Introduction Robert P. The construction will be completed in late with four new pools, refurbished toilets - and the new entrance building and program pool.

The focus of the trimester will be on some manifestations of this program, including: Course Notes: Geometric Langlands and Derived Algebraic Geometry My set of handwritten course notes for the lecture series of Prof. Langlands duality, D-branes and quantization. Early sources, like the Rhind Papyrus, writ-ten around BCE by Ahmes, contains methods for solving linear equations. Shuichiro Takeda's research interests lie in the theory of automorphic representations, which is sometimes called the Langlands program.

In mathematics, the Langlands program is a web of far-reaching and influential conjectures that relate Galois groups in algebraic number theory to automorphic forms and representation theory of algebraic groups over local fields and adeles. The Langlands program aims to relate systems of polynomial equations with integer coefficients to automorphic forms, i. Sponsosrship for this workshop has been provided by: Construction has commenced on the Langlands Park Memorial Pool upgrade.

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The research of Fedorov is about the Langlands duality for Hitchin systems, the Langlands program with ramifications, and motivic classes of moduli spaces occurring in Langlands program. I will describe some of the history of, progress in, and future prospects for the p-adic Langlands program.

Each topics is expected to be of developed independently, while the overall plan will encompass most of the ideas and tools underlying research in the p-adic local Langlands program: Galois deformation spaces, automorphic forms, modular representation theory, classical Langlands conjectures.

Langlands of the Institute for Advanced Study, Princeton, USA for his visionary program relating representation Preproposal: The Langlands program: extensions and computations 1 Introduction In this proposal, we advance fundamental research in several mathematical areas brought together by the Langlands program. The trace formula is a The lectures went from elementary topics such as Pythagoras theorem, prime numbers and symmetries to Fermat's last theorem and the general Langlands conjectures, and to the recent work connecting Let me give it a quick go.

The goal of this book is to make entering into the subject a little easier.

## Arun Ram: Oeuvres

Langlands suggested a far-reaching generalization of what was already known concerning a deep connection between… Read More; Ngo Bao Chau The Langlands program has seen a lot of progress in the past. The new program pool will remain open for programs and limited public access.

How would I fix this. In the Langlands Program, one development is a very general trace formula due to James Arthur and his collaborators. Statement of Conjecture 2 2. At rst sight these are very simple objects. The school will consist in a series of specialized courses at graduate or early postgraduate level. The p-adic Langlands program is an exciting recent generalisation of the Langlands program, which has already led to major results innumber theory, in particular the proofs of the two-dimensionalFontaine—Mazurconjecture by Emertonand Kisin [2],[4].

Langlands, Shimura varieties and the Selberg trace formula , Canad. Notes from the Princeton workshop on the Langlands correspondence and physics Contents 1. A general reciprocity theorem for all orders which covered all other known reciprocity theorems when proved by E. A grand unified theory of mathematics which includes the search for a generalization of Artin reciprocity known as Langlands reciprocity to non-Abelian Galois extensions of number fields.

### 1st Edition

May 4 - August 21, Thus, to some extent, we will try to follow the same path. The conjectures of the Langlands program have served to guide deep research in number Langlands program is a mathematical philosophy and area of mathematical research. It is an attempt to unify many different areas of mathematics, such as representation theory and number theory. I'll be quite vague and restrict myself to special cases some of the time. We start with a motivated introduction to the Langlands Program, including its geometric reformulation, addressed primarily to physicists.

For abelian groups, Langlands duality is closely connected to the much more classical Pontryagin duality in Fourier analysis. Introduction to the Langlands Program. For example, an important first instance of the Langlands program is the modularity theorem for elliptic curves over the rational numbers, an essential ingredient in the proof of Fermat's last The Langlands Program Seminar Tian An Wong July 29, Abstract These are notes from the ongoing Langlands Program Seminar organized since Spring It recounts the story of the early years of Langlands and the first years of his mathematical career leading up to his letter to Andre Weil in which he outlines his conjectures, which would become known as the Langlands program.

### Publications and Preprints

James Arthur's advanced research resulted in generalizations of Langlands' conjectures. Number theory consists primarily in the study of the ring of integers Z and the eld of rational numbers Q. From browsing my publications, you might notice that my research area changed after my PhD. The Langlands program is not at all what string theory is. He graduated from the University of British Columbia with an undergraduate degree in and an M.

The conjectures of the Langlands program have served to guide deep research in number MSRI Summer School: Automorphic forms and the Langlands program Ed Belk Lectures 1 mod 4 , Jesse Han Lectures 2 mod 4 , Sheela Devadas Lectures 3 mod 4 , The p-adic Langlands program is an exciting recent generalisation of the Langlands program, which has already led to major results innumber theory, in particular the proofs of the two-dimensionalFontaine—Mazurconjecture by Emertonand Kisin [2],[4].

Langlands' works. Witten and others are developing geometric Langlands program which is a generalization of Langlands program from number fields to holomorphic function fields defined at 2-dimensional Riemann surfaces.

Another global aspect is related to the modu-lar degrees of freedom of the partonic 2-surface, or more precisely to the regions of partonic 2-surface associated with braids. A kind of Grand Unified Theory of Math.

Emerton gets by with much weaker hypotheses at p, using [BE]. The goal of the program is to bring together experts researching in automorphic kernel functions to foster interaction, collaboration and the exchange of ideas on the new approaches. The nal section looks at This special school aims at giving a thorough overview of the current state of research in this field. Its tamely rami ed case has not been explicitly studied in detail, but the current state of knowledge should allow to bring it to the same status as the unrami ed case. The Langlands program is a hugely ambitious project to bridge harmonic analysis and number theory, initially by showing deep connections between automorphic forms and Galois groups.

## Group Characters, Symmetric Functions,and the Hecke Algebra by David M. Goldschmidt

A detailed investigation of Eisenstein series and their constant terms was, in part, what led Langlands to his conjectures. The Langlands Program An overview of these modular forms. This article is an introduction to automorphic forms on the adeles of a linear. And still today, equations and their solutions Langlands conjecture. The Langlands program describes the representation theory of many important algebraic groups. This short article about mathematics can be made longer. In studying these conjectures, integrals on p-adic groups arise that may be expressed in terms of characters of representations of complex Lie groups.

Hi, I'm a high school student and I've been learning number theory and higher mathematics on my own for the past couple of years. Grojnowski indicates that, according to Langlands, the representations of a reductive group are described in terms of a the Langlands dual group and b some Galois group. It depends a lot what you mean by 'understand'. Home Questions Tags Users Unanswered. Representation Theory Symmetric Group Book? Ask Question. Asked 4 years, 11 months ago.