Related papers: Lecture on Langlands Functoriality Conjecture

This is a credit mini-course in French prepared for a Summer School at the University of Sherbrooke. The course consists of three one-and-half hour lectures and three credit exercises for a class of advanced graduate students.

This article is a summary of four introductory lectures on ``Neutrino Experiments,'' given at the 2006 TASI summer school. The purposes were to sketch out the present questions in neutrino physics and to discuss the experimental challenges…

These are the lecture notes from a five-hour mini-course given at the Winter School on Galois Theory held at the University of Luxembourg in February 2012. Their aim is to give an overview of Serre's modularity conjecture and of its proof…

In this note, we establish the validity of a conjecture recently proposed in Mathematics Magazine and connect it to the existing interesting results

These are expanded lecture notes for the summer school on Berkovich spaces that took place at the Institut de Math\'ematiques de Jussieu, Paris in 2010. They serve to illustrate some techniques and results from the dynamics on…

These lectures notes are based on courses given at National Taiwan University, National Chiao-Tung University, and National Tsing Hua University in the spring term of 2015. Although the course was offered primarily for graduate students,…

The goal of these notes is to give a short introduction to Fukaya categories and some of their applications. The first half of the text is devoted to a brief review of Lagrangian Floer (co)homology and product structures. Then we introduce…

This paper presents an extended version of lecture notes for an introductory course on Berkovich analytic spaces that I gave in 2010 at Summer School "Berkovich spaces" at Institut de Mathmatiques de Jussieu.

This is an informal paper presenting historical results around the recent paper of the author about Lang's Conjecture and torsion of elliptic curves. This paper also discusses a few aspects of the proof.

Notes from lectures given at the Autumn School on Algebraic and Arithmetic Geometry at the Johannes Gutenberg-Universit\"at Mainz in October 2017.

These are notes of a series of lectures on sieves, presented during the Special Activity in Analytic Number Theory, at the Max-Planck Institute for Mathematics in Bonn, during the period January--June 2002.

This workshop about triangulations of manifolds in computational geometry and topology was held at the 2014 CG-Week in Kyoto, Japan. It focussed on computational and combinatorial questions regarding triangulations, with the goal of…

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.

This is a survey of open problems in different parts of combinatorial and additive number theory. The paper is based on lectures at the Centre de Recerca Matematica in Barcelona on January 23 and January 25, 2008.

This report on the topics in the title was written for a lecture series at the Southwestern Center for Arithmetic Algebraic Geometry at the University of Arizona.It may serve as an introduction to certain conjectural relations between…

A summary of the recent experimental, phenomenological and theoretical results presented in the Structure Functions working group at DIS2012 workshop.

These are notes related to a 12-hour course of lectures given at the Centre de Recerca Mathem\`atica near Barcelona in February, 2010. The aim of the course was to explain results on curves and their Jacobians over function fields, with…

These are lectures notes for a 4h30 mini-course held in Ulaanbaatar, National University of Mongolia, August 5-7th 2015, at the summer school "Stochastic Processes and Applications". It aims at presenting an introduction to basic results of…

These are lecture notes from the Austral Winter School on Microlocal Analysis and Non-elliptic Fredholm Theory, held at the Australian National University, Canberra, June 30 -- July 11, 2025.

Fracture functions and their evolution equations are reviewed. Some phenomenological applications are briefly discussed.