Elliptic curves and complex multiplication: the talk

So, here comes the link for the Jupyter notebook I used during my presentations. The English notebook is already in its final location. Just a few words of caution, though:

• apparently Sage does not support opening Jupyter notebooks directly so please use either the non-interactive html version or save the file into any of your projects on Sage cloud,
• it includes both the Jupyter notebooks and my notes for the talk, which served as a guideline for me and an attempt how to summarise my thoughts on the matter,
• the notes are by no means in their final version, they were meant for personal use,
• feel free to do whatever you with with these resources and please, do contact me if you have any questions or have anything to say, even just "Hello, it was a fun read" would be great: then I would know that this format is good and perhaps I should finish and post some other endeavours in number theory I am toying with from time to time,
• none of the things include any references whatsoever: The standard reference for elliptic curves is Joseph Silverman's books, then I read some parts of some articles by René Schoof and Francois Morain, Reinier Bröker's thesis, good sources are past elliptic curve crypto conferences, I enjoyed Andreas Enge's slides and Ben Smith's and then, of course, the best source for me is everything written by Peter Stevenhagen, from whom I am learning how to enjoy algebraic number theory via playing with curves. And that's a lot of fun.

This is an updated link to the folder with all the files:

https://cloud.sagemath.com/projects/d2b6ab7d-a1b1-4f3d-a4f7-3ae39b7ff889/files/

Elliptic curves and complex multiplication

So, the second semester has started already in Regensburg. I don't know what that feels like, though, as I am only going there tomorrow. I had my reasons for staying home at the beginning of the week and as I was still home, I took the opportunity to talk at the number theory seminar in Prague. And I think it was a great decision as it made me really happy.

But first things first, I had a practice round the day before, in Brno at a nascent student seminar or meeting group. The attendance of my first attempt was amazing and people said they enjoyed it, even though they did not manage to slow me down. I do acknowledge that it was not the best but I simply speed up if things do not slow me down. I was not pressed on time that much but maybe I just wanted to say too many things and took the wrong way to get there. But still, some people liked it and I am glad I had the opportunity to try things out.

It took the whole evening and the terrific travel to Prague today to put the talk into some presentable shape; second train accident in one week in my hometown resulted in a very stressful time for when it was not clear at all whether the train will come and I already knew that no other connection would take me to Prague on time... Well, the train did come and I did manage to calm down enough to focus...

But in any case, I talked about elliptic curves and complex multiplication. It is not the best topic for people who have never heard about elliptic curves nor algebraic number theory and since, in addition, I tried a more complex approach in Brno, it was a lost case no matter what I tried to do in Brno. So that was the wrong attitude. In Prague, I was more lucky with an audience who have heard about elliptic curves and seen some algebraic number theory so I could talk about more things and I got some very interesting questions from the audience and I think I managed very well. People were smiling in the end and I believe those smiles were not out of pity.

But here's the actual talk summary: I gave a talk using mostly Jupyter notebook as a long notebook with empty spaces to separate my "slides", I tried to give a lot of Sage examples and explain the things on what could be seen. I am not sure if that was more helpful or confusing but for me, it was very beautiful. The talk was in Czech but I am willing to give it a bit more time, fill in the details I wanted to mention and publish my notes and the notebooks in English as well.

But for those eager to see what I did and those willing to learn some Czech, I am going to upload the notebooks with some explanations and clarifications when I get connection decent enough for the cloud to work ;)

Update: for those eager to see the notebooks, please follow this link and read a bit of background info on the files.

This is an updated link to the folder with all the files:

https://cloud.sagemath.com/projects/d2b6ab7d-a1b1-4f3d-a4f7-3ae39b7ff889/files/