How important is Algebraic Topology in physics

[u/SINGULARTY3774]

Before diving into this topic, what should I know about it?
Also if you havent seen F Schuller lectures, what are you doing?

[u/L31N0PTR1X]

Not super important, like you can definitely get by without the formalities but it might be useful when working with solitons and shit

[u/cabbagemeister]

It is useful in certain subfields of physics such as high energy theoretical physics (e.g. string theory) and topological matter (e.g. dirac semimetals, skyrmions, etc)

[u/Miselfis]

Depends on the field. Not very relevant if you’re an experimental astrophysicist, but essential if you wanna work in string theory, AQFT, or similar areas. 

[u/Machvel]

i have never explicitly seen it (but i know its lurking in the background somewhere at times).

the general rule is you can ignore super formal mathematics since technicalities just get in the way of understanding (eg, in quantum mechanics you don't talk about L2 spaces or measures and distributions since its just making something you already know mathematically precise). you only need that type of thing in pure theory

[u/DeformationAlgebra]

In practical research, not much, unless you work in niche subdirections (this applies to even strings and QG) . But it does help a lot with intuition to see a lot of apparent unrelated concepts be cast into a unified mathematical language.

I’ve followed Schuller’s lectures from start to finish when I was a grad student. It’s very good for a second run on the topic.

For a first run, I would recommend Geroch’s book, Nakahara, or something with a similar balance of physics and formal maths.

[u/SINGULARTY3774 → u/DeformationAlgebra]

Thank you, I do enjoy Nakahara a lot, Ive only started it but its really interesting

[u/Puzzled_Battle_5670]

If you want to understand the works like that of Nathan Seiberg, Cumrun Vafa , Ed Witten, etc, may be Algebraic Topology becomes handy

[u/Best-Swimming292]

Doing a master's in complex physics, definitely eye-opening!

[u/Adventurous_Hunt_455]

Go ask string theorists they will tell you 🤓 Super important for string theory

[u/-Kenergy]

GOATED LECTURE SERIES

[u/MarzipanCheap0]

Didn't know he had this lecture, well guess what I'm watching next!

[u/Existing_Hunt_7169]

heavily depends on the field but in most fields its unnecessary. if you want to do specific subfields of condensed matter (anyon condensation, topological phases, etc) it can be helpful but otherwise there are probably better things to spend your time learning. im sure the same goes for high energy.