Kaisa_2012_3_photo by Veikko Somerpuro

This topics course concerns the study of Rademacher's differentiation theorem in the setting of general metric spaces. Specifically, we will present a new proof of Cheeger's celebrated generalisation of Rademacher's theorem when the domain is replaced with a metric measure space that satisfies a Poincaré inequality.

This proof relies on recently developed techniques in analysis on metric spaces. We will also cover more standard aspects of this theory, in particular Gromov-Hausdorff convergence and weak tangent spaces.

There are very few prerequisites. You must know basic measure theory (e.g. Egorov and Lusin's theorems) and have an interest in analysis. All other requirements will be covered.

Lecture notes and exercises are here https://davidbate.gitlab.io/rademachers-theorem-and-alberti-representati...

Enrol
13.8.2018 at 09:00 - 13.12.2018 at 23:59

Timetable

Lectures are on Tuesdays 12-14 and Thursdays 10-12 and there is an exercise session on Tuesdays 10-12.

DateTimeLocation
Tue 4.9.2018
10:15 - 12:00
Tue 4.9.2018
12:15 - 14:00
Thu 6.9.2018
10:15 - 12:00
Tue 11.9.2018
10:15 - 12:00
Tue 11.9.2018
12:15 - 14:00
Thu 13.9.2018
10:15 - 12:00
Tue 18.9.2018
10:15 - 12:00
Tue 18.9.2018
12:15 - 14:00
Thu 20.9.2018
10:15 - 12:00
Tue 25.9.2018
10:15 - 12:00
Tue 25.9.2018
12:15 - 14:00
Thu 27.9.2018
10:15 - 12:00
Tue 2.10.2018
10:15 - 12:00
Tue 2.10.2018
12:15 - 14:00
Thu 4.10.2018
10:15 - 12:00
Tue 9.10.2018
10:15 - 12:00
Tue 9.10.2018
12:15 - 14:00
Thu 11.10.2018
10:15 - 12:00
Tue 16.10.2018
10:15 - 12:00
Tue 16.10.2018
12:15 - 14:00
Thu 18.10.2018
10:15 - 12:00
Tue 30.10.2018
10:15 - 12:00
Tue 30.10.2018
12:15 - 14:00
Thu 1.11.2018
10:15 - 12:00
Tue 6.11.2018
10:15 - 12:00
Tue 6.11.2018
12:15 - 14:00
Thu 8.11.2018
10:15 - 12:00
Tue 13.11.2018
10:15 - 12:00
Tue 13.11.2018
12:15 - 14:00
Thu 15.11.2018
10:15 - 12:00
Tue 20.11.2018
10:15 - 12:00
Tue 20.11.2018
12:15 - 14:00
Thu 22.11.2018
10:15 - 12:00
Tue 27.11.2018
10:15 - 12:00
Tue 27.11.2018
12:15 - 14:00
Thu 29.11.2018
10:15 - 12:00
Tue 4.12.2018
10:15 - 12:00
Tue 4.12.2018
12:15 - 14:00
Tue 11.12.2018
10:15 - 12:00
Tue 11.12.2018
12:15 - 14:00
Thu 13.12.2018
10:15 - 12:00

Description

Optional course.

Master's Programme in Mathematics and Statistics is responsible for the course.

The course belongs to the Mathematics and Applied mathematics module.

The course is available to students from other degree programmes.

Bachelor studies

Geometric properties of metric spaces

Recommended time/stage of studies for completion: 1. or 2. year

Term/teaching period when the course will be offered: varying

The actual content may vary, including eg. notions of curvature in metric spaces.

Lectures and exercise classes

Exam and excercises, Course will be graded with grades 1-5

Exam, other methods will be described later