Serre duality

So today, in Regensburg, at our student seminar on Riemann surfaces, I gave a wonderful talk on Serre duality. It was a rather long talk (80 minutes), we had to prepare some sort of detailed handouts for people and we were actually supposed to prove things rigorously. I had already given one such a talk on simplicial topology earlier this semester and it went very well, so, at least, the format seemed to be suitable for me.

I think I managed just fine. It is difficult to give a long proof in such a limited time (at least for me), especially if you need to build up all the theory beforehand. The book my talk was based on is the "Lectures on Riemann surfaces" by O. Forster, in which the proof is, to my taste, rather convoluted and unmotivated. And, admittedly, too long to present in public. And except for the last five minutes of the proof, in which I had to use a certain diagram for one sheaf and then, in reality, used a different one,  I am quite confident that I could give people more than just the book.

Moreover, I used a slightly different approach than the book, because I could not afford the luxury of the clean, uninterrupted, yet unmotivated exposition. I put a great emphasis on how the various objects I defined will be used in the proof or why we care. Unfortunately, the audience was traditionally ranging from dispassionate to impassive and had it not been for the experience gained for me and some details falling into place in my mind as I spoke, I would have preferred to spend my afternoon differently.

For those of you interested in my impression of the Serre duality, here is a link to my notes (beware of the last part, which is a bit inaccurate and I relied more on my hand-written comments from my own perusal of the proof)
https://www.dropbox.com/s/2frsw8ywxm3xl79/Serre_duality.pdf?dl=0

And bonus points to those who correctly identified which meaning of perusal I used there.

Regensburg yesterday.

Germany in the new year

So, a happy new year! It is still 2016 so I am not late at all. I have been getting a lot of amazing rest and truly enjoyed my Christmas holidays. Study-wise I was mostly concerned with the metaphysical questions and seem to have come to some conclusions regarding my own motivation for studying and the purpose of my life.

Admiring the beauty of my homelands.

With some exceptions and taking into account my exceptional amount of bad luck, which has persisted since I've got here, I am getting used to being in Regensburg. I am particularly amazed by my elliptic curves and modular forms course by professor Guido Kings and also my topology experience with Clara Löh is rather positive, so there is interesting content for me to study, but somehow I am still unable to arrange the conditions for me here to actually study and, you know, learn things?

So I am still struggling with finding any kind of solution to this problem: I sincerely acknowledge that some people are happy and productive here and it is a motivating and supporting environment for them, on the other hand, I honestly feel a significant decrease in convenience from my previous places. And as much as I am trying to get things done, I am not feeling I am accomplishing anything of that sort.

Eagerly awaiting snow also in Regensburg!

So, the big question still remains and I do apologise to all my poor friends who have suffered from me being singularly annoying and disheartening with bringing it up over and over again, as the advice is most strikingly divided between "go now" and "definitely stay". It makes it especially difficult as I am rather convinced that I do want to do math and do not end up feeling resigned that I am just going to suffer through this period, hoping that it will improve in some vaguely defined future.

As for the happy things, I have been learning Serre duality and I am rather impressed with the beauty of the ideas there. I have a bit of a difficult time trying to structure my talk but I am getting to grips with it. Wish me luck, I will share more next time.

Home versus the rainy Regensburg. Well, whatever.