Můj svět, moje matematika
neděle 4. září 2022
Academic FOMO
I often feel like my life and academic experience is different from the people around me. Of course, everybody is unique and we don’t all do exactly the same things, but I think most people in Academia would agree what the “typical” or “average” (and in reality non-existent) trajectory is. We all understand that there isn’t one “correct” way of doing things, but without actively questioning our assumptions, we would probably paint exactly the same picture. Let’s call the imaginary person that has the average experience “Everyone Else”.
When I started doing math, I was still an athlete. I had to run to my trainings from my lectures, shower and eat quickly just to make it back, and kept at it for a few years. I was lucky to have received a lot of mentoring early on, so in my classes I was a bit more advanced than others, got to travel to summer schools early on and was exposed to wonderful math. So I did things Everyone Else didn’t get to do that much. When I got to Berkeley, I had already done a masters degree, and again had slightly different needs and expectations from Everyone Else. This sounds like by now, I should be used to being slightly different. But I still have to work with it. I am still often comparing myself with whatever Everyone Else is doing, and find it hard to focus on the things that are good for me instead.
This summer, I attended an amazing 3-week grad student summer school. I loved being there, learned so much, worked really hard, made many meaningful mathematical and human connections. But, I was also a TA for one of the courses – again, a bit different from Everyone Else. Of course, I ignored what that meant, the extra work, the extra mental load, and tried doing as many things as Everyone Else. Instead of taking a break, I was still answering questions and trying to help others learn. I loved doing it, but even at the time, I did recognize that it came at a cost. I ignored it, because I did not let myself be different from Everyone Else, did not admit that my work that week most mostly my TAing, and that I did not actually have to attend all the other things – but Everyone Else went to everything, so I tried to do the same.
Moreover, I am very lucky to work in a field – isogenies – that is so beautiful that many people want to talk about it. So that’s what we did. We set up extra meetings to talk math. But, rather than skipping one exercise session on a topic perhaps not interesting to most isogenistas, we did it in the… evenings, after a full day of math. I liked these meetings because I enjoyed the people and the math we did together. But, as my friends rightly pointed out, we were crazy to do it on our Friday nights. And, honestly, I went because it was the “one isogeny thing” that I did not want to miss, and also Everyone Else went!
I am now at home, and my life has been incredibly stressful in the last few weeks. Quite a rollercoaster ride, but I’m almost at the end of it. On top of that, I am still recovering from the mental damage the covid years have caused, I worry about the war in Ukraine, I was exhausted from the summer travel (it was very much worth it, but traveling isn’t instantaneous, and I was working hard during that time). But, when I look around me, I see Everyone Else is already back in the office and working hard and doesn’t seem to be affected by the same things… Wish me luck with focusing on what I need to do for myself, and let Everyone Else do their own thing!
čtvrtek 28. ledna 2021
How to isolate yourself because you don't feel good enough
I have been silent for a long time and today I want to tell you why. I will talk about how I've been isolating myself and why.
The last two years had been difficult. I decided to leave my PhD program at UC Berkeley and jump into post-quantum cryptography. I was exhausted, close to being burned out. It was the right decision, things turned out okay, but dropping out - see how I internalize the negative narrative? - can mess you up. I've only ever heard encouragement and gotten a lot of support from everyone around me. But, because of the impostor syndrome, it feels like a big failure and that by leaving Berkeley, I am losing out. I am losing so much that my life will never be as good as it could have been.
This is, of course, absolute nonsense. But things did not improve when I left Berkeley. I changed fields, sort of. I still work in number theory and play with elliptic curves (topic for another time, perhaps?). But, suddenly, I found myself in a quantum algorithms group. And among cryptographers. I did quite some self-study before starting, but I was far from ready to understand the seminars or have any idea of what people would talk about over lunch. And whenever I had some questions that felt basic to other people, they just referred me to this one set of lecture notes...
You can imagine how this made me feel. I left my relatively safe space in Berkeley, where I could be anyone who I wanted to be. And I was suddenly this new person at the department that I did not know with a very mismatching background. And I was teaching right from the beginning, I could not find housing in the city, so I had to commute from far, the paperwork at the start was far from smooth and took time to figure out.
Did I feel at home at my new institute? I don't think so. I did not have enough time to adjust to my new place and was still trying to get around the invisible walls that I put up around myself. When corona hit, I did not have the safety net yet, it was difficult to find people to reach out to. I have managed with some, failed with others. But the more you isolate yourself, the less sense it all makes. To give just one absurd example. I worked hard to catch up with all stuff that I thought I should know to belong to the group. But then I simply did not talk to anyone about any of these things for months.
You can't blame others for not reaching out to you. But if you don't, especially in this online world, people will not notice. If you interact with someone online, it takes a lot of energy to reach the human being behind the face on the screen. And the people who did not show up are so abstract nowadays that you don't even care anymore. And what about the people who showed up in the beginning and then stopped coming? In real life, you would notice the empty chair. But online meetings are all such a blur that you can show up suddenly after three months - and most people will not notice anything.
Funnily enough, I have been such a misfit all my life. I usually find my way around, sooner or later. For the athletes, I was the weirdo mathematician. During my undergrad, I was among the weird mathematicians, but I always had to run off to my workouts. Then I moved abroad and moved several times, changing communities, meeting new people, losing contact with the old ones, over and over. Despite all the stress, I found myself in Berkeley, thanks to the I-House and the TAC workouts. Everyone in there was coming from a different place, it was easy to live free of assumptions.
So why am I making assumptions about myself now? I was not hired to be a cryptographer. I was definitely not hired as a quantum algorithms expert. My job is to be a number theorist who can learn enough about cryptography and quantum algorithms to do something cool with it. I am now focusing on doing things my way. I am organizing a reading group to force myself to discuss the things I am learning with other people. I am setting up my own social events, giving new chances to things I thought would not work for me.
Like writing this blog: I am missing conversations about many topics now. Once I started talking to people, it turned out that I am not the only one. So I want to share with you. It already makes me feel less isolated. I hope you will, too.
sobota 20. ledna 2018
Some numbers for you
I started off with a combination of shot put and javelin. This was the first time I was holding a javelin in ages, and I wanted to finish all my javelin throws before my shot put, which didn't work out well - I had to do three shot put attempts in a row and then finish my javelin :) But still, 10.67 with a 4kg shot without a glide is not bad. Javelin was much worse, from the 10 or so throws that I did (4 in competition), basically, only 2 were measurable and none of them were anywhere near nice.
After that, I did some sprinting races. It was a funny order, but I don't get to pick anymore :) My god, it's been so long, I completely forgot how to warm up (was ready way too early) and so the running itself was very very far from good - which is great, as I am confident I can improve greatly. The times are basically what was expected, given that I've been training for some 2 months now, took a very relaxed 3 week winter break, and had my spikes on for the first time on Monday. Moreover, it was still a bit chilly and with the wind -0.9 it was far from ideal sprinting weather!
Now, you might ask, why am I doing this? In two months, I want to do a heptathlon. And I am still on my way to my goal of 5k, which would be a fantastic result. Please wish me lots of luck! But again, why am I doing this? I like it. And I need it. Just being a grad student would drive me insane. I need to train, I need to meet people who are not doing maths, who are not studying at Berkeley, I like being exhausted at the end of the day, happy about my training and being so hungry I can eat anything at our dining hall.
It takes a lot of energy to fit my trainings into my schedule. Especially now, as I am starting a 50% GSI position and the teaching will simply eat up a lot of my time. And with all the classes and seminars, travels for conferences and there being only certain times during the day that I can train, it's going to be rough. But today I loved it. It is definitely worth it, being so tired and stressed for time, having to wait the long lines in the university gym when that's the only time I can do my workout, dying on the stairs in Mark Jellison's TAC class or getting up for his 7.15am studio... It is not easy, but it is definitely worth it.
Thank you all for your support. It means a lot to me. Please help me push myself in the next two months to make the 5k. My trainings mean a lot to me and my progress with my training strongly correlates with my progress in my studies. I already have so many big goals and I am glad that today I got some actual numbers, and that these numbers mean that I am on the right track! In two weeks, I will test my hurdles. That's the big test for me!
PS: I've been learning some really cool math now. I will write about it soon.
neděle 19. listopadu 2017
The Paris-Berkeley syndrome
this has been some long time. I've moved to Berkeley in the meantime, I'm almost done with the first semester, basically, two more weeks to go, a few more homework sets to finish and a project paper, but that's it. It has been a semester full of things happening, full of emotions, full of frustration, full of stress...
So yeah, the culture shock has been pretty bad, given that I had a perfect life in Leiden: living a quiet small life full of maths, biking around in the fields, cooking, and baking... Now I am in a very hyped-up (Bay) area, in a community of hard-working, success-oriented, incredibly smart and ambitious people. Berkeley is a big bubble, around the university it's difficult to see someone who's not an undergrad, let alone outside of the university (actually, maybe I am adjusting well, looking down on undergrads ;) sorry!). I'm living in conditions that are very suboptimal for me, I am definitely not satisfied with my I-House experience, and though I am grateful to all the donors whose generosity helps make living at I-House an excellent experience for many people, I do not think the environment is a very fostering one for me. It's just not for everybody.
Math-wise it's been a bit of a misfit, too, I am still trying to find a topic for me, I tried learning a few new things, had a few shots at algebraic geometry again, but so far it's not working that well for me. But I did get very excited about Iwasawa theory, so I am looking forward to the Arizona Winter school already (even though that's in some 3.5 months). There is still maths that I love, maths that makes me happy. However, being burnt out the way I am, it's not easy to keep studying. There are days that I can do it, there are days I do just a little, but there are days in which even a bit costs me too much energy that I just can't do it anymore. But I'm learning to deal with that, slowly, too.
Having many people around me who are always studying, always doing great things, getting so much done, being so excited about being at Berkeley, that is perhaps the hardest part of it all. I tend to simply shut down and as a result, I can't do much, not even the little bit that I was hoping I could get done. So yeah, if you feel like you're not doing enough, just look at me, you are still doing much more. And I am still fine. I am slowly getting my stuff done, I'm slowly getting where I want to be. And all of this is improving. These three months have been big and challenging, but I have come a long way since the intial shock of moving here. I've had a lot of help from many of my friends and I am also grateful for the unwavering support of the man dearest to my heart, who's gone through a lot of very bad days with me and without whom I would have gone back home already.
But otherwise, the Bay area is fun. And I love driving around. And I love being away from Berkeley. Finally not hearing the city, finally not hearing all these millions of fire trucks and ambulances always driving around. The sunsets are unbelievable, the campus is nice to just walk through, it's not all that bad. I also like American coffee and burgers and so at least I can feed myself here.
Also, what really helped me and made a big difference is that I decided to start training again, this time it's not just me, I'm being Totally Athletically Conditioned by Mark Jellison (TAC is a class in our sports center) and we're also doing really awesome gyms together. It's been some two weeks now and I still like it. I think my body is responding quite well to this training and all these newly found endorphins are doing miracles for my mind as well. So I think I have finally found some sustainable exercise regime for myself and if life goes well, I should do some races in the Spring. So wish me luck and persistence :)
Anyway, I hope to be checking in more often now. I think I am over the worst part of it and though there are still some pretty tough decisions left to make, I think I am back in control of my life.
The sunset, the Bridge in the distance, the City... |
středa 5. července 2017
My master's thesis
my master thesis is done. That's actually not that accurate: I submitted already on Friday, June 16, on Monday the 26th I had my defense talk and I still need to give a talk during the Algant graduation days, (July 24-26) which could potentially change my grade :) But yesterday I sent the final version and I no longer have to write anything or change anything.
It's so great to have such a big chunk of work done. It went rather well: I was lucky that my advisor gave me a problem that was interesting to think about and solvable within the few months I had for my thesis and the math was beautiful and challenging as always. The defense talk was also lots of fun. My boyfriend forced me to prepare well - he even went to the department with me on Sunday afternoon to practice with the chalkboard. I also chose to give a talk that was a bit different than my thesis, telling a different story: more of a motivation and a bit more coherent. In short, I think I sold my thesis there much better and I am very happy with my talk.
Even though that after the talk I still had some time to fix the small mistakes and improve the exposition, I didn't really find it in myself to sit down and rewrite it to reflect my slightly different point of view on my thesis that I formed during the talk preparation. It does help to clear your mind when you try to summarize in 45 minutes what you'd been doing the past half a year or so. Even more so when you try to explain it to someone from the beginning, say to your fellow master students, not just to people who know already what you will be talking about. So there would be many things I could write better in my thesis, I've received some very helpful comments that perhaps should have been included in the thesis, but yeah, it's finished now.
Even more so, as there are other things I need to be doing now. I moved out from my house last Friday, I need to secure my degree also from my second university, Regensburg, which might be a bit bureaucratically challenging again, I'm moving to Berkeley in less than six weeks and need to get my visa and finances sorted out... Lots of things to do now. And the weather is finally a bit nice again, so there are also things I want to do, like biking around, swimming in the sea, genuinely enjoy my summer :)
But for those of you who are spending their summers more actively, here is a link to my thesis and also a link to the notes from the preparation for my talk. The talk notes are without any references and I didn't follow them that closely, so some bits might be imprecise, if not completely wrong.
https://sites.google.com/site/sotakovajanahomepage/master-s-thesis---class-invariants
úterý 11. dubna 2017
Wow, it's April already.
Now, seriously. I have been a bit busy, after the Christmas break I had my exams (5 of them), then I visited Czech, worked on my thesis a bit, then I had to go to Czech again, then I worked on my thesis a bit more and here I am now: happy about my maths, less into writing things down but it is the last step in my masters' that I need to complete. Well, I still have one more exam to do and possibly I will choose to finish my Dutch course, but that is now somewhere at the back of my mind.
The weather in Leiden has improved magically, it's sunny so often, warm and not-windy, almost as if I were in California already. Oh, that's the big news, I've just accepted a place at Berkeley, so starting from August I will be hanging around mostly in the Bay area. For the summers I will likely be coming back to Holland, as long as I have such wonderful reasons to come back, but I will also spend some time back home. Maybe I will even do some math-related travelling, who knows?
So now that I am mostly bound to my desk and typing things down in our dark Algant office, not seeing all the amazing weather outside, I decided to take up running again. I am spending an hour or two on the track almost every day, provided the weather is nice, partly sunbathing, partly running around, almost like the good old times. If everything goes smoothly, my mother will even bring my old spikes to me and I want to run my first race in two months, here in Leiden. Probably not hurdles: though my technique was basically unaffected by those two long years of chilling on various couches all around the world, running-wise it's still a misery.
So that's it. Almost. There are tulips everywhere, seagulls all around the department make me feel like it is some sort of a beach resort, occasional trips to the beach and naive attempts at wading through the water remind me that it is still the Netherlands, I am grateful to the people around me for putting up with me and making this such a great time here. Hopefully writing will go well, training will still be fun, my Dutch will improve enough so that I won't panic anymore and life will in general be good.
Kijk! And this is just the beginning of the season :) |
čtvrtek 8. prosince 2016
A long update after a long time
In any case, I still have a few moments to take a deep breath and do things that I want. Therefore, what have I been up to? My last post is sometime in mid September, since then so many things have happened.
- I am applying for graduate school in the US. It is as much fun as it sounds. So far it involves an incredible amount of bureaucracy, writing and browsing, but the situation has been good so far. I got the Fulbright scholarship, which means that there is somebody doing most of the bureaucracy for me (applying to six universities on my behalf, five of which I would have happily applied to myself) and offering to pay for my first year of studies in the US. The results of my standardized tests have also been good (and now follows a detailed description of the tests I've taken):
- I've demonstrated I can speak some English with my TOEFL test. That's just a normal English test involving some reading, some writing, some speaking and some listening. Nothing too ambitious, less absurd tricky grammar questions (compared to CAE&CPE), the format of the questions was easy to get used to, so if someone chooses to "train" for the test, it's more about improving English than just standardized useless questions. Surprisingly the only thing I cannot do very well is to speak about familiar topics. Well, perhaps I am turning into an introvert. Who knows.
- I've almost aced my GRE General score, if you don't look at the results of my essays. Those would have been superhard for me even in Czech. This test is a longish one, with some random English part, Math part and the aforementioned tricky essays. The Math part was easy to train for and also lots of fun, because the questions were just high school mathematics, occasionally sprinkled with questions resembling very simple Olympiad math reasoning. It was precisely what I liked: questions that were doable with hard work and preparation, but if one had the luxury of time, one could save lots of time just finding a smart solution. And the English part was fun, part of it was about reasoning about the text and careful reading, but a huge chunk was just these funny questions with 1-3 blanks and lots of choices for beautiful random English words: the task is to get a general feeling of the message of the sentence and then choose a combination of words that together make the most sense; typically all the words could be used to fill the blank, but only one combination would give a meaningful sentence. I like that a lot.
- And finally GRE Subject math, which is just a speed test in calculus. There are many past tests available and good books for review questions, so practice makes perfect I guess. Funnily enough, none of my practice tests ever went over 800 (on a scale to 900), but my final score was much better. I did enjoy revisiting first year mathematics and answering again all the questions about limits and derivatives, I also managed to use up a stack of scrap paper that I had been hoarding on my desk, so I guess it help. Of all the tests, this was the most important one, where preparation was essential. I think I did just enough to obtain a fairly decent score, more preparation probably would have helped to make me more confident, but that would have meant maybe a few months instead of 2-3 weeks.
- I am attending some courses. Some of them I am attending more often than others, sometimes there is simply too much homework to actually go to school. It sounds ridiculous but given that my classes are in Amsterdam and Utrecht, going to school means spending 3-4 hours a day on public transport, and sometimes I simply don't want to invest so much time into getting to school. But I have been quite lucky with my classes:
- I am immensely enjoying my class in commutative algebra. Both our lecturers are good in the class and if I forget about all the homework I messed up, there is just lots of math I enjoy: all the integrality questions and dimension of (affine) varieties is really dear to my heart. Also, most recently we talked about Hilbert series and Hilbert polynomials and understanding these brings so much joy into my life (because they just tell you so much about the ideal / variety / meaning of life). Except for the policy on homework that is ridiculous: it does make me a way worse mathematician. We are forbidden from discussing the (graded) homework with other students, we have a page limit on our solutions, which just damages the writing skills so much. I think imposing a stigma if someone wants to ask a question is the worst thing a teacher can do to their students and also encouraging people to write math in large blocks of unintelligible text full of shortcuts (because nice layout and indenting takes up space, you know, let alone diagrams, equations and god forbid careful case distinction) is also in the opposite direction to what should teachers do. Still, the material in the course is good and luckily there were only three graded assignments, so now I can happily talk to people about commutative algebra again...
- Another excellent class is my p-adics course. We are closely following the book of Koblitz (p-adic things and zeta functions in the name). The instructors are amazing and the homework is just the best homework I have seen: really engaging, interesting questions for which we have just enough tools to solve them, the problems do not take hours to type down and I've just felt so happy doing most of them (except for one part of the lastest homework sheet that stressed me out incredibly much). I don't actually like the things we are doing in this course, all the analysis and series and such, but it does make me feel like I am learning a lot and I am simply getting so much from this course.
- I am taking some more algebraic geometry, too, because there's never enough algebraic geometry. Some of the lectures have been a bit hectic, but the homework is fun, the things we are doing are engaging: we still only talk about varieties, but knowing a bit more from the viewpoint of sheaves just helps me appreciate the beauty of the classical theory even more. I think I am not precise enough in all my statements about geometry, so it is also a good drill having instructors that are far from lenient in mathematical reasoning. Just good practice and like I said, there is never enough algebraic geometry, especially for someone like me who has never really bothered learning it properly...
- Then there's the Galois representations. The course is fairly advanced and we are covering so many new topics that it is a bit over my head at the moment, the homework typically takes the whole week to sink in and understand what one is supposed to do. But I am taking my time, slowly getting through all this representation stuff. But it is getting too far into representation theory, in which I just have to take so much stuff for granted, that it doesn't make sense to me to try to understand it so deep: there are too many gaps still left. I will see how that goes further, I have already learnt so many interesting things from there so I hope I will be able to consolidate the knowledge at some point.
- I would almost forget about algebraic topology, well, that's in Utrecht, so that doesn't happen to me that often. Also, most of the homework has been standard homological algebra, took too long to write down (seriously, typing down the homework shouldn't take twice as long as solving it). But it's a fairly standard course in algebraic topology so I hope I know what I am doing.
- And Dutch. I am almost fluent in Dutch now, well, at least in my personal dialect that includes a lot of made up words from English or German. People don't understand me very well but I don't understand them either, so I guess we are even. I still have a few months to continue learning, so hopefully the mutual understanding will only improve.
- I've been also living, at least a bit. We started baking with my flatmates, so far only simple things, but brownies are always good and the marble cake we had was also amazing. We also dare to cook some more interesting dishes than pasta (which is what I would cook for myself basically daily), with the pinnacle so far being a leek quiche and spinach pancakes. I am running a bit, exercising and trying to get fit again.
- And I have mostly been in Leiden. I like it here. Seriously. This is an awesome place. Come and see for yourself!
pátek 16. září 2016
Leidenlove
The sea. |
čtvrtek 18. srpna 2016
The end of my German year
středa 29. června 2016
Season finale
I have lavished so much of my energy and chiefly inner resources on transmuting my situation into an advantageous experience. Though unsure about the tangible outcomes, many a thing has changed, much to my delight at times but alas, way too often it was much to my horror. Irreversible though some of the changes may be, I am generally enthusiastic about and open to what the future might bring.