![]() |
![]() |
University of Birmingham > Talks@bham > Theoretical computer science seminar > Magnitude of Metric Spaces
Magnitude of Metric SpacesAdd to your list(s) Download to your calendar using vCal
If you have a question about this talk, please contact Paul Taylor. The notion of Euler characteristic is found all across mathematics, with the notions of dimension and cardinality being special cases. Notions of Euler characteristic exist for finite sets, finite groups and finite posets. Tom Leinster generalized these three to a notion of Euler characteristic for finite categories. Then he generalized again to finite enriched categories. Metric spaces can be viewed as a type of enriched category and so we obtained a notion of Euler characteristic which Tom and I named the magnitude of a metric space. This can be thought of an ‘effective number of points’ of the metric space. I will explain all of the above in the first part of the talk. Following calculations, it became clear that the notion of magnitude could be extended to infinite metric spaces such as compact subsets of a Euclidean space; however, it seems that it is hard to calculate the magnitude in general. In the second part of the talk I will explain how some interesting combinatorics of counting lattice paths enters the story for calculating the magnitude of balls in odd dimensional Euclidean spaces. No previous knowledge of magnitude will be assumed. This talk is part of the Theoretical computer science seminar series. This talk is included in these lists:
Note that ex-directory lists are not shown. |
Other listsOptimisation and Numerical Analysis Seminars Cold Atoms Type the title of a new list hereOther talksModelling uncertainty in image analysis. Provably Convergent Plug-and-Play Quasi-Newton Methods for Imaging Inverse Problems Ultrafast, all-optical, and highly efficient imaging of molecular chirality Quantum simulations using ultra cold ytterbium When less is more - reduced physics simulations of the solar wind Geometry of alternating projections in metric spaces with bounded curvature |