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My speciality is arithmetic geometry, a field that aims to uncover the properties of integers through a geometric perspective.

One of the central concerns of arithmetic geometry is studying the geometric properties of the shapes defined by equations in order to understand the integer/rational solutions of those equations.

An important ingredient in this pursuit is the technique so-called “mod p reduction”, which means rethinking equations in “the world of remainders modulo each prime number p”, yielding shapes that are, in a sense,”shadows cast by primes p” and contain a wealth of information. However, it is known that these shadows live in a completely different world from the original shapes and have significantly different geometric aspects.

In my study in the Hakubi project, I will investigate the behavior of “mod p reduction” for shapes with interesting symmetries called irreducible symplectic varieties, using revently developed theory of geometry in mixed characteristic.

I hope that this study lead us to reveal the nature of “mod p reduction” for more general varieties, and I also want to apply these ideas to number theory.