A Day off and Recap of RNT

The others are at the museum

• I decided to take a day off today to rest (while the rest of the group went to an Art Museum and to a Games Arcade), do laundry and get some work done on my Lean learning. I had done the readings before, but there are exercises to do and that sort of thing, and I want to get more comfortable with the Hilbert syntax. The mathematical notation itself is straightforward for me, but not the sort of notation that we are using (because that is based on Logic systems), so I want to get comfortable writing that and formulating programmes in Lean. I want to be clear that I don’t care about programming languages, but I do care about learning Lean, and I wouldn’t mind learning some theorem proving / formal methods on my own, since my university doesn’t really have a strong programme in that sort of thing (we tend to focus more on programming languages, which is not really my jam). And this is entirely self-serving towards my being and staying in the Mathematics community, of course.

RNT

• Over the past two weeks, I participated in the Rethinking Number Theory (RNT) workshop, which was remote. The motivation for the workshop is to reimagine and have better spaces in the mathematics community, specifically within Number Theory. You never know if you’ll get a spot in these kinds of workshops, as a lot of people do apply, but I was fortunate enough to get in (score!) and also get into the exact research group I wanted to get into (double score!). So I was elated.
• My group is working on a project in coding theory, which is something I have always wanted to learn more about, and had in earnest started working with a professor on in my university, but neither of us really had the proper background for it. So this was the perfect introduction, and the group plans to publish the work in a journal, I believe.
• I am able to talk about this work because the author has already published a paper, which we will be extending upon, so the idea itself is not going to be scooped.
• I guess I shouldn’t be so unkind to myself; my undergrad and my time in Hollywood exposed me to quite a few practical applications of coding theory, and I do know about file formats, as that is the kind of stuff we worked with daily (and I was a member of SMPTE for several years), but understanding them from working purely in a theoretical setting is unfamiliar to me.

What is Coding Theory

• In our final presentation, we gave a talk on our project (about 8 minutes so each member had around 2 minutes to speak) and what we had done over the two weeks, and how we plan to proceed. I introduced the topic, which is what it is, and what we are doing in our paper. In communication, you can think of two people; one which is a generator or encoder (i.e. the speaking party) and the other which is a decoder of a message (i.e. the listening party). And we have a linear code, which gives us information over a finite field as to how many messages we can encode, and our hamming weight tells us what our errors might look like (in particular, people in this area care about the minimum distance or the bound, and based on whether the codes are linear or not, there are certain bounds that are known, and others which are more difficult to determine). And these things are important because they give us information about the strength of our ability to encode and decode (in terms of our algorithms), as well as our errors. They also tell us about our efficiency of our codes, which is important in terms of computation. For this project, I was also really happy that there was a mathematician in our group who enjoyed coding more than I did; that was also relieving, because sometimes when people hear that you are a Computer Science major, they immediately think you just want to sit at home and code all day, and I legitimately just like Number Theory, theory and Mathematics a lot more, as well as writing (as evidenced by my blog posts). And I’m happy that immediately we were allowed to take parts that interested us, so I worked with an Assistant Professor who recently completed her postdoc and we validated by hand polynomials over finite fields and made generalizations about what this could mean. She was so smart and so knowledgeable, and I learned so much from her, and I was given room to fail, and I absolutely did make mistakes, but no one treated me like I was less than capable. I really am SO appreciative of that.
• And on one day when I couldn’t attend a meeting because I was flying to Austin, I had a 1:1 with my PI, and he took the time patiently to explain what we did, writing out notes, answering my questions, admitting things he did not know but had to think about, and gave me an example to try on my own that will contribute to the larger paper.

Workshop structure and birds

• In terms of the actual workshop, not only did we engage in research, but we also held sessions in which we spoke about different ideas for reimagining pedagogy and in things that could just be better within the Mathematics community, and how we might provide more impactful solutions or contributions in these spaces. So that was really rewarding, and I really enjoyed every day of the workshop. We communicated mainly on Zulip, which is an application I initially resisted, until I realized that Mathematicians and Number Theory cryptographers really seem to like using it. This may in fact be because of the ability to use LaTeX so readily to write a bunch of mathematical notation, the ability to immediately set a meeting and have it displayed in the participant’s / reader’s local time (so everyone doesn’t have to do the translation between timezones themselves), and of course, the custom emojis (which is hugely a thing in that community! Two of my favourite emojis are the elliptic curves emoji and the ocotopus arms emoji).
• Finally, each research team (and even organizer team) had a bird-themed name; ours was the Code-Carrier Pigeons, and we had a fabulous emoji to match, that looked like a multi-coloured pigeon doing a bunch of spectral / vector multiplication in the background, which is hilarious. The teams had outstanding names, such as the Counting Crows (which is an amazing Number Theory bird name in general), the Dynamic Dancing Penguins (because they were doing Arithmetic Dynamics) etc, and the organizers were the Chickadees. I loved their sense of humour and just had a blast!

Collaborations past and moving forward

• All of these things contributed to my having a fantastic collaboration experience where I learned so much about a topic I genuinely would love to also continue publishing in, and it fits quite nicely with my actual research topic, too! And I made a bunch of friends with whom I can collaborate!
• Furthermore, the entire experience was so joyful for me; it made me realize that sometimes in grad school, if you feel like deep down you still have an interest in doing research, but things aren’t clicking yet, a suggestion to students (actually both in undergrad and grad tbh) is to try working with different types of environments and people. I learned that I enjoy female collaborators generally a while ago, and especially mathematicians, but I would not have discovered that if I didn’t venture outside of what was put on my plate in grad school. It’s so important to try things out and to fail in grad school, pick yourself up and go again. I guess that’s a good life-lesson, too!
• Meeting all these wonderful people at RNT makes me so hopeful, and excited to continue, because I want to return and to continue to meet and work with and maybe one day even mentor in that community! It was just so awesome! I can’t even remember how many times I kept saying thank you because our mentor would tell us we’re doing a great job (which I seldom heard at the beginning of my research experience in grad school; in fact, I often found myself surrounded by a bunch of guys who would spend the whole time telling me I was good for nothing, didn’t contribute anything, tore me down over and over again for every little thing I did, and just bragged about how awesome they were the whole time, how smart they were and how “hard” the things they were doing were to work on (in retrospect I realize this was not true!), which is not an something anyone should ever have to experience, because it’s just self-serving (if you’re so awesome, why don’t you just go into a corner and write awesome papers by yourself and submit them to a conference where you, the awesome reviewer and organizer of your own awesome conference, can give a talk in a conference that only you attend? Ugh.). This workshop built me back up, and it was so encouraging when members said I did things, they wanted to continue working with me, I was even asked if I wanted to give a talk at a university by someone in my group, and the PI gave me a specific example to work on for our next meeting in three weeks!
• This year, I’ve been pleasantly surprised, after being torn down in the past that (i) I could be valued for my perspective and for research (ii) quite a lot of people want to work with me. It’s been an overwhelming but very rewarding year for me, and very validating for having stuck with research, in spite of these initial setbacks. So I’m keeping my eyes forward, and continuing to learn from and enjoy each day. Thank you for those who continued to believe in me and to support me, and to encourage me; I’m happy to have made it this far, and I love my current research community!

And that’s it