Richard E Borcherds

Algebraic geometry

Number theory

Lie groups

Galois theory

This is mostly mathematics lectures for graduate courses on algebraic geometry, commutative algebra, and group/rings fields. There are also a few math talks at an undergraduate or high school level and a few short courses on other topics such as complex analysis, theory of numbers, modular forms, category theory, representation theory.

For the current list of courses, see the playlists page for this channel.


For anyone who wants to copy the format of the lectures, I'm using a program called OBS studio with a logitech webcam and a document camera and a yeti microphone. I use sketchpad for the thumbnails.

Representations of GL2

Representations of GL2
Mordell-Weil theorem

Mordell-Weil theorem
Selberg trace formula

Selberg trace formula
Теорема Римана об отображении

Теорема Римана об отображении
Vinberg lecture part 4. Automorphic forms

Vinberg lecture part 4. Automorphic forms
Лекция Винберга часть 3. Алгебры Каца-Муди

Лекция Винберга часть 3. Алгебры Каца-Муди
Vinberg lecture part 2. The reflection group of II25,1

Vinberg lecture part 2. The reflection group of II25,1
Vinberg lecture part 1.Vinberg's algorithm

Vinberg lecture part 1.Vinberg's algorithm
Elliptic functions lecture 4. The sigma function

Elliptic functions lecture 4. The sigma function
Borwein integrals

Borwein integrals
Elliptic functions lecture 3. Jacobi functions

Elliptic functions lecture 3. Jacobi functions
Elliptic functions lecture 2

Elliptic functions lecture 2
Elliptic functions 1. Weierstrass function.

Elliptic functions 1. Weierstrass function.
Введение в теорию чисел, лекция 53. Три калькулятора для специалистов по теории чисел

Введение в теорию чисел, лекция 53. Три калькулятора для специалистов по теории чисел
Introduction to number theory lecture 52. Nonvanishing of L series at s=1.

Introduction to number theory lecture 52. Nonvanishing of L series at s=1.
Introduction to number theory lecture 51. Proof of Dirichlet's theorem

Introduction to number theory lecture 51. Proof of Dirichlet's theorem
Introduction to number theory lecture 50. Dirichlet characters

Introduction to number theory lecture 50. Dirichlet characters
Introduction to number theory lecture 49. Dirichlet's theorem

Introduction to number theory lecture 49. Dirichlet's theorem
Introduction to number theory lecture 48 Proof of the prime number theorem

Introduction to number theory lecture 48 Proof of the prime number theorem
Introduction to number theory lecture 47. The prime number theorem

Introduction to number theory lecture 47. The prime number theorem
Introduction to number theory lecture 46. Products of Dirichlet series

Introduction to number theory lecture 46. Products of Dirichlet series
Introduction to number theory lecture 45 Dirichlet series

Introduction to number theory lecture 45 Dirichlet series
Introduction to number theory lecture 44 Pythagorean triangles

Introduction to number theory lecture 44 Pythagorean triangles
Introduction to number theory lecture 43 Gaussian integers

Introduction to number theory lecture 43 Gaussian integers
Introduction to number theory lecture 42. Examples of indefinite binary quadratic forms.

Introduction to number theory lecture 42. Examples of indefinite binary quadratic forms.
Introduction to number theory lecture 41: More examples of binary quadratic forms

Introduction to number theory lecture 41: More examples of binary quadratic forms
Introduction to number theory lecture 40. Examples of positive definite forms

Introduction to number theory lecture 40. Examples of positive definite forms
Introduction to number theory lecture 39: Equivalence of binary quadratic forms

Introduction to number theory lecture 39: Equivalence of binary quadratic forms
Introduction to number theory lecture 38. Binary quadratic forms

Introduction to number theory lecture 38. Binary quadratic forms
Introduction to number theory lecture 37 Continued fractions

Introduction to number theory lecture 37 Continued fractions