WUPPERTAL UNIVERSITY
The investigation team
McKay’s conjecture has been unanswered since 1970 – even a group of mathematicians had a push. The then student Britta Späth did the rest of the magic.
In 2003, the German graduate student Britta Späth started studying with McKay conjecture, Dated from the 1970s, one of the biggest open problems in the domain of mathematics known as group theory.
Marc Cabanes, another mathematician, joined her in search of an answer to this great mathematician problem. While working together, the two fell in love And they ended up constituting a family.
The conjecture formulated by John McKay states that, to formulate a complete description of a group-an important mathematical entity that can become prohibitively difficult to study-it is only necessary Look at a small part of it.
A group is a set of elements combined with a rule on how these elements relate to each other. In fact, the groups are currently, according to, on the basis of all modern mathematics.
McKay observed the elements that form a special and smaller group – called sylow standardizer – Within the original group.
A sylow normalizer may contain only a fraction of a fraction of 1% of the number of larger group elements. In addition, the sylow normalizer often has a very different structure. This is also why it has always been so difficult to solve the McKay problem.
It was “years of hard, hard, hard work, and she did it, they got it,” says Persi Diaconis, a researcher at Stanford University. 2Past years, the problem was solved.
Who started to make this problem on a “treatable” subject was, in fact, the mathematician Gabriel Navarro, who, with the help of two colleagues, proved that the McKay’s conjecture had to be true for all finite groups.
“Tons and tons of conjectures have now been reduced using this as a model,” said mathematician Mandi Schaeffer.
From there, Späth took the reins. “It has a crazy and very good intuition,” says Schaeffer Fry, his friend and collaborator. “It is able to see that it will be like this.”
Cabans, who joined the investigation, “was always protesting: ‘These groups are complicated, my God,'” he recalls. Despite his initial hesitation, he also fell in love with the problem (and his own math). It became “our obsession,” he said.
Over the past six years, the couple has worked exhaustively to a single Lie -like group category. Once the process was completed, they had resolved McKay’s conjecture.
“It’s a absolutely spectacular“Commented the mathematics Radha Kessar from the University of Manchester.
Mathematicians can now study with confidence important group properties looking only at their sylow normalizers – a much easier approach to make sense of these abstract entities and that can have practical applications.
Navarro leaves a note of praise: what Späth did was a “A beautiful, wonderful and deep math. ”
