2018 Fields Medal Award Winner Peter Scholze


Alex Wierbinski's picture

By Alex Wierbinski - Posted on 03 August 2018

AT THE FOREFRONT

The Newest-New Math

A Master of Numbers and Shapes Who Is Rewriting Arithmetic,
Quanta, August 1, 2018.

2018 Fields Medal Award Winner

Peter Scholze

"...30-year-old Scholze was awarded the medal (the Fields Medals — mathematics’ highest honor) at the International Congress of Mathematicians in Rio de Janeiro, making him one of the youngest Fields medalists ever. His award cites “the revolution that he launched in arithmetic geometry...”

"...developing a unified theory called prismatic cohomology, which envisions these different cohomologies essentially as bands of light in a cohomological rainbow."

A Fascinating Story

"...profile of Scholze from June 28, 2016..."

"Scholze’s key innovation — a class of fractal structures he calls perfectoid spaces — is only a few years old, but it already has far-reaching ramifications in the field of arithmetic geometry, where number theory and geometry come together."

"...perfectoid spaces are hard for other researchers to grasp..."

"Scholze’s result expanded the scope of rules known as reciprocity laws, which govern the behavior of polynomials that use the arithmetic of a clock..."

"Reciprocity laws are generalizations of the 200-year-old quadratic reciprocity law, a cornerstone of number theory and one of Scholze’s personal favorite theorems."

“You can interpret a lot of modern algebraic number theory as just attempts to generalize this law."

"...“Langlands program,” a collection of interconnected conjectures and theorems about the relationship between number theory, geometry and analysis. When these conjectures can be proved, they are often enormously powerful..."

"By constructing a perfectoid version of hyperbolic three-space, Scholze has discovered an entirely new suite of reciprocity laws."

Smart Germans

"...in March, for example, he became the youngest recipient ever of Germany’s prestigious Leibniz Prize, which awards 2.5 million euros to be used for future research..."

Future Maths

"Scholze continues to explore perfectoid spaces, but he has also branched out into other areas of mathematics touching on algebraic topology, which uses algebra to study shapes. “Over the course of the last year and a half, Peter has become a complete master of the subject...He changed the way [the experts] think about it.”

Peter Scholze

“I’m still in the phase where I’m trying to learn what’s there, and maybe rephrasing it in my own words,” he said. “I don’t feel like I’ve actually started doing research.”

 

 

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