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I care a lot about improving the world around me. On this page, I describe some thoughts and activities in this realm (at least the ones related to mathematics), organized by the various problems that they attempt to address: underrepresentation, environmental impact, public relations, and mathematics education.

underrepresentation: Though mathematics is a pursuit which is in theory equally available to all, in practice our community suffers from underrepresentation of a number of different groups, based on a wide range of factors including race, class, gender, etc. While there are certainly broader and well-documented reasons to be unsatisfied with the current state of affairs, I also think it's just plain unfortunate that the community surrounding something so beautiful remains so insular (see also "public relations").

I taught 7th grade math for Breakthrough Collaborative, a program for high-potential students from underserved communities, which strives to break the cycle of poverty through education by supporting its students in becoming first-generation college graduates. While I'm no longer involved with Breakthrough, I think it is a fantastic program, and I would highly recommend the experience to anyone interested. I found their success rate both impressive and inspiring: whereas their demographics would dictate that their students should be graduating high school and going to college at a rate of under 20%, when I worked with them Breakthrough was approaching the 70% mark for this metric.
I'll be serving as an associate editor for a (not yet launched) journal based in Morocco, which supports the growing African mathematics community. Though many of the finer aspects have yet to be determined, we've obtained an agreement from Compositio to support our initiative.
One of the particularly difficult aspects of the issue of underrepresentation is that mathematicians are all human, and as such are just as prone to cognitive biases as anyone else. I believe that it's crucial for us to openly discuss these biases, in non-judgmental terms. For example, I've caught myself numerous times wondering what someone was doing at a seminar, only to immediately realize that I had mistakenly classified them as "not a mathematician" for entirely superficial reasons. Whenever this happens, I'm certainly disappointed by my own subconscious mental processes, but far more than that I'm scared to once again reminded of the fact that someone who doesn't consider themselves to be actively discriminatory (racist / sexist / etc.) is nevertheless so very prone to these sorts of thought patterns; they can have very real effects, and by all simply reverting to the "I'm not racist!" knee-jerk reaction to any form of constructive criticism on this front, we actually prevent our community from truly moving forwards.
There are many ways in which our community can be unwelcoming to outsiders, even without anyone making it so intentionally. As a particularly visible example, I've often seen female mathematicians being repeatedly interrupted, talked over, ignored, and worse. I'm sure I've done this plenty myself, and I hereby request to be respectfully called out on it. I promise to take a deep breath before responding, to give myself the space to remember that it's okay to make mistakes and that the best thing I can do is smile, apologize sincerely, and express my gratitude for the opportunity to improve my impact on those around me.

environmental impact: Mathematicians -- and academics more generally -- tend to travel quite a bit for conferences. This has serious negative impacts on the environment. A complicating issue here is that it'd unfortunately be pretty detrimental to a young academic's career to refuse to travel, since conferences are a primary means of interacting with one's research community and making one's name, face, and work known.

I am an active proponent of "double conferences", a new eco-friendly conference format whose purpose is to reduce long-distance travel while still fostering long-distance interactions. Events take place in two different locations connected by live video stream, with the cardinal rule that everybody attends at the closer location. (In general, we expect the two locations to be on opposite sides of the Atlantic, though of course this could change.) The first two -- Higher algebra and mathematical physics in 2018 and Geometric representation theory in 2020 -- are co-hosted by the Perimeter Institute in Waterloo, Canada and the Max Planck Institute for Mathematics in Bonn, Germany. (You can see the websites here: 2018 PI/MPIM, 2020 PI/MPIM.) Organization of the third double conference is also underway.

public relations: The field of mathematics serves as a means of probing the outermost reaches of human understanding. For this reason (and many others), I think it's important that we share our art with society at large. But we do a really, really bad job of this, and the average person not only has little idea of what we do and why we think it's beautiful, but also harbors some residual fear and distaste for the field. For contrast, consider astronomy. The average's person's day-to-day life is probably roughly equally affected by astronomy and theoretical math, and yet the general public attitudes towards these two fields differ dramatically. In particular, people tend to feel like they have some basic understanding of advanced astronomical concepts such as black holes, whereas there is essentially no analogous general sense of familiarity with advanced mathematical concepts. It's a long-term goal of mine to change this. I hope that someday we can instill in the general public the same sense of awe wonder for the collective human endeavor of mathematical thought and inquiry that programs such as NASA and CERN already inspire.

Non-mathematicians frequently ask me about my research, and I've spent a fair amount of time coming up with a whole hierarchy explanations of what I work on and why I think it's interesting -- which task I find quite interesting in its own right. In particular, I generally tweak my explanations depending on who's asking, what level of detail they're interested in, how much time they'd like it to take, etc.
I maintain a website that lists snippets of toy examples and analogies to help mathematicians explain advanced mathematical concepts to non-mathematicians.
I have worked with Guerilla Science to bring mathematics outreach to festivals and other cultural events.

mathematics education: Mathematics can be an extremely effective vehicle for teaching students how to think. But at all levels, mathematics education is in dire need of improvement. Part of this is that we don't seem to do a very good job of educating our educators. Once, in middle school, I "proved" that 1=-1 through some tricky (and incorrect) applications of square roots of complex numbers; when I showed this to my teachers, not only were they unable to point out what was wrong with my argument, but they didn't even care that I had broken the entire system! Of course, part of the issue here is the general public idea of what mathematics even is (see "public relations").

I've served as a consultant to Mind My Education, a startup working to provide materials that enable K-12 students to take charge of their own education, which emphasizes students' enthusiasm, sense of agency, and metacognition as primary goals.
A key issue that's not often addressed is the difference between the clarity of a lecture and the students' actual take-home understanding. In order to combat this, I try to provide my students with an understanding of both the rigorous formalism and the intuitive thought processes that go into the material.