From group actions and metrics to singularities and all the way back
Seminar in Mathematics
Abstract: In this talk, I will explain how certain singularities arise from very elementary considerations encountered in everyday life. Reasonably enlarging this realm of singularities, we can keep some of their good properties. This in turn leads to a deeper understanding of the underlying elementary concepts such as group actions and metrics. In the end, the investigation of the fundamental groups of our singular spaces leads to degenerate (or 'odd') Riemannian metrics, which may fail to measure angles but still allow to measure distances everywhere. Particularly interesting are the flows of the corresponding 'odd' vector fields, which generalize usual nonsingular vector fields.
Abstract: In this talk, I will explain how certain singularities arise from very elementary considerations encountered in everyday life. Reasonably enlarging this realm of singularities, we can keep some of their good properties. This in turn leads to a deeper understanding of the underlying elementary concepts such as group actions and metrics. In the end, the investigation of the fundamental groups of our singular spaces leads to degenerate (or 'odd') Riemannian metrics, which may fail to measure angles but still allow to measure distances everywhere. Particularly interesting are the flows of the corresponding 'odd' vector fields, which generalize usual nonsingular vector fields.
Practical information
- Informed public
- Free
- This event is internal
Organizer
- Institute of Mathematics
Contact
- Prof. Maryna Viazovska, Director