Hey everyone, I’m back after a short hiatus. I’ve decided to change the format a little: instead of documenting a complete learning journey (which, honestly, was quite strenuous), I’ll be giving a weekly (fortnightly?) summary of the things I’ve been working on/reading up on.
Since October, I’ve been doing a lot of physics, not much mathematics or programming at all - but this has changed recently after I started proper differential geometry: fibre bundles and connections (for mathematical gauge theory, etc.) - naturally, this lead to characteristic classes (Chern classes are useful for Calabi-Yau manifolds). I’m also looking at spontaneous symmetry breaking, cf. the Higgs mechanism and chiral symmetry breaking. 2+1D gravity also piqued my interest (particularly BTZ black holes) but I left it aside for the time being since I couldn’t find any resources that didn’t involve Chern-Simons theory (something that I should learn properly, now that my DG is also up to speed - not full-fledged cobordism TQFT though!). I also started a bit of string theory, from David Tong’s Lecture Notes (currently I am taking refuge in the Conformal Field Theory chapter!). Finally, I’m reading on the Petrov classification of Weyl tensors and, a blast from the past: Regge Theory! (since it’s from the early string theory days, and it also precedes the analyticity of the S-matrix). I was active quite a bit on Physics SE - I managed to gain around 1,000 reputation in a little over a month (mostly QFT and particle physics answers).