Related papers: In the beginning: Langlands' doctoral thesis
This is a draft version of an invited article for a forthcoming book `The genesis of Langlands Program', eds. Julia Mueller and Freydoon Shahidi, which will be published by Cambridge University Press. This is a survey of Langlands spectral…
This article gives some memories of Thomas Hales of his years at Princeton as a graduate student under Robert Langlands. It has been prepared for the book "The Genesis of Langlands' Program," edited by Dr. Julia Mueller and Dr. Freydoon…
These notes are very informal notes on the Langlands program. I had some pleasure in daring to ask colleagues to explain to me the importance of some of the recent results on Langlands program, so I thought I will record (to the best of my…
This is a report on the work of Robert Langlands, following his award of the Abel Prize in 2018. It includes his contributions to the general areas of Representation Theory, Automorphic Forms, Number Theory and Arithmetic Geometry. We have…
These lecture notes give an overview of recent results in geometric Langlands correspondence which may yield applications to quantum field theory. We start with a motivated introduction to the Langlands Program, including its geometric…
These are lecture notes (by the first author) from a course (by the second author) given over two extended semesters at the University of Sydney. The first part provides an introduction to the Langlands correspondence from an arithmetical…
This paper serves as the announcement of my program---a joke version of the Langlands Program. In connection with this program, I discuss an old hat puzzle, introduce a new hat puzzle, and offer a puzzle for the reader.
The Langlands Programme, formulated by Robert Langlands in the 1960s and since much developed and refined, is a web of interrelated theory and conjectures concerning many objects in number theory, their interconnections, and connections to…
We present topics in the Langlands Program to graduate students and a wider mathematically mature audience. We study both global and local aspects in characteristic zero as well as characteristic $p$. We look at modern approaches to the…
These notes give a statement of the "fundamental lemma," which is a conjectural identity between p-adic integrals that arises as part of the Langlands program.
These are informal notes written in 2007 that outline the local and global quantum Langlands program. (I decided to make them public in view of the revived interest in the subject.)
These lecture notes have been converted to a book titled Network Information Theory published recently by Cambridge University Press. This book provides a significantly expanded exposition of the material in the lecture notes as well as…
This is a preliminary version of the textbook on integrable systems. The work has been partly supported by Grant Nr.10/2006-RU, Austrian Academic Exchange Service \"OAD and Grant P20164-N18, Austrian Science Fund FWF
This is a survey lecture note on the applications of Langlands functoriality which were obtained recently by some people at the Langalnds school. This lecture was delivered at the Department of Mathematics, Kyoto University, Japan on June…
The aim of this paper is to present a self contained introduction to the Hubbard model and some of its applications.The paper consists of two parts: the first will introduce the basic notions of the Hubbard model starting from the…
We explain how the geometric Langlands program inspires some recent new prospectives of classical arithmetic Langlands program and leads to the solutions of some problems in arithmetic geometry.
The aim of this text is to provide a linguistically accessible, but comprehensive introduction into a variety of topics in dynamical systems and its applications. Whilst preliminary knowledge of dynamical systems is useful, it is not…
These notes provide a short, focused introduction to modelling stochastic gene expression, including a derivation of the master equation, the recovery of deterministic dynamics, birth-and-death processes, and Langevin theory. The notes were…
The purpose of this paper is to survey some of the important results on Langlands program, global fields, $D$-shtukas and finite shtukas which have influenced the development of algebra and number theory. It is intended to be selective…
These are the notes for an undergraduate course at the University of Edinburgh, 2021-2023. Assuming basic knowledge of ring theory, group theory and linear algebra, the notes lay out the theory of field extensions and their Galois groups,…