South Middlesex Times

A Rutgers University-New Brunswick professor has resolved two fundamental mathematical problems that have challenged experts for decades. Pham Tiep, a distinguished professor of mathematics at Rutgers, completed a proof of the 1955 Height Zero Conjecture by Richard Brauer. This conjecture is a significant challenge in the representation theory of finite groups and was published in the Annals of Mathematics.

Tiep remarked, “A conjecture is an idea that you believe has some validity,” explaining his dedication to the problem over his career. He expressed surprise at solving it, stating, “I never expected to be able to solve this one.”

The second breakthrough involved solving a complex problem in Deligne-Lusztig theory, part of representation theory's foundational machinery. This work focuses on traces in matrices and was detailed in Inventiones mathematicae and Annals.

Stephen Miller, chair of the Department of Mathematics at Rutgers, praised Tiep’s contributions: “Tiep’s high-quality work and expertise on finite groups has allowed Rutgers to maintain its status as a top world-wide center in the subject.”

Tiep noted that insights from these solutions could lead to further breakthroughs in mathematics, including conjectures by John Thompson and Alexander Lubotzky. Representation theory plays a crucial role across various fields such as number theory and particle physics.

Tiep emphasized his reliance on traditional methods: pen and paper. Despite advancements in technology used by colleagues, he stated that progress often comes during moments of reflection or daily activities.

Collaborators on these projects included Gunter Malle from Technische Universität Kaiserslautern, Gabriel Navarro from Universitat de València, Amanda Schaeffer Fry from the University of Denver, Robert Guralnick from the University of Southern California, and Michael Larsen from Indiana University.

Miller highlighted the significance of their findings: “It’s a mature subject which is important from many angles, so progress is hard – and applications are many.”