Author Archives: gregoriousmaths

Spectral sequences are among one of the most useful tools for topology, geometry and algebra. However, they have the reputation for being difficult to grasp. Roughly, they approximate the homology of some chain complex, by breaking it up into many little pieces. A nice example of this arises in topology, where we can filter suchContinue reading “Some Half Baked Thoughts on Spectral sequences”

Because of my upcoming video about higher category theory, I thought I would make this short blog post introducing categories and some related ideas about them. Therefore, this will be a pretty long blog post, with lots of advanced examples sprinkled in (they aren’t necessary for actually understanding the category theory itself, but they areContinue reading “Warm up for the talk: Categories”

I did a K theory talk, covering the homotopical point of view of K theory and the cohomological point of view. The notes are here: Here is the video, with annotations filled in: https://www.youtube.com/watch?v=rVe97vpbZU4&t=2830s

please check out my latest video, thanks !

Computing homotopy groups of spheres is an extremely complex topological problem, where much progress has been made, but there is much more still to do. There are many different approaches to their computations: fiber bundles and fibrations, spectral sequences etc. Here I will give an overview of some results with elementary methods which have beenContinue reading “Some remarks on Homotopy Groups of Spheres”