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It was more than 2,000 years ago that Pythagoras held that “all things are made of numbers”. I came to the same conclusion and became a mathematician. My field is of course “number theory”, or more specifically, “arithmetic geometry”.

The Langlands conjecture is a conjecture that there is a mysterious relationship between two seemingly unrelated objects, and is rooted in the mystery of prime numbers. Affine Deligne-Lusztig varieties and Shimura varieties are arithmetic geometric objects known to be useful for the Langlands conjecture. Interestingly, it has become gradually clear in recent years that important information about these varieties can be computed in certain combinatorics, which originally came from mathematical physics and representation theory. My research in the Hakubi project aims to develop this further, bringing a new combinatorial approach to arithmetic geometry and ultimately contributing to the Langlands conjecture.