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Lie groups, Lie algebras and their representations
Lie groups, Lie algebras and their representations
Spring 2023
Spring 2023
Given by: Erlend Grong (Bergen) and Dennis The (Tromsø)
Given by: Erlend Grong (Bergen) and Dennis The (Tromsø)
Course description
What will be taught: Introduction to matrix Lie groups and their Lie algebras. Associated representation theory, including root systems and weights. See more details at the end.
What you need to know before taking the course: Basic linear algebra (vector spaces, matrix multiplication, determinants, trace, etc) and basic abstract algebra (non-commutative groups).
Syllabus: Chapter 1-9 of Brian C. Hall “Lie Groups, Lie Algebras, and Representations”, Springer, ISSN 0072-5285 + separate notes.
Knowledge of manifolds will not be required, but some extra material will be provided to give some extra context for students familiar with the subject.
Taught at UiT as MAT-3810 and at UiB as MAT323. Students from UiT and UiB can take the exam at their own university.
A playlist of the videos is found below. Use the navigation buttons to change videos in the playlist. Notes are also below (more to follow soon).
Final Exam Information
LieTh-FinalExamSchedule.pngQuestions Oral exam.pdfCourse videos
Start up Mat323.pdfSemester plan and notes
Semester plan.pdfLieTheoryErlend.pdfLieTheory2023-CourseNotes.pdfweight-lattices.pdfTromsø gathering
Bergen gathering
Stochastic differential equations and their applications
Stochastic differential equations and their applications
Spring 2022
Spring 2022
Given by: Adrien Laurent and Sylvie Vega-Molino (both Bergen)
Given by: Adrien Laurent and Sylvie Vega-Molino (both Bergen)
This course gives an introduction to the basic aspects of continuous stochastic processes and stochastic integration.
A playlist of the videos is found below. Use the navigation buttons to change videos in the playlist. The room we are using unfortunately has a lot of echo, so it is advisable to use headphones and only listen to the left ear. Notes are available upon request by email.
Geometry of Riemannian homogeneous spaces
Geometry of Riemannian homogeneous spaces
Spring 2022
Spring 2022
Given by: professor Yurii Nikonorov (Vladikavkaz, RUSSIA)
Given by: professor Yurii Nikonorov (Vladikavkaz, RUSSIA)
This is a mini-course of 4 lectures that has been given in the spring. It gives an introduction to Riemannian homogeous spaces, their isometry groups and Killing vector fields, their Ricci curvature as well as focusing on some special classes of these homogeneous spaces.
You can find the slides for all lectures here and a playlist of videos.
HomSpacesTalks_new_slides_final.pdfPage updated
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