This blog is a collection of reading notes of things that I try to learn. Often they are nothing more than summaries of various pages on the nLab, but collated, (over)simplified, and reordered to be more easily understood by, e.g., me. There will almost certainly be mistakes and bad viewpoints, so caveat lector.

I find myself in a mathematical rut more often than I would like. It is very easy, especially as a PhD student, I think, to become disillusioned with maths, the work that one can do, and academia as a whole. I realised only the other day, after talking to my family, some of the things that can contribute towards this. Hopefully this post can serve as a reminder to myself that I am human being who is trying to be a mathematician, and not the other way around.
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As I mentioned in the previous post, I recently saw a talk by Rachel Hardeman on the Ahomotopy theory of graphs, and it really intrigued me. In particular, it seemed to me that there was some nice structure that could be abstractified: that of a “graded homotopy structure”, as I’ve been calling it in my head. Rather than trying to type out everything in
#math.CT:matrix.org
, I’ve decided to post it here, in the hope that I might be able to get some answers.Continue reading ⇾

This week was the Young Topologists Meeting at EPFL in Lausanne, and had courses by Julie Bergner (on 1 and 2Segal spaces) and Vidit Nanda (on the topology of data), as well as a bunch of great talks by various postdocs and PhD students. I was lucky enough to get the chance to talk about twisting cochains and twisted complexes for half an hour, and you can find the slides on my GitHub here.
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What with all the wild applications of, and progress in, the theory of $\infty$categories, I had really neglected studying any kind of lower highercategory theory. But, as in many other ways, CT2019 opened my eyes somewhat, and now I’m trying to catch up on the theory of 2categories, which have some really beautiful structure and examples.
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categorytheory 
algebraictopology 
spectra 
operads 
homotopytheory 
birds 
quicktip 
questions 
quantumphysics 
quantumcomputing 
differentialgeometry 
complexgeometry
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