tldr: growing, but into what
For some a recent fellowship requirement, I was asked to fill out a form regarding the ways I expect to / want to grow as a graduate student these next few years. A sort of brainstorming exercise that actually asks that you think about how you’re going through the education process. On the form, there were spots to put how you hope to grow across the five years. While (to be completely transparent) it is more than likely they only wanted me to fill in my goals/aspirations for the first/second year, I ended up filling them in for all five (to save myself work in case this is precisely what they wanted me to do in the first place). I found this to be a helpful exercise, and through the process found myself reflecting on what I’ve been up to this first year. Plus, I’ve been meaning to do a post on what I’ve been up to recently… so here we go.
When it comes to my first year in particular, there are some very real and concrete goals I hope to achieve for my career, not the least of which includes studying for and taking my qualifying exams. My goal is to take them by the end of Summer 2026, for reasons I will discuss later on in this post. For those interested, here is what I plan to take. [For those who don’t know: qualifying exams in the math department involve one major and two minor topics of your choosing (with approval from your advisor), and are done orally.]
(1) Harmonic Analysis [my major topic]: Naturally as a harmonic analyst, this is going to be my main topic taken under my advisor Larry Guth. It seems likely that the topics this qual will cover will involve a mixture of projection theory and restriction theory (the former of which I’ve studied through my research, the latter of which seems to appear everywhere, terrifies me, and that I fundamentally need to know as a person in this field). The setup for this qual is to “Read things I am interested in this semester, and through this reading we will pick topics to study from there.” This currently has included Falconer distance-type problems via restriction theory (e.g. Du-Zhang) and the Elekes-Sharir framework over finite fields (e.g. work of Iosevich). This reading popped out of investing and analyzing the regularity of solutions to PDE (such as the free Schrodinger equation).
(2) Stochastic Calculus: Before I had landed on this topic in probability, I had originally suggested a few other topics to Larry (e.g. chaotic and/or homogeneous dynamics), but to be completely fair to him this topic is quite closely related to my interests in harmonic analysis (e.g. projection and restriction theory). That said, the topic of stochastic calculus (and rigorously studying stochastic processes) is very nicely analytical. It’s giving me a completely new perspective on problems and tools from analysis, and I in large part have Nike Sun (who I will be taking the qual with) and Le Gall (the author of the book I am reading on this topic, for which I bought a personal copy as it’s so well written) to thank. To study for this qual I am simultaneously taking the class on Stochastic Calculus this semester, and while it has been hard it has been a nice change of pace in comparison to my other quals. My other topics I am having to read and learn about on my own– at least this way I have to study for the midterm, do the PSETs, and follow along at the pace of the class.
(3) Algebraic Combinatorics: As a projection theorist, I often encounter the Grassmannian (the space of k-dimensional linear subspaces in Euclidean space) or relatedly the affine Grassmannian (the space of k-dimensional affine subspaces). As such (largely motivated by my research interests), I am interested in learning about the combinatorics of the Grassmannian which starts to get into the topic of algebraic combinatorics. I am planning to take this topic with Alexander Postnikov, with whom I am meeting on Monday to discuss what this qual will look like in practice. My hope, ideally, is to learn that material from Fulton’s Young Tableaux Part 3 (on geometry), and the material necessary for understanding that part of the book.
. . .
I’ve been enjoying getting to just sit down and learn this semester. Both because it works towards the tangible goal of completing my qualifying exams, and because learning a foundational topic that is well-studied/exposited is immensely fun. I have been enjoying my current research projects, but at the same rate it feels so important to be able to have other things going on that utilize another part of your brain.
To this end, let’s now discuss the ways I want to grow as an educator / mentor, which this brainstorming exercise also asked me to reflect on. And let me tell you: I have a lot of updates on this topic. My first year has already been busy as hell regarding educational projects.
(1) This year, I began coorganizing PRIMES Circle: a free math reading program with undergraduate mentors at MIT for Boston-area high school students. This fall I was working through the PRIMES Circle admissions process, and am now running the program with my coorganizer Mary. It’s so cool being on the other side of this program having been an undergraduate mentor for it 3 out of the 4 years I was an undergrad. It especially feels cool to take on this project as next year I will be taking over the program as Mary will be graduating. [I need to find a new coorganizer… anyways.]
(2) This is my first year as the residential director of MathROOTS! I’m enjoying learning the ropes and getting this ship up and running. We are currently in the application process (with a LOT of submitted applications). I can’t believe that in a few months we will have a new cohort of 20 new campers.
(3) Lastly, I’ve also been mentoring and running various projects around the department. I am currently doing my first reading project with an undergraduate student under Larry (as I did all those years ago). So far, this project has involved investigating Peano’s space filling curve, and soon will segue into learning about Lebesgue measure. Additionally, as of *checks watch* two days ago, I told a friend I would be interested in running the PUre MAth GRAduate Student Seminar (PUMAGRASS) next year [it is typically run by second year students, and the way I see it is that I only have one year to be a second year]. I am very excited about the prospect of getting to work on that project.
. . .
The last thing big part of the brainstorming activity asked us to reflect on what we have accomplished and are proud of, and ways we want to grow. This was quite a fun topic to think about, especially as I feel I’ve grown a lot this past year.
(1) Firstly, I got a fucking master’s degree. I wrote a 112 page thesis that I’m proud of, and am officially the first in my family to have gotten a graduate degree. [One down…]
(2) Secondly, my world is physically growing. Going to MIT was my first time really out of California (unless you count Las Vegas, which was a lovely trip but I wouldn’t say that I really got to Know Nevada), and UBC was my first time out of the States. I am very proud to say that this next year I will get to visit Europe not once, but twice: Once to Hungary for a workshop and summer school at the Renyi Institute, as well as Sweden for a semester school at the Institut Mittag-Leffler (both dream locations to visit). [Note: the Mittag-Leffler semester school is the key reason why I am looking into completing my qualifying exams this summer—so I don’t need to worry about them there.] Who knows, maybe soon I will be able to visit Asia, Africa, and South America to pursue mathematics.
(3) Finally, I have been able to foster new collaborations through the American Institute of Mathematics SQuaREs program! This has been an astounding experience with close friends.
. . .
But all of that pertains to this year. When I thought about how I want to grow in my career over the next few years (as I did for the brainstorming activity), I came to the conclusion that I look forward to transitioning away from things. Away from high school mentoring programs to help transition to new leadership, and away from travelling to focus in on my doctoral research.
When I wrote this down, I felt surprised at myself. I mean, don’t get me wrong, if come my 4th year no one steps up to direct MathROOTS or PRIMES Circle, or I get invited to some cool opportunity abroad, I’ll certainly consider continuing. But nonetheless, planning to move away from these programs feels like a way in which I need to grow. I need to learn how to not just let go, but to pass on— to take the next step. And as much as my dream job would be to help people organize and run mentorship programs (from the high school to graduate student level), such a dream job feels purely like a fantasy. Not just that— it feels like it’s actively competing with my dreams of pursuing academia and being a professor. My dreams of getting a postdoc at one of the few places I dare not speak nor write for fear of jinxing myself in 5 years time. [Nearly 4 years… yikes.] And while I can dream that one day I might be able to return to the ‘tute and be a professor running such programs, that’s a long shot by any means of the word. Furthermore, even if I should get the privilege of getting to pursue such a career, I feel that I will regardless need some time away (say, to do a postdoc). So, in any case, I’ll need to learn to let go. And I am excited to do so.
Something something if you love something…
i'm just projecting 