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Hiro Lee Tanaka - Mathematics



Hiro Lee Tanaka – Mathematics

The Project

Hiro Tanaka - Mathematics Symplectic geometry is a field of geometry that efficiently encodes laws of motion dictating classical problems in physics. The last few decades have seen a burst of activity in the field thanks to the emergence of powerful algebraic tools called Fukaya categories. At the same time, the development of a new language for “spectral algebra”—an algebra that mixes traditional notions of adding and multiplying with more contemporary tools for studying shapes of arbitrarily high dimensions—has allowed us to organize sophisticated structures using algebraic intuitions. 

These two storylines have been highly fruitful but have yet to cross-pollinate. This project aims to construct a long-sought-after bridge: to not only produce spectral methods for studying symplectic geometry but also to establish symplectic tools for studying spectral algebra. The end result would accomplish a task that mathematicians have been unable to achieve for over 25 years and create new opportunities for understanding the fundamental building blocks in both branches of mathematics.

The project will also support numerous educational initiatives aimed at enriching and diversifying the mathematics community. These include the creation of a math podcast for and by students, a workshop for students to learn contemporary mathematical techniques of interest, and various co-curricular activities aimed at fostering communities of emerging mathematicians.

CAREER Journey

My first two applications for NSF grants were unsuccessful. So, this time around, I decided to send early drafts to colleagues to solicit feedback. I was lucky to hear back from colleagues who had served on CAREER grant review panels; their feedback allowed me to significantly reframe my grant proposal. I also had a chance to serve on a review panel for an unrelated grant. The NSF often seeks researchers to serve on panels, and I would encourage everybody to reach out to program officers to ask if there are any upcoming panels needing reviewers. The panel experience shed light on all my past rejections; I certainly don’t feel nearly as bad for being rejected. Finally, I can’t speak for other fields, but my NSF program officers have all been incredibly helpful. Speaking to them and asking questions earlier on would have greatly streamlined my grant-writing process. I would encourage anybody applying for a grant to reach out to the relevant POs to ask questions, including what kinds of budget items are allowed.