Peter Scholze was a massive hit at this year’s ICM, and was a favorite to win the Fields Medal months before the winners were announced on Wednesday 1st August. His plenary lecture on ‘Period Maps in p-adic Geometry’ was so popular, Riocentro staff had to open additional seating in Pavilion 6 on Saturday morning.  Everyone wanted to see the young mathematician in action.

 

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The Jimi Hendrix of mathematics took to the stage to explain his breathtaking and groundbreaking work in the field of geometry using his own, homemade, handwritten slides.

 

 

Scholze discussed recent developments in p-adic geometry, ranging from foundational results such as the degeneration of the Hodge-to-de Rham spectral sequence for ‘compact p-adic manifolds’ over new period maps on moduli spaces of abelian varieties to applications to the local and global Langlands conjectures, and the construction of universal’ p-adic cohomology theories.   He concluded his plenary with speculations on what a theory that combines all primes p, including the archimedean prime, might look like.

Scholze’s work has stunned the math community since his early twenties at Bonn University in Germany. “Peter’s work has really completely transformed what can be done, what we have access to,” said collaborator Ana Caraiani.

Humble about his greatness, Scholze constantly refers back to his forebears and contemporaries in the field.  Most of his colleagues agree that his best work is still to come.