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.

- 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.

- Together with David Ayala, Kevin Costello, Owen Gwilliam, Andre Henriques, Theo Johnson-Freyd, and Peter Teichner, I am working to organize a "double-conference": this will be a conference that is held in two locations on opposite sides of the Atlantic simultaneously, joined by live video feed, with the cardinal rule that nobody flies across the Atlantic to attend. We're currently working to secure the respective locations of the Perimeter Institute for Theoretical Physics (in Waterloo, Ontario) and the Max Planck Institute for Mathematics (in Bonn, Germany). We're also grateful for the consultation of Daniel Thorpe, who is an expert on engineering and sustainability. In order to multiply the impact of our efforts, we also plan to write a handbook to help others organize double-conferences in the future.

- 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 plans to work with Guerilla Science to bring mathematics installations to festivals and other cultural events.

- 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.