Last week of classes and An Amazing week!

Once again, I am busy!

• But great news! My research proposal was accepted and I get an award for it, and get at least one publication out of it. Hooray!!!
• I also gave a Math talk! Look at such a nice compliment from an attendee!

• I’m doing a podcast this upcoming week, taking part in a research documentary, and have to follow up on some other tasks.
• This week was amazing! I ended up hanging out with Maths friends to get Jamaican patties, going to a grad school barbecue and sitting with Pure Maths friends and talking about graph-coloring problems around a table (inevitably!) and basically just having a great time!
• I also ended up doing really well in at least one of my classes unexpectedly! I kept doing proofs and was planning on doing more this weekend, too! I want to keep doing them and getting really good at them! I enjoy it so much! I’m excited to take more of these classes next semester! I’m also going to a concert this weekend! I will post pics of some of the fancy VIP stuff I get (I got a ticket and am going with some Math grad students!). I’ve really felt like I’ve found my groove with this group and this department and want to continue with this community; I’m so happy with everything right now because of this Pure Maths group!

• This was a shocker and completely, in my opinion, because of the culture of the Pure Maths department (and to be honest, I still have a long way to go, but I’m learning, and everyone has been super patient with me, and I’m grateful!) ; between the awesome professors and the students, who really work with you to get better, I really feel like they have my back. And I’m also going to be honest; writing proofs when I first came in to grad school was super frustrating, because I was grappling with a lot of things I hadn’t learned about (in my country, at least, when I attended, proofs weren’t really a thing we spent any time on (if we did, I would have learned to love them, I am sure, because they also tie in nicely with logic and the humanities in clarity of writing, I think! Recall when I was in LA, a vfx supervisor saw the way I wrote and made a wry comment that I might make a very good programmer (I write the way I do because because my dad is a stickler for clarity in writing, would give us essays to write and reflect when we were naughty growing up, and would ask us to look at and review econometric proposals. He is also notorious for disagreeing with the answer chosen for assignments and writing really long letters (for the teacher) that I would bring to class the next day when he thought that the answer was not clear and that the book was written badly lol. I was in the Principal’s office a lot growing up, but that was because my parents were very involved in raising me, and had choice words for things they thought were not done properly. Coincidentally, I’ve noticed a common thread of people who are my PhD peers; they typically come from families with more than one parent (immigrant / non-immigrant ie regardless of our differences, I keep hearing “my parents” in conversations in Academia). That’s interesting because it might legitimately be a struggle for someone who did not have that but wants to attend grad school; maybe there are things we can do better about that (especially since most of us aren’t teaching 100% students with both parents). Anyways, my dad can give a good screed on that sort of thing and is really well read and taught Master’s students for a while, and would hire them if they did well enough in his class).
• So anyways, the vfx guy told me I would probably be a good programmer, which amused me because I have family members who are very good ones (ie did Math + CS Olympiads and stuff growing up)); I’m beginning to think that our lack of proofs in our curriculum is because, as I wrote in an application for a workshop I am attending this summer, our Mathematics curriculum is geared towards making engineers and not Mathematicians (Maths as a tool rather for its own sake, although quite a few of guys did end up becoming Maths professors and Maths educators; I know at least 1 in Canada, 1 in the UK, 1 in NY and a couple at home); Mathematics isn’t taught for the love of Mathematics (bear in mind, one of my best friends loved the subject growing up, and now has a PhD in Philosophy and kicks everyone’s butt on the planet in Wordle; she’s literally a genius in Wordle and everyone (even herself) is shocked at her scores constantly! Then again, this also goes back to what a lot of us internalized growing up about our intellectual ability culturally, but that’s a post for another day!).
• I put proofs down for a while as a thing that was weird and that I would probably never get and focused on machine learning (we did a fair amount of linear algebra, integration, differentiation in high school, and I did stats in O and A levels), but I realize now that maybe it wasn’t (the information) being relayed to me in a way that was helpful (ie through a CS class). It was wrapped in a layer of something I was grappling with, and it was also something (underneath that layer) I was grappling with. And semesters are too short for all of that. So I just felt stupid, and some of the students (also in another adjacent lab that shared a lab with us; this is why I distinguish and say Pure Maths in speaking about my experiences) were quite awful to me and I even begged to find a way to have my own space, and I had one female friend who was graduating who helped me that semester (another brilliant person who loves Plant Biology and legitimately gave up an opportunity to interview at a brilliant lab most researchers would kill to work (or hear from at all) for because she wanted to have a certain quality of life). She was my only friend that semester and I began to think about either dropping out or switching to another university.
• The first person who really helped me begin to understand is a good friend of mine (who is legitimately a genius and incredibly witty and just fun and I’m going to miss him but Rust needs him! I look forward to hearing people talk about him in the future as a great success, and my smiling and thinking that I knew him back when..); he happened to be TA-ing a class I was doing. Sometimes just having someone who is rooting for you and correcting your work is the first step (which is what I needed to get good at this stuff; show me where I took a wrong turn, don’t laugh at me and say I’m stupid for not just getting it 100% on the first day). And that is apparently how the whole Pure Maths department is; many of them also teach and see Maths as a thing that is beautiful so they will sit with you, as long as you have the curiosity and want to put in the work, and teach you everything. It’s been the best part of my grad experience; well, that and seeing them argue passionately over Pure Maths things :) This week, we were on a bus and two of them started debating about topology lol. So, there’s nowhere else to go but up, right? My point is, especially for grad school, the whole point is to fill in gaps. If there is a skill that one thinks might benefit what they want to do, fail over and over again until you get it. Who cares what other people think. The point is to gain the skill and get good at it to answer the questions and do the research you need to do. Teachers / Researchers literally do this when they pivot to publish in areas of research that aren’t their original area of expertise (look at any senior researcher and you might see pivots to other areas during a span of say, ten years; how did they do it?). I wished we normalized just teaching others, instead of gatekeeping because certain people want certain other people who look like them to keep the information in a small circle; it’s very “high school” and we could be cutting off potentially brilliant contributors who could change the field as we know it! Plus, just the act of failing and getting up again until you get it also builds your endurance for research, too!

• Bear in mind that my Pure Maths peers also care less about grades and I wanted to get better (which means I wanted more practice), so there is also probably a reason for this message (certainly not because of any constraint on their ability, because they’re really smart and fun and talk about graphs and topology and Abstract Algebra all day with you! Most of all, out of all the departments I’ve been in, they seem to be the most normal in terms of having a supportive, collaborative, “I’m not just waving my d!ck at you because I know a thing”-culture. They are legitimately funny, clever and most of all, humble, and in my mind, whatever I can do to help them as my peers, I’m always happy to do so. I’m actually excited to go back to class with them in Fall, even though quite a few of them are graduating this semester, which makes me a bit sad!). It’s been an incredible semester!

• I also started connecting more with summer people and plans, and I’m ecstatic. It’s going to be a lot of fun! As usual, there is a lot I can’t post about, but this will be my first internship of this type, and I’m super intrigued!

Things this week

• Elliptic Curves: Moduli spaces, Fundamental Domain cont’d, Katz Mazur, Cartier Divisors, Gamma-5 problem, Scholie’s Theorem
• Number Theory: Pause Week: My prof said that Silverman would win in a match between Yoda vs Silverman for May 4th (I gave a talk and got to insert Star Wars references!)
• Algebra IV: Nakayama’s Lemma, Cayley-Hamilton Theorem, Adjugate Matrices, Kronecker delta, Summary of class and plan for Barbecue (!!).
• Other things we spoke about to learn on own (Smith-Normal Form), Fundamental Theorem of Modules over PIDs, Rational Canonical Form, Jordan Canonical Form, Dimension Theory, Krull Dimensions, Krull’s Principal Ideals Theorem, Homological Algebra / Derived Functors, Algebraic Geometry in the Time of Covid, Dynkin Diagrams, Lie Theory
• Random Prob Graphs: finishing up last assignments, Ramsey Numbers K(n,n) graphs, Harris-FKG,
• Went to a Math meetup: Mercator projection, the goat problem, Archimedes’ Hat Box Theorem, Slow Diverging Series, etc
• Rigorous Statistics (based in Japan and California): Convergence in Random Variables, estimators and asymptotic theory
• Graphs, Networks and ML (randomly learning with some Californian friends for fun every couple of weeks): Granovetter, Zachary’s Karate Club example (pretty hilarious explanation) and cuts, Making of a Null model and expectation of edges between nodes for multigraphs, Louvain Modularity and Modularity gain, Super nodes, Label Propagation, Triadic closure, NOCD, BigCLAM, AGM (Community Affiliation Graph Model), Lovain for disjoint communities vs overlapping communities. Next session is on generative models, knowledge graphs and recommender systems!

Favourite quotes this week (by one of my favourite people in the whole world here!)

• “I’m sorry; Elliptic curves are female in french, so the big ones are mamas not papas!”
• “It can tell you by having the baby elliptic curve hom into the mama elliptic curve”

Oh, Weird Al

• My prof gave myself and two other students tickets to a show she couldn’t go to, and it ended up being VIP tickets, and I ended up getting an autograph.
• I took it in good spirit, and it was a fun show, but autographs are funny / awkward (??) for me, considering I used to work in entertainment. I mostly feel happy for entertainers these days, as a lot of people I know in that sector lost income in 2020 and 2021 so I know they’re hustling to make it back this year, as things re-open slowly. Knowing how the sausage works, I know it’s a pyramid, in that many people are just getting by on those shows, travelling long hours, being away from family, but hopefully they (freelancers) are treated well and the union (for those who aren’t non-union contract workers) took care of them. Things are a lot different from pre-pandemic days with respect to that, and a lot of sectors didn’t make it (and there were some structural issues with that industry before, too). I feel kind of badly sometimes about it and try to, when I can, support their sector.

And that’s it!