Rutgers-Professor lüftet zwei der größten Geheimnisse der Mathematik

> A Rutgers University-New Brunswick professor, dedicated to unraveling the mysteries of higher mathematics, has resolved two separate, fundamental problems that have baffled mathematicians for decades.

> These breakthroughs could significantly deepen our understanding of the symmetries in natural and scientific structures, as well as the long-term behavior of random processes across diverse fields including chemistry, physics, engineering, computer science, and economics.

> Pham Tiep has completed a proof of the 1955 Height Zero Conjecture posed by Richard Brauer, a leading German-American mathematician who died in 1977. Proof of the conjecture – commonly viewed as one of the most outstanding challenges in a field of math known as the representation theory of finite groups – was published in the September issue of the Annals of Mathematics.

> “A conjecture is an idea that you believe has some validity,” said Tiep, who has thought about the Brauer problem for most of his career and worked on it intensively for the past 10 years. “But conjectures have to be proven. I was hoping to advance the field. I never expected to be able to solve this one.”

> In the second advance, Tiep solved a difficult problem in what is known as the Deligne-Lusztig theory, part of the foundational machinery of representation theory. The breakthrough touches on traces, an important feature of a rectangular array known as a matrix. The trace of a matrix is the sum of its diagonal elements.

> Both breakthroughs are advances in the field of representation theory of finite groups, a subset of algebra. Representation theory is an important tool in many areas of math, including number theory and algebraic geometry as well as in the physical sciences, including particle physics. Through mathematical objects known as groups, representation theory also has been used to study symmetry in molecules, encrypt messages and produce error-correcting codes.