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Richard E Borcherds
United States
Приєднався 9 кві 2020
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.
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
This lecture is an overview of the complex representations of the group GL2(F), for various fields F.
Переглядів: 6 677
Відео
Mordell-Weil theorem
Переглядів 9 тис.4 місяці тому
This lecture sketches the proof of the Mordell Weil theorem, showing that the group of rational points on an elliptic curve or abelian variety is finitely generated.
Selberg trace formula
Переглядів 6 тис.4 місяці тому
This lecture gives an overview of the Selberg trace formula for SL_2(R).
Riemann mapping theorem
Переглядів 10 тис.5 місяців тому
The Riemann mapping theorem says that any proper simply connected open subset of the complex plane is isomorphic to the open unit disk. This lecture will sketch a proof of it.
Vinberg lecture part 4. Automorphic forms
Переглядів 2,5 тис.5 місяців тому
This lecture is part of a series which gives an expanded version of the Vinberg lecture on "Vinberg's algorithm and Kac-Moody algebras". This video is part 4 and describes the relation between hyperbolic reflection groups and automorphic forms. In the problems at the end I forgot to mention the problem of relating Bugaenko's cocompact reflection groups to automorphic forms. The paper by Sun, Wa...
Vinberg lecture part 3. Kac-Moody algebras
Переглядів 2,8 тис.5 місяців тому
This lecture is part of a series which gives an expanded version of the Vinberg lecture on "Vinberg's algorithm and Kac-Moody algebras". This video is part 3 and describes how to associate Lie algebras to some hyperbolic reflection groups. The original version of the Vinberg lecture is here: amathr.org/Borcherds-vinberg/ For the other lectures see ua-cam.com/play/PL8yHsr3EFj50MVfqGTj4VF3CBS-bJe...
Vinberg lecture part 2. The reflection group of II25,1
Переглядів 2,8 тис.6 місяців тому
This lecture is part of a series which gives an expanded version of the Vinberg lecture on "Vinberg's algorithm and Kac-Moody algebras". This video is part 2 and describes Conway and Sloane's interpretation of Vinberg's results Belolipetsky's survey paper is here arxiv.org/abs/1506.03111 Vinberg's paper can be found at mathweb.tifr.res.in/sites/default/files/publications/studies/SM_07.pdf The o...
Vinberg lecture part 1.Vinberg's algorithm
Переглядів 9 тис.6 місяців тому
This lecture is part of a series which gives an expanded version of the Vinberg lecture on "Vinberg's algorithm and Kac-Moody algebras". This video is part 1 and describes how Vinberg used his algorithm to calculate the reflection groups of some Lorentzian lattices. Vinberg's paper can be found at mathweb.tifr.res.in/sites/default/files/publications/studies/SM_07.pdf The original version of the...
Elliptic functions lecture 4. The sigma function
Переглядів 4 тис.6 місяців тому
This lecture is part of a series of lectures on elliptic functions. It covers the sigma function, the simplest theta function, and discusses line bundles over C/L. For the other lectures in the course see ua-cam.com/play/PL8yHsr3EFj50t6hrPaJ0GruNrN-xPcFTI.html
Borwein integrals
Переглядів 11 тис.6 місяців тому
This lecture is about the strange properties of Borwein integrals. For more details about them see www.ams.org/notices/200505/fea-borwein.pdf
Elliptic functions lecture 3. Jacobi functions
Переглядів 4,5 тис.6 місяців тому
This lecture is part of a series of lectures on elliptic functions. We describe the Jacobi functions sn, cn, dn, and show how to view them as sections of order 2 line bundles. For the other lectures in the course see ua-cam.com/play/PL8yHsr3EFj50t6hrPaJ0GruNrN-xPcFTI.html
Elliptic functions lecture 2
Переглядів 7 тис.6 місяців тому
This lecture is part of a series of lectures on elliptic functions. This lecture discusses the addition formula for the Weierstrass P function For the other lectures in the course see ua-cam.com/play/PL8yHsr3EFj50t6hrPaJ0GruNrN-xPcFTI.html
Elliptic functions 1. Weierstrass function.
Переглядів 28 тис.6 місяців тому
This lecture is part of a series of lectures on Elliptic functions This lecture covers the basic properties of the Weierstrass P function The pictures of elliptic functions in the video come from the book by Jahnke and Emde, which can be found here: archive.org/details/in.ernet.dli.2015.212842 For the other lectures in the course see ua-cam.com/play/PL8yHsr3EFj50t6hrPaJ0GruNrN-xPcFTI.html
Introduction to number theory lecture 53. Three calculators for number theorists
Переглядів 17 тис.2 роки тому
This lecture is part of my Berkeley math 115 course "Introduction to number theory" For the other lectures in the course see ua-cam.com/play/PL8yHsr3EFj53L8sMbzIhhXSAOpuZ1Fov8.html We discuss some of the number theory features in 3 pocket calculators: the Casio fx-300ES PLUS, the SwissMicros DM42, and the HP 50g. The free simulator for the DM42 can be downloaded from thomasokken.com/free42/ The...
Introduction to number theory lecture 52. Nonvanishing of L series at s=1.
Переглядів 7 тис.2 роки тому
This lecture is part of my Berkeley math 115 course "Introduction to number theory" For the other lectures in the course see ua-cam.com/play/PL8yHsr3EFj53L8sMbzIhhXSAOpuZ1Fov8.html We sketch how to show that Dirichlet L functions do not vanish at s=1, completing the proof of Dirichlet's theorem. The textbook is "An introduction to the theory of numbers" by Niven, Zuckerman, and Montgomery (5th ...
Introduction to number theory lecture 51. Proof of Dirichlet's theorem
Переглядів 8 тис.2 роки тому
Introduction to number theory lecture 51. Proof of Dirichlet's theorem
Introduction to number theory lecture 50. Dirichlet characters
Переглядів 7 тис.2 роки тому
Introduction to number theory lecture 50. Dirichlet characters
Introduction to number theory lecture 49. Dirichlet's theorem
Переглядів 9 тис.2 роки тому
Introduction to number theory lecture 49. Dirichlet's theorem
Introduction to number theory lecture 48 Proof of the prime number theorem
Переглядів 9 тис.2 роки тому
Introduction to number theory lecture 48 Proof of the prime number theorem
Introduction to number theory lecture 47. The prime number theorem
Переглядів 8 тис.2 роки тому
Introduction to number theory lecture 47. The prime number theorem
Introduction to number theory lecture 46. Products of Dirichlet series
Переглядів 3,5 тис.2 роки тому
Introduction to number theory lecture 46. Products of Dirichlet series
Introduction to number theory lecture 45 Dirichlet series
Переглядів 6 тис.2 роки тому
Introduction to number theory lecture 45 Dirichlet series
Introduction to number theory lecture 44 Pythagorean triangles
Переглядів 6 тис.2 роки тому
Introduction to number theory lecture 44 Pythagorean triangles
Introduction to number theory lecture 43 Gaussian integers
Переглядів 4,8 тис.2 роки тому
Introduction to number theory lecture 43 Gaussian integers
Introduction to number theory lecture 42. Examples of indefinite binary quadratic forms.
Переглядів 2,4 тис.2 роки тому
Introduction to number theory lecture 42. Examples of indefinite binary quadratic forms.
Introduction to number theory lecture 41: More examples of binary quadratic forms
Переглядів 2,4 тис.2 роки тому
Introduction to number theory lecture 41: More examples of binary quadratic forms
Introduction to number theory lecture 40. Examples of positive definite forms
Переглядів 3 тис.2 роки тому
Introduction to number theory lecture 40. Examples of positive definite forms
Introduction to number theory lecture 39: Equivalence of binary quadratic forms
Переглядів 3,9 тис.2 роки тому
Introduction to number theory lecture 39: Equivalence of binary quadratic forms
Introduction to number theory lecture 38. Binary quadratic forms
Переглядів 4,9 тис.2 роки тому
Introduction to number theory lecture 38. Binary quadratic forms
Introduction to number theory lecture 37 Continued fractions
Переглядів 6 тис.2 роки тому
Introduction to number theory lecture 37 Continued fractions