San Francisco and the like

Dear all,

it is me again. I am currently on a short break in San Francisco and this place is insanely wonderful again. I love where I am staying at and I am enjoying my sunny days to the fullest. Tomorrow, a tougher regime will start as I need to get going with algebraic geometry at last, however, with the amazing garden I can use and the quiet and easy neighbourhood I think I should succeed this time.

While this is not the view from my window, it is almost as pretty!

So, what has happened in my life since the last post? I gave another talk, this time as a part of my regular coursework in Regensburg and on geometric group theory, on the topic of Coxeter groups: these are abstract reflection groups, which means that they are generated by "reflections" (elements of order 2) and their Cayley graphs (with respect to the generating reflections) have some very nice geometric properties. For those interested, the notes for my talk are available here (I talked about various definitions of these groups and why these definitions are equivalent):

https://www.dropbox.com/s/ospztlbnz0vhkf9/Coxeter%20groups%20talk.pdf?dl=0

However, that is not all I have been up to. I have started looking into things I could be doing with my life and realised that there is a lot of math I enjoyed and somehow stopped doing. Also, I tend to perform much better when I have a long-term goal ahead of me, be it preparing for a seminar talk, writing down a set of notes of what I am entertaining myself with, preparing for summer schools I want to attend... So, I decided to find some topic for me at last and devote myself to a more systematic building of the theory, perhaps writing some things down.

And what could be better than things I have already thought about for some time and for which I do know the people to talk to and get new insights and ideas? Yes, I am talking about my thesis, the revision of which is long overdue, I could finally include the parts I didn't have time to write down before, I could restructure it. There are a few reasons for doing that:

• I changed a bit during the year since I wrote the thesis. I still want to tell a story when I write about mathematics, only I have become more aware of the preferences of other people and learnt how to write slightly differently, in a more structured way.
• I have since learnt and understood much more than was is included in my thesis. And then I have forgotten half of it. To remedy this unfortunate thing, I decided to write down the things I remember, go over them several more times and figure out the details that have (since) slipped my mind.
• As I said, having a long-term goal is a better incentive for me than just learning things randomly for the sake of continuing my studies (and I fear I have been slipping into that since the beginning of my semester).
• It is difficult to get things done when you do not need to do them, so by announcing my commitment publicly, I hope to put myself under just enough pressure to actually work on this task regularly, because I tend to work differently if I am supposed to deliver a result in the real world, not just in my head.

So, wish me good luck and please, do support me on this journey. I hope it will work out eventually.