The Biggest Project in Modern Mathematics
In a 1967 letter to the number theorist André Weil, a 30-year-old mathematician named Robert Langlands outlined striking conjectures that predicted a correspondence between two objects from completely different fields of math. The Langlands program was born. Today, it's one of the most amb
From playlist Explainers
Bao Chau Ngo - 3/3 Orbital integrals, moduli spaces and invariant theory
The goal of these lectures is to sketch a general framework to study orbital integrals over equal characteristic local fields by means of moduli spaces of Hitchin type following the main lines of the proof of the fundamental lemma for Lie algebras. After recalling basic elements of the pro
From playlist 2022 Summer School on the Langlands program
Bao Chau Ngo - 1/3 Orbital integrals, moduli spaces and invariant theory
The goal of these lectures is to sketch a general framework to study orbital integrals over equal characteristic local fields by means of moduli spaces of Hitchin type following the main lines of the proof of the fundamental lemma for Lie algebras. After recalling basic elements of the pro
From playlist 2022 Summer School on the Langlands program
Robert Langlands - The Abel Prize interview 2018
00:17 The esthetics and beauty of mathematics 05:13 Creative moments and revelations: are numbers beautiful or are they satisficing 07:55 Langlands background from British Columbia and “lack of academic ambition” 10:30 Langlands on why he chose mathematics after all and science interest 1
From playlist The Abel Prize Interviews
Brief introduction to the Langlands program
Popular presentation by Alex Bellos on the Langlands program, by Robert Langlands. This clip is a part of the Abel Prize Announcement 2018. You can see the full announcement here: https://youtu.be/6Zob3MeMIvc You can view Alex Bellos own YouTube channel here: https://www.youtube.com
From playlist Popular presentations
Sam Raskin - 2/2 What does geometric Langlands mean to a number theorist?
Sam Raskin (Univ. Texas)
From playlist 2022 Summer School on the Langlands program
Concluding Remarks - Peter Sarnak
Automorphic Forms Peter Sarnak Institute for Advanced Study April 7, 2001 Concepts, Techniques, Applications and Influence April 4, 2001 - April 7, 2001 Support for this conference was provided by the National Science Foundation Conference Page: https://www.math.ias.edu/conf-automorph
From playlist Mathematics
Elementary Introduction to the Langlands Program, by Edward Frenkel (Part 1) [2015]
"Do we discover mathematics or do we invent it?" One of the most fascinating and important developments in mathematics in the last 50 years is the Langlands Program, a collection of ideas that provides a grand unification of many areas of mathematics. In September 2015, Edward Frenkel g
From playlist Number Theory
Can p-adic integrals be computed? - Thomas Hales
Automorphic Forms Thomas Hales April 6, 2001 Concepts, Techniques, Applications and Influence April 4, 2001 - April 7, 2001 Support for this conference was provided by the National Science Foundation Conference Page: https://www.math.ias.edu/conf-automorphicforms Conference Agena: ht
From playlist Mathematics
Basic Mathematics for Everyone
This is Basic Mathematics by Serge Lang. Here is the book: https://amzn.to/3GN97j3 This is my affiliate link. As an Amazon Associate I earn from qualifying purchases.
From playlist Books
Geometry and the fundamental lemma - Robert MacPherson
Automorphic Forms Robert MacPherson Institute for Advanced Study April 6, 2001 Concepts, Techniques, Applications and Influence April 4, 2001 - April 7, 2001 Support for this conference was provided by the National Science Foundation Conference Page: https://www.math.ias.edu/conf-auto
From playlist Mathematics
Michael Harris "Shimura varieties and the search for a Langlands transform" [2012]
Michael Harris, Institut de mathématiques de Jussieu "Shimura varieties and the search for a Langlands transform" The Langlands reciprocity conjectures predict the existence of a correspondence between certain classes of representations of Galois groups of number fields and automorphic re
From playlist Number Theory
The Abel Prize announcement 2018 - Robert Langlands
0:52 Introduction by Alex Bellos, British writer, and science communicator 2:26 The Abel Prize announced by Ole Sejersted, President of The Norwegian Academy of Science and Letters 1:38 Citation by John Rognes, Chair of the Abel committee 7:18 Popular presentation of the prize winners work
From playlist The Abel Prize announcements
Philsang Yoo: Langlands duality and quantum field theory
Abstract: It is believed that certain physical duality underlies various versions of Langlands duality in its geometric incarnation. By setting up a mathematical model for relevant physical theories, we suggest a program that enriches mathematical subjects such as geometric Langlands theor
From playlist Algebra
Michael Harris, Tony Feng - 2/3 Derived Aspects of the Langlands Program
We discuss ways in which derived structures have recently emerged in connection with the Langlands correspondence, with an emphasis on derived Galois deformation rings and derived Hecke algebras. Michael Harris (Columbia Univ.) Tony Feng (MIT)
From playlist 2022 Summer School on the Langlands program
Higgs bundles, harmonic maps, and applications by Richard Wentworth
Higgs bundles URL: http://www.icts.res.in/program/hb2016 DATES: Monday 21 Mar, 2016 - Friday 01 Apr, 2016 VENUE : Madhava Lecture Hall, ICTS Bangalore DESCRIPTION: Higgs bundles arise as solutions to noncompact analog of the Yang-Mills equation. Hitchin showed that irreducible solutio
From playlist Higgs Bundles
Robert Langlands - "The Elephant" [2001]
Conference on Automorphic Forms: Concepts, Techniques, Applications and Influence April 4, 2001 - April 7, 2001 https://video.ias.edu/Automorphic-Forms
From playlist Number Theory
Yiannis Sakellaridis - 2/2 Local and Global Questions “Beyond Endoscopy”
The near-completion of the program of endoscopy poses the question of what lies next. These talks will take a broad view of ideas beyond the program of endoscopy, highlighting the connections among them, and emphasizing the relationship between local and global aspects. Central among thos
From playlist 2022 Summer School on the Langlands program
The Practice of Mathematics - Part 5
The Practice of Mathematics Robert P. Langlands Institute for Advanced Study November 23, 1999 Robert P. Langlands, Professor Emeritus, School of Mathematics. There are several central mathematical problems, or complexes of problems, that every mathematician who is eager to acquire some
From playlist Mathematics
Peter Sarnak "Some analytic applications of the trace formula before and beyond endoscopy" [2012]
2012 FIELDS MEDAL SYMPOSIUM Date: October 17, 2012 11.00am-12.00pm We describe briefly some of the ways in which the trace formula has been used in a non comparative way. In particular we focus on families of automorphic L-functions symmetries associated with them which govern the distrib
From playlist Number Theory