My JSPS DC1 application

The results of 2022 JSPS DC1 fellowship applications just came out today. Unsurprisingly, I was not selected for the fellowship, but on the bright side, my reviews were much better than what I had expected. I received a classification of “A” (which means I was in the top 20% of all unsuccessful applicants), and my T-score (Tスコア) was 3.230, which means that I was ranked approximately in the top 35% of all applicants.

Retrospection

My proposed project was very much on the pure mathematics side of things, in terms of my research intersts. The official title of my research proposal was “様相型理論に基づく新しい数学基礎論及び代数幾何学への応用” (“A new foundation of mathematics based on modal type theory and applications towards algebraic geometry”). Broadly speaking, it is about the applications of modal HoTT and other modal type theories towards mathematics, and especially towards algebraic geometry. Every modal type theory models a specific kind of topos (for example, cohesive HoTT models cohesive toposes), and each topos corresponds to a kind of geometry. Therefore, using a topos theoretic “bridge”, a type theory corresponds to a kind of geometry; one could even say that a type theory is exactly a geometry, interpreted in a synthetic way. This could be used to develop geometry in a synthetic way, and could also facilitate computer-assisted reasoning, as well as computational applications. If you are interested in the mathematics, I have posted my application online.

Unfortunately, however, my research proposal did not receive a good enough score (3.17); it was passable, but not good. I guess several factors contributed to this:

• I classified my proposal as one about “foundations of mathematics” rather than “algebra” or “geometry”. In any case, it did not fit well into any category, but retrospecting on my application, it seems that algebra or geometry would have been better classifications; the story I was telling probably just wasn’t so exciting to logicians;
• I simply wasn’t able to spend enough time on my proposal, being very busy about my thesis;
• I probably should have consulted more with algebraic geometers and algebraic topologists.

For DC2, I suppose writing a proposal leaning more towards computer science and the applied side of things would help, as this would help me play to my strengths.

The other part of my evaluation, “qualities as a researcher” went unexpectedly well (I received a rather high score of 4.0). I guess having publications and talks helped, although they are not so directly connected to my proposal. I understand, however, that for DC2, more applicants would have had published papers, so the competition would be even more fierce on this front.