Winter semester evaluation, pt. 3

Some you might object: wait, where is part 2? The reason is, I still haven't come to terms with that happened to me last semester, how little I did, how poorly I performed in my classes, how bad simply everything worked out for me. I don't want to spend time on those very unhappy moments for me again, especially as I am feeling much better again, after a lot of hard work from me and everyone around me. I am so disappointed with my past semester and super-disheartened, so I am postponing my summary of the previous semester until I am confident it will not get me down again. Seriously, I very much prefer doing maths to crying all the time, so...

And now for the plans for the future. I still need to take all my exams: algebraic geometry I (schemes), elliptic curves and modular forms (self-contained course that allows you to define modular forms as sections of line bundles) and linear groups and heights (Breuillard's results on growth of linear groups and Lehmer's conjecture, a pleasant mix of height estimates, eigenvalues, logic and nice people). So there is indeed a lot for me to do. This is approximately the end of March and the greater part of April.

As for travel plans, I went to a school in Heidelberg, studying topics relating to L-functions and automorphic forms. It was more analytic so it did not suit my taste very well, but I survived and learnt some bits.But then I got to meet my mentor from Leiden in Amsterdam and that changed so many things for me. Simply coming back to Leiden made me so excited about mathematics again and having someone listen to me complaining and analyzing what was happening made me feel positive that I can change things. Or that I even want to change things...

Now I am in Mexico at a more algebraic school on moduli of curves. I love all the various facets of this theory: there is a bit (in fact, a great deal) of everything. Classical theory, minimal model program, geometric invariant theory, some tropical geometry. Lots to enjoy Guanajuato is an UNESCO World Heritage site, so I am excited about all the baroque collonial architecture.

Though, I will not move from the analytic topics for long as I am attending this year's Arizona winter school on analytics methods in arithmetic geometry. The reasons for this is that I had been interested in Sato-Tate's conjecture so spent a fair amount of time on more analytic topics this semester. Moreover, it ties in nicely with some of the questions I encountered in my cryptography endeavours, so I am rather excited about the school.

And then back and some studying for my exams. Yay!

Then, I am staying in Regensburg for the Spring semester, beginning mid April. And with a gorgeous selection of courses (not their official names, but presumed contents):

• Arithmetic of modular forms (as has been advertised/promised so many times when dealing with the analytic aspects and principal bundles this semester, as if it is going to be any easier), Shimura-Eichler (allegedly the goal of the course), L-functions
• More schemes and coherent sheaves in algebraic geometry
• Seminar on the Weil conjectures for elliptic curves, following Silverman (so the proof using the Weil pairing)
• Coxeter groups seminar (a big unknown for me, though I am giving the first talk of the seminar, seems to be a generalisation of symmetry groups including nice pictures)
• Representation theory and automorphic forms seminar. Having offended my professor with not knowing any functional analysis, we will also focus on the decomposition of representations for compact operators and other important topics every mathematician should know. We could also discuss Tate's thesis.
• Deja-vu's in local class field theory seminar (for which I chickened out again and decided to give one of the introductory talks on local fields, my favourite topics) with grou cohomology for me. Perhaps class field theory is still cursed for me, however, we will be reading Neukirch, so I hope it will finally work out!

So, lots of things to do for me! But I guess it is time for me to work hard, math is beautiful. There will be a bit more travelling for me to do, but in general I hope it will be a more relaxed and quiet semester for me than the last two. So, we'll see! I am excited. Sort of. But worried about my future semester... I don't want things to get all messed up like the previous sememster. I still don't know whether I am still falling into this abyss or whether I am finally climbing up again...

Winter semester evaluation, pt. 1

So, my semester in Regensburg is over. I think it is time for a small evaluation of my study process, some of which has been implied in my previous posts. First I would like to focus on the human topics, with follow-ups on more specific issues, like math and future and traveling.

Perhaps the most important realisation for me was that I cannot do mathematics without substantial support of my social group and perks of the first world society. I need to talk to people to avoid falling into depressions and possibly to people outside mathematics to realise how amazing mathematics really is. In this respect, my German class was immensely helpful, I met several amazing people there who have been very supportive and fun to be around.

Also, I have come to appreciate the role of my family and a place one truly belongs to without question. It feels great to have an amazing home one can come back to whenever needed. I had been feeling out of my place many times last year and it has negatively impacted my well-being. Long travels home might be time and money consuming, but even if so, this is certainly a way one can buy happiness. I don't know anything more beautiful than a walk in the winter forest, breathing the sweet fresh air and feeling at peace. And feeling like a part of the particular place, not just a visitor.

For various reasons, I have not been able to relate to my own classmates as much as I would have liked, but one cannot force math onto themselves and my math appetite has moved towards the evening hours. Also, as I have not been in the best of my moods basically all the semester, I had been grumpy and careless and frankly happy just to be holding my head up at times, so I hope the following semester will be better.

There have also been some unfortunate news from my personal life, some of which shook me more than others. But I am lucky enough to have people around me who helped me overcome these shocks. And compared to my previous semester, life has been rather nice to me.

Still, by the end of the semester I was feeling so overwhelmed that I decided to just stop pushing and go for holidays. This was a great decision and I am happy my partner has been incredibly understanding and flexible enough to drive me to the mountains and spend an amazing week with me. It was a good decision as now I am full of energy and willpower to work hard and since I've got back, I have already done better math than in the week before. And I am still ready and eager for more!

So, that's the human discoveries. As for math, it will be the contents of my following post.