Mathematics professor honored by national research journal


Rhonda Zurn, College of Science and Engineering,, (612) 626-7959

MINNEAPOLIS / ST. PAUL (08/12/2013)—The most recent issue of the Springer journal, Foundations of Computational Mathematics (FoCM), has been published in honor of Peter Olver, College of Science and Engineering mathematics professor and head of the School of Mathematics.

A world leader and a champion of computational applied mathematics, Olver is being recognized for his valuable role in FoCM as a board member, conference organizer, and former managing editor of the journal.

For 30 years, Olver has been considered the world’s best mathematician in the application of Lie group actions to differential and discrete systems, including Hamiltonian and integrable systems. With more than 130 articles and five books (not counting his numerous proceedings volumes), his work has reached all corners of the mathematical world, from undergraduate education to professional research. 

Among his publications, two bodies of work have been the greatest influence—his graduate textbook “Applications of Lie groups to differential equations,” and his series of papers on Lie group-based moving frames. The former includes a fully detailed, computational proof of the exactness of the smooth variational complex, together with a rigorous discussion of Noether’s conservation laws and computational methods for infinite dimensional Poisson geometry and Hamiltonian systems. The book is commonly found in the library of any researcher working on differential equations, and has been used all over the world as a reference book for graduate classes. It is the best-known and most widely used book on the subject. 

Olver’s papers on group-based moving frames opened the door to using both geometric and algebraic methods in other fields. As it refers to moving frames, it was the last step in the full realization of the Erlanger program to move geometry into the realm of group theory, also fully in line with Cartan’s vision, of which Olver is a great connoisseur. The papers are based on the simple idea of equivariance, described in a way that is free from the confines of any one particular field—that of differential geometry—where frames had been used traditionally. Given Olver’s preference for widely applying simple ideas, moving frames are now being applied in many settings beyond Cartan’s original path, including discrete systems, computer vision, numerical methods, and image processing. Thus, group-based frames have served as bridge between different branches of mathematics, invigorating them, and their interaction. 

Oliver is known for the inclusive nature of his research group, always welcoming, encouraging, and nurturing interested researchers. He has 20 graduate students and countless collaborators. 

To read more, visit the Foundations of Computational Mathematics journal website.