From June 4 — 10, 2017, there will be a workshop on homotopy type theory as one of the AMS’s Mathematical Research Communities (MRCs).
The MRC program
nurtures early-career mathematicians—those who are close to finishing their doctorates or have recently finished—and provides them with opportunities to build social and collaborative networks to inspire and sustain each other in their work.
MRCs are held in the “breathtaking mountain setting” of Snowbird Resort in Utah. The HoTT MRC will be organized by Dan Christensen, Chris Kapulkin, Dan Licata, Emily Riehl, and myself. From the description:
The goal of this workshop is to bring together advanced graduate students and postdocs having some background in one (or more) areas such as algebraic topology, category theory, mathematical logic, or computer science, with the goal of learning how these areas come together in homotopy type theory, and working together to prove new results. Basic knowledge of just one of these areas will be sufficient to be a successful participant.
So if you are within a few years of your Ph.D. on either side, and are interested in HoTT, please consider applying! I think this has the potential to be a really exciting week, and a really great way to “jump-start” a research program in HoTT or related to it. Even though the application deadline isn’t until March 1, we would appreciate it for planning purposes if interested folks could apply as soon as possible. (The majority of places are for U.S. citizens or those affiliated with U.S. institutions, though there may be space for a few international participants. Women and underrepresented minorities are especially encouraged to apply.)
There are a lot of things that might happen at this workshop. There is a general list of topics posted with the description, and as the date approaches we’ll make further plans depending on our participants and their backgrounds (which is one of the reasons we want you to apply now). One topic that I think is a good candidate for quick progress is synthetic homotopy theory, where I suspect there’s still a lot of low-hanging fruit ready to be picked by collaborations between people familiar with classical homotopy theory and people with more experience thinking type-theoretically. Another topic that’s less of a sure thing, but that I am really hoping to get more people working on, is the problem of semantics for univalence: although I’ve about exhausted my own ideas in this direction, I still have hopes that there are model categories with strict univalent universes out there that present all -toposes, which might be found by fresh eyes. And, as you can see, there are plenty of other potential topics as well.
Feel free to ask any questions of me or any of the organizers.