čtvrtek 28. května 2015

Thesis: A bit of nostalgia...

So my thesis is printed and submitted already, even though I shall wait a bit for my defense. So, the result is here:

Tak, moje bakalářka už je vytištěná a odevzdaná, i když na obhajobu si ještě chvíli počkám. Výsledek je zde:


Pretty, isn't it? I am quite happy about my thesis, I think I managed to include a lot of interesting things, most of which are true, I learnt a lot while reading upon several topics that piqued my interest and I think my thesis fulfilled the expectations I had for it.

Pěkné, co myslíte? Jsem se svou prací docela spokojená, myslím, že jsem tam vecpala spoustu zajímavých věcí, většina z nich je dokonce pravdivých, naučila jsem se spoustu během toho, když jsem se zajímala o témata, na které jsem během psaní narazila. A myslím, že moje práce splnila má očekávání.

Frankly, my goals were simply to write a coherent text, possibly including some interesting mathematics, but with a feeling that I added something. I am not sure how well I succeeded, but I feel that there are some pretty things I figured out for myself and I am satisfied with the way I look at certain little things in my thesis. Most importantly, I managed to get rid of my fear of many things - such as localisations and discrete valuation rings, so I hope that my thesis is a celebration of this progress of mine.

Popravdě, moje cíle byly pouze napsat souvisý text, pokud možno obsahující zajímavou matematiku, ale s pocitem, že jsem k tomu něco přidala. Nejsem si jistá, jak se mi to podařilo, ale jsou tam drobnosti, které jsem si rozmyslela sama a jsem spokojená s tím, jak se na určité věci dívám. Ale nejdůležitější je, že jsem se přestala bát některých věcí - třeba lokalizací a DVR, tak věřím, že má práce je toho hodnou oslavou.

There are so many things I wish I had included in my thesis, such as some of the estimates for class number, more about Chebotarëv, write in detail, why random polynomials have Galois group $\mathbb{S}_n$, but there simply isn't enough time to do everything. In any case, it is done now.

Ale je tolik věcí, které bych si byla přála do mé práce přidat, jako odhady na class number, víc o Čebotarjovovi, rozepsat se, proč náhodný polynom má Galoisovu grupu $\mathbb{S}_n$, ale na všechno prostě čas není. Nicméně, teď už je to hotové.

So, here some the nostalgic bit - submitting my thesis almost concludes the three years I have been studying here in Brno, some of the time was beautiful, some less, sometimes I felt like I am learning a lot, at times I felt I was not learning enough. Masaryk gave me a lot of freedom and did not interfere with my interests much, but I am not sure it was the right option for me. However, what kind of background I have managed to gain here remains to be seen. I hope I do have a nice starting point now anyway.

Takže teď přichází ta nostalgická část - odevzdáním mé práce jsem téměř završila ty tři roky, co jsem studovala tady v Brně, něco z toho bylo krásné, něco míň krásné, občas jsem si připadala, že se učím spoustu, občas jsem se cítila, že se toho nenaučím dost. Masarykova univerzita mi dala spoustu volnosti a nevměšovala se do mých záležitostí, ale nejsem si jistá, jestli to pro mě bylo to správné. Nicméně se teprve ukáže, jaký základ jsem si zde dokázala vybudovat. Doufám, že budu mít pěknou startovní pozici.

Almost there... / Ještě kousek...


neděle 24. května 2015

Women and mathematics: the trip

I am still very much overwhelmed by all the beautiful things I've experienced here in the US. So there is just a few notes I want to share, not beautifully structured, with no special aim, but these things deserve not to be mentioned before I forget:

  • There are a lot of great women in mathematics. Surely, we are still underrepresented, not every female mathematician is my best friend, but there are a lot of women who are simply awesome. Supportive, understanding. I really enjoyed my two weeks in Princeton because there I didn't have to keep my face, I could ask anyone even about the simplest definitions and silliest problems, there would be always someone to help me out. I am not sure this is a gender-related thing, but I have never experienced this level of understanding and acceptance in predominantly male groups. 
I admit it could have been the spirit of the school, but I hope we will all carry it in us for long.
  • It is good to start with easy problems. There is no shame in doing elementary mathematics and revising the things you have learnt before. It could be immense fun, especially if you do it with someone similarly gifted in memory, it is definitely worth it. And again, forgetting things is natural and doesn't make you any less of a mathematician. 
  • Neither the US nor Canada is used to pedestrians. I crossed the Peace Bridge between Buffalo and Canada on foot and in addition to having to walk basically twice the distance through all the under- and overpasses that were built for my walking convenience, the officers tended to send me to and fro before they let me in. 
  • Also, if the officer at the custom says "How much money are you bringing to the States / Canada?", it is not advisable to react "Ehm, none" or "Next to nothing, I guess, 3 dollars!". But that was the truth and I had my 3 credit cards, none of which seems to work at certain strategical spots like the train stops and the like... But shops and counters are all okay.
Canada looked quite nice.
  • I seem to be doing things wrong, eating Chinese, Indian, Italian and French food in the US and Boston burgers in Canada. But I had some tacos (and really sucked at eating that) and a lot of things that I do associate with the American cuisine. Okay, frankly, I ate some bagels. And I ate a lot of strawberries, blueberries, and raspberries, and that was the biggest impression on me here, so the rest hardly matters.
  • Everything is so big here. I had a burger yesterday for lunch and I am not really hungry yet (though I've had some chocolate bread today). The streets are wider, the cars are bigger, the buildings are simply huge. Despite these places being so crowded, I still have this nice feeling of space around me, so the cities are energizing, the forests and parks are revitalizing. 
  • The more I travel, the more I love my home. It is all so beautiful, but I look forward to being home.

pátek 15. května 2015

IAS


Yes, this is a fantastic place. No question about it. The maths is great (tough and I am frankly overloaded), people are awesome and the surroundings? Heaven. Paradise. Nirvana. It is simply awesome. I feel happy, after a long time...

Yes, I am quite excited. I have every right to be. I have been quite lucky in my life to get to such beautiful opportunities to do mathematics, such as this lovely program for women in mathematics:


I think the organizers here are doing tremendous work and this program is running every year, with the topics sort of matching the topics of the special years here at the Institute. So this year, it's some algebraic geometry. What does that entail?


  • Lectures: Liz Beazley gave a beautiful, hands on series on Grassmannians and Flag varieties, it was all very concrete, with great examples and intuition to see what was really happening. And we could draw some pictures, that was so nice... Claire Voisin talked about birational invariatns, mostly way beyond my understanding, but I have learnt a lot from the first few days. And did away with my fear of sheaves and bundles and it was all so beautiful. It is good to see some hard maths sometimes, discuss it with others and try to form some sort of a picture. It does feel like jumping right into the middle of the lake and learning how to swim well enough to survive until someone comes and fishes you out. Some faster swimmers reach the dry land, some drown...
  • Seminars: intensive talks, some people do some amazing stuff. Really beautiful things. We have talks both on very advanced and complicated research and accessible topics, most of the speakers are so great. It shows how big the mathematical world is, sometimes you discover links that you were not aware of before, some things start making more sense afterwards... And it's fun.
  • Socializing. The girls here are quite cool and everyone has an interesting story to tell, be it life, mathematics or all together, most of the people really are fun to be around. One can make great new friends and enjoy lots of beautiful discussions with similarly minded people.
  • Sunbathing, coffee breaks and beautiful dinners. Tonight we had some tacos. I must admit that I was a desperate and ridiculously incompetent diner tonight. 
So that's it for now. I am still overwhelmed by all this happening. More to come...



středa 6. května 2015

Můj adoptivní domov

No jo, Leiden jsem si pořádně oblíbila. Je to magické místo a měla jsem docela štěstí na příjemné ubytování s milými spolubydlícimi, dokonce i počasí mi vychází naprosto dokonale - na nizozemské poměry tu překvapivě málo prší. I když včera tu byla nádherná bouřka, hučel vítr, tolik energie... Konečně když jsem měla úplně volný den a chtěla vyrazit na pořádný výlet. Tak jsem aspoň psala...

Yep, I have taken to Leiden quite a bit. It is a magic place and I have been lucky with a nice accommodation with cool flatmates, even the weather is so beautiful: for the Dutch standards, it's not raining at all. Even though yesterday we had a marvellous storm, with gusty winds, so much energy in the air... When I finally had a day off and wanted to go for a huge trip. So at least I was writing.

Když nemůžu za tulipány, přijdou tulipány za mnou!
If I can't go see the tulips, the tulips come to see me!

A jak je na tom moje bakalářka? Skvěle! Bohužel, můj vedoucí odhalil několik míst, které jsem doufala, že nebudu muset rozepisovat. Dokonce jsem je ani neuvedla slovy "zřejmě", "jistě" či "snadno", snažila jsem se o psychologický nátlak prostým "protože ...". Avšak byla jsem odhalena a za každou takovou drobnost jsem musela přidat odstavec či dva roztomilých výpočtů, argumentů, samé radosti. No jo, raději to udělat pořádně naproprvé...

And how is my thesis? Brilliant! Unfortunately, my supervisor found several places I hoped I would not have to give much detail about. I even didn't claim they were "obvious", "clear" or "easy", I tried a bit of a psychological pressure with a simple "as...". However, I was exposed and for each such a deceit I had to add a paragraph or two of computations, explanations, so much fun. It's probably better to do things properly on the first try...

Nicméně, po hodinách a hodinách sázení jsem vzala zavděk tužce a papíru. A myslím si, že v ruce to vypadá mnohem líp. Myslím si, že bych dokázala napsat svou bakalářku v ruce, avšak všichni, co po mně kdy něco četli, Vám řeknou, že to není dobrý nápad. Připomíná mi to staré dobré časy, kdy jsme vymysleli šifru založenou pouze na tom, že moje m,n, u a w vypadají prostě jen jako hromada stejných obloučků...

Even though, after hours and hours of typing I settled for my pen and paper. And I think it looks much better in hand. I think I would be able to write my thesis in hand, but everyone who has ever read anything after me, would tell me that it is not a wholly good idea. It reminded me of the good old times when we based a cipher based solely on my m's, n's, u's and w's looking just like a bunch of identical arcs...
vlevo mé poznámky, vpravo již natexováno
Hlasujte!
left my notes, right in LaTeX
Vote!

PS: Pokud to jde vidět snadněji a lépe, tak za to budu jedině ráda ($\mathfrak{O}$ je libovolný order a $\mathfrak{O}_K$ je okruh celých čísel ve stejném číselném tělese).

PS: If you can see it in an easier way, I would be happy to hear it ($\mathfrak{O}$ is an arbitrary order and $\mathfrak{O}_K$ is the ring of integers in the same number field).