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答えは期待していないので、独断と偏見で勝手に書きますよ
今年の宇宙際タイヒミューラー理論サミットで、新しい人やテーマを下記に抜粋します

https://www.maths.nottingham.ac.uk/plp/pmzibf/files/iut2.html
宇宙際タイヒミューラー理論サミット２０２１
https://www.maths.nottingham.ac.uk/plp/pmzibf/files/schedule4.pdf
Abstracts

Speaker: Benjamin Collas
Title: Principles of Inter-universal Teichm¨uller Geometry
Abstract: Grothendieck’s original functorial algebraic geometry of rings and schemes,
once exposed to further classical questions as can be seen in the examples of the sheaf
model category of motives and the group-theoretic anabelian geometry, crystallizes into
new fields which then thrive on new techniques and new questions.
We here review some key techniques and principles of IUT geometry, a categorical
monoidal weakened version of scheme theory whose symmetries reflect the anabelian
geometric point-reconstruction of spaces in terms of Galois-rational data, which then
results in a new kind of anabelian-diophantine geometry.
This talk should be considered as a modest and first attempt to throw a transversal
light on IUT theory.

Speaker: Ivan Fesenko
Title: IUT and modern number theory
Abstract: I will discuss the potential of IUT and anabelian geometry to cause or influence
developments in parts of modern number theory including the Langlands program, higher
class field theory and arithmetic of elliptic curves.

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