Apologies for the hiatus in maths posts; I've had some personal issues (trying to find food, fending off homelessness, grieving the death of my friend.) The past few weeks have been pretty stressful. I'm now in Colorado and shouldn't be worried about those important distractions for the next three weeks (when I return to London I should also have a place to live, and student loan money should be coming too.) I'm glad I'm here and that I get a chance to see my friend's family. I will be resuming maths post from today (inshallah!) Here's the plan for the next few days:

Yesterday and Today: catching up on some algebra - modules, algebras, group rings, group algebras, c* group algebras.

Sunday: Etale groupoids & category Theory

Monday: C* algebra construction of the bost-connes system

Tuesday until ? : Hecke algebras and their corresponding construction, plus the equivalence of the two.

My Advisor and I had set a goal of understanding the construction of bost-connes system by the end of August. I'm ashamed to say I'm a bit late. But I think I'll be able to make up lost ground and start working on the symmetries of the system here in the next few days. I don't think that schedule is too ambitious. I should have time to catch up and even enjoy the miles of mountain bike singletrack just outside my parent's house!

Additionally, one might expect some non-project related blogs to come soon too, particularly ones on the UCL undergrad colloquium, my talks there, and some other reading.

Right. enough talk, lets get to work

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