A couple of mathematics solves the problem of the main group theory – after 20 years of work

But one of the graduate students in Malley was in the case. Preta Sebeth.

“Our obsession”

In 2003, SPäth arrived at Castle University to start a doctorate with Malle. It was perfectly suitable to work on McKay Conjecture: Even in high school, she could spend days or weeks in one problem. I have been particularly discovered that that tested her endurance, and remembers with pride in long hours, she spent the search for “tricks that, somehow, even very deep.”

SPäth spent her time studying group representations as much as she could. After completing a graduate degree, I decided to use this experience to continue cutting in MCKAY Conjcture. “She really has this intuition and good,” said Chevir Fry, her friend and collaborator. “She is able to see it will be like this.”

Compliment from Quanta magazine

A few years later, in 2010, Späth began working at Paris Cité University, where I met Cabnes. He was an expert in the narrower collection of groups in the re -formulated version center from MCKAY Conjecture, and Späth often went to his office to ask questions. He recalls that Kabanz “has always protested”, “These groups are complicated, my God.” Despite his initial frequency, it eventually grew up with the problem. It has become “our obsession”.

There are four categories of lying type groups. Together, Späth and Cabnes began to prove the guesswork of each of these categories, and they are I mentioned several The main results During the next decade.

Their work led them to develop a deep understanding of groups of the type of lie. Although these groups are the most common basic building blocks for other groups, and therefore the great sporting interest, it is difficult to study their actual acts. Kaban Warsb has often depended on the unusual theories of different mathematics areas. But in digging these theories, they have provided some of the best descriptions so far from these important groups.

As they did, they started dating and continued to have two children. (They finally settled together in Germany, where they enjoy working together in one of the three white panels in their home.)

By 2018, they had only one category of the remaining lying groups. Once you were completed, they would have proven guess.

This final case took another six years.

“Amazing achievement”

Sabeth said that the fourth type of the lying group “faced many difficulties, and a lot of bad surprises.” (This did not help in 2020, the epidemic kept two young children at home from school, making it difficult for them to work). But gradually, she and Kabanz managed to show that the number of shows for these groups match their SYLOW lovers – and that the way in which the representations link meet the necessary rules. The last case has been implemented. It was automatically followed that guessing Macai was correct.

In October 2023, they finally felt adequate confidence in their evidence to announce the room of more than 100 mathematicians. After a year, they are Publish it on the Internet For the rest of society to digest. “It is a very amazing achievement,” he said Radha Kisar From Manchester University.