MATJ5114 MA2: On the Geometry of Rectifiable and Purely Unrectifiable Subsets of a Metric Space (JSS32) (2 cr)
Study level:
Postgraduate studies
Grading scale:
Pass - fail
Language:
English
Responsible organisation:
Faculty of Mathematics and Science
Curriculum periods:
2023-2024
Description
- Rectifiability in metric spaces: basic definitions and Kirchheim's description of rectifiable metric spaces. Comparison to classical rectifiability.
- Sufficient conditions for rectifiability: bi-Lipschitz decompositions of functions; rectifiability from topology; Alberti representations.
- Gromov--Hausdorff convergence of metric measure spaces and the various definitions of tangent metric measure spaces.
- Characterising rectifiable metric spaces in terms of flat tangent spaces.
Learning outcomes
The main objective is to give a concise introduction to the theory of rectifiability in an arbitrary metric space and to draw comparisons to classical rectifiability in Euclidean space. The students will also become familiar with concepts in analysis on metric spaces and Gromov--Hausdorff convergence.
Description of prerequisites
Standard theory of undergraduate analysis and measure theory
Completion methods
Method 1
Description:
Lectures and exercises. During the exercise sessions, participants discuss homework problems and course contents with the lecturer and course assistants. Room is reserved Mon-Fri at 4-5 pm for participants who would like to work on the exercises.
Select all marked parts
Parts of the completion methods
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Participation in teaching (2 cr)
Type:
Participation in teaching
Grading scale:
Pass - fail
Language:
English
Study methods:
Lectures and exercises. During the exercise sessions, participants discuss homework problems and course contents with the lecturer and course assistants. Room is reserved Mon-Fri at 4-5 pm for participants who would like to work on the exercises.