A small #math thread about #barycenter, #torsor, and #extension.

A torsor for a group object (in a topos), or a principal homogeneous space under a group, or a principal bundle wrt a group (in differential geometry) are more or less the same thing: you are given a group G, an object P with a free and transitive action of G on P ((g,p)↦g⋅p) which tells you that P and G are very close: you have some p ∈ P, or you have such a p “locally”.

This is slightly complicated, I admit, but…

Free resources for teaching:
* Planetary orbits and barycenters
* Proof that Earth revolves around the Sun (stellar aberration)
* Asteroid, comets, and meteors
* Meteor impacts
* Exoplanets

and for extra fun
* Why are some asteroids & moons spherical while others are shaped like potatoes?

https://kaiserscience.wordpress.com/astronomy/planets/

@edutooters
@science
@scienceteachers
#science #STEM #NGSS #highschoolteachers #scienceteachers #astronomy #earthscience #comets #meteors #exoplanets #barycenter #orbits

New #preprint: "Unbalanced Kantorovich-Rubinstein distance and barycenter for finitely supported measures: A statistical perspective" by F. Heinemann, M. Klatt, A. Munk

https://arxiv.org/abs/2211.08858

#KantorovichRubinstein #barycenter #Statistics #Methodology #Mathematics

Made a quick #travelblog update for my starship simulator travels on a #mission to the #barycenter of the #milkywaygalaxy

https://youtube.com/shorts/H4LVQ63KvEQ?feature=share

Heinemann, F., Klatt, M. & Munk, A. Kantorovich–Rubinstein Distance and Barycenter for Finitely Supported Measures: Foundations and Algorithms. Appl Math Optim 87, 4 (2023).

https://doi.org/10.1007/s00245-022-09911-x

#article #appliedmathematics #optimization #barycenter #wasserstein #kantorovich-rubinstein