A week #4
Comparatively mild week.
I really didn't want to get behind on my Lie theory homework again so I made sure to start early and I'm making slow progress, but progress. We've been covering representation theory which I've been wanting to learn for a really long time. It's really fascinating to learn about, and understand some of the things I've seen but never had time to really dive into. I'm struggling to understand some of the motivations, and more recently struggling to understand wtf weights and roots are, but hopefully that will come. I'm trying to look at a few different sources to help with all of these problems. Since our professor isn't touching on any of the physics I'm reading some of these notes from 't Hooft and occasionally some of this book by Woit. Both have been helpful getting some insight into how these ideas are used in physics, but I'm definitely still at the “spinning in circles, not quite sure where I am phase”.
The Open Quantum Systems class has only had one lecture in the past 1.5 weeks and no new homework. It feels like I'm taking one class this semester, but I'm not complaining because that one class feels like a lot.
My research was going well, but I think a touch too slow for my advisor and so he made some progress on the problem and sent me and another teammate/colleague some notes on a possible solution. In the notes he's using tools from Lie theory that I haven't really learned yet so I'm trying to understand things about Cartan subalgebras and KAK decompositions to understand the work. I put on hold the numerical work to start studying some of this stuff. I definitely felt a little defeated when he stepped in and solved the problem because I was having fun with it and getting to work on it with Matthew often. I'll probably voice that feeling to Joel at some point, but I also understand it's been multiple months since he suggested this problem and I didn't even work on it for the first few. That said, I've come a long way in understanding the problem since he gave it to me and I should be proud of that and all that I've learned.
Again, cleaning up things on S3, and not much else.