Whether he wants to be or not, Peter Scholze is the big star of this year’s ICM. He was also a huge favourite 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 needed to open the upper levels of seating in Pavilion 6 on Saturday morning. Everyone wanted to see the young rock star 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.
He 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.
Peter finished with some speculations on what a theory that combines all primes p, including the archimedean prime, might look like.
Ever since bursting onto the scene in his early twenties studying at Bonn University in Germany, Peter’s work, along with collaborators, has stunned the math community.
“Peter’s work has really completely transformed what can be done, what we have access to,” one of his collaborators, Ana Caraiani has said.
Always referring back to his forebears and contempories in the field, Scholze is humble with his greatness. The really exciting thing is that most of his colleagues believe that his best work is still ahead of him.