Lecture
Introduction to the Langlands program

Introduction to the Langlands program: Lecture

Prof. Dr. Timo Richarz

Time and Place

Lecture: Tuesdays, 9:50-11:30

Starting: October 13, 2026

Ending: February 09, 2027

No lectures on October 27, December 15, 22, 29 and January 5 (total of 13 lectures)

Hybrid: Room S215 401 and via Zoom (654 2542 5948, largest six digit number)

Course Description

The Langlands program is a far-reaching network of conjectures linking number theory, representation theory, and algebraic geometry. Among other things, it predicts correspondeces between number-theoretically defined L-functions and automorphic L-functions arising from representation theory, thereby generalizing Artin reciprocity in class field theory. The aim of this course is to formulate the Langlands conjectures and to illustrate them through examples.

  • Lecture Notes by Johannes Anschütz: https://janschuetz.perso.math.cnrs.fr/skripte/lecture_notes_arithlang.pdf
  • Chao Li‘s notes of a course taught by Jack Thorne: https://www.math.columbia.edu/~chaoli/docs/AutomorphicForm.html
  • J. Getz, H. Hahn, An Introduction to Automorphic Representations, avaiable under https://sites.duke.edu/jgetz/files/2022/04/Graduate_Text.pdf
  • R. Langlands, A little bit of number theory: https://publications.ias.edu/sites/default/files/a-little-bit-of-number-theory_rpl_7.pdf
  • J. Bernstein, S. Gelbart, An Introduction to the Langlands Program, Birkhäuser (2004).
  • J. Mueller, F. Shahidi: The genesis of the Langlands program, https://www.cambridge.org/core/books/the-genesis-of-the-langlands-program/FDE4BFC05DF4074D04520FDF9CC67A4E

Exam

This is an oral exam. If you would like to take it, please contact the lecturer directly by email.