There has been some spectacular progress in geometric measure theory: Hong Wang and Joshua Zahl have just released a preprint that resolves the three-dimensional case of the infamous Kakeya set con…| What's new
Is this the oldest example of the well-foundedness of the naturals being explicitly mentioned?| theHigherGeometer
Here’s a fun thing: if you want to generate a random finite space, instead select a random subset from , the -fold power of the Sierpinski space , since every space embeds into some (arbitrary) product of copies of the Sierpinski space. (Recall that has underlying set , and the only open subsets are . … Continue reading Small fun observation about finite topological spaces, and some challenges| theHigherGeometer
Bundle gerbes are a class of objects that are my bread and butter, but there are many different ways of thinking about them. In my paper with Raymond Vozzo we wrote a different take that starts from the point of view of plain Lie groupoids (which we allow to be infinite-dimensional) and slowly builds in … Continue reading Abelian differentiable gerbes – recap| theHigherGeometer