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...