Robert Guralnick of mathematics is elected a fellow of the American Association for the Advancement of Science (AAAS)

Robert Guralnick, professor of mathematics at USC Dornsife, has been elected a fellow of the American Association for the Advancement of Science (AAAS), the world’s largest general scientific society. Guralnick earned the honor “for being perhaps the central figure at the moment in the very broad domain of group theory,” the AAAS said in a statement.

Founded in 1848, the AAAS is a nonprofit and publisher of the journal Science. The organization launched its tradition of electing fellows in 1874.

Election as an AAAS fellow honors members whose efforts on behalf of the advancement of science or its applications in service to society have distinguished them among their peers and colleagues.

Guralnick said he was very pleased and happy to receive the honor.

“I do mathematics because I love doing mathematics, but it’s always nice to get endorsements of your work from other people,” he said. “It’s evidence that your work has been found to be important and has made significant contributions to the field, so it’s a nice symbol of recognition.”

Guralnick said he felt particularly honored as many AAAS fellows are recognized as being among the top mathematicians in the world, including several of his colleagues at USC Dornsife, among them Susan Montgomery, Susan Friedlander and Michael Waterman.

Eric Friedlander, Dean’s Professor of Mathematics and chair of mathematics, said Guralnick is probably the world’s leading group theorist.

“His research output is incredible, including more than 230 published papers in leading journals with 135 coauthors,” Friedlander said. “Bob’s research establishes properties about groups — both finite and infinite — and applies these results to diverse mathematical subjects such as number theory, algebraic geometry and combinatorics.

“Since AAAS is the largest and most influential scientific society in the world, to be a fellow of AAAS is especially significant and a most well deserved honor for Bob  — and indirectly for the USC math department.”

Leading group theorist

Groups are a fundamental object in mathematics, naturally appearing during the study of symmetry in mathematics and the physical world. They are a fundamental tool in physics, chemistry and cryptography, as well as in most areas of mathematics.

Guralnick contributed to the classification of finite simple groups, a remarkable theorem in group theory that was completed in 2004 following 60 years of serious work by a large, international team of mathematicians. The final proof encompasses more than 10,000 pages.

Guralnick is one of the leaders in using this theorem to make significant progress in problems in group theory, including representation theory and cohomology. Just as importantly, he has obtained fundamental results and solved long-standing conjectures in other areas of mathematics, such as number theory and algebraic geometry.  

As well as having served as managing editor of America’s oldest mathematics journal, Transactions of the American Mathematical Society, Guralnick is currentlymanaging editor of the Forum of Mathematics, published by Cambridge University Press. He has given many distinguished lectures, including an invited talk at the International Congress of Mathematicians in Seoul in 2014 and a plenary talk at the annual American Mathematical Society meeting in 2013. He was an inaugural fellow of the AMS in 2012 and was the G. C. Steward fellow at the University of Cambridge in 2009. 

Four Trojans in all

In addition to Guralnick, three other USC scientists were among the 391 AAAS members to be elected fellows this year because of their scientifically or socially distinguished efforts to advance science or its applications. They are Wendy Cozen, professor of preventive medicine and director of the Population-based Tissue Procurement Core at the Keck School of Medicine of USC; Roger Ghanem, professor of civil and environmental engineering at USC Viterbi School of Engineering; and Michael Paine, director and professor of the master’s and doctorate program in craniofacial biology at the Herman Ostrow School of Dentistry of USC.

Guralnick and the other new AAAS fellows will be presented with a certificate and a gold and blue rosette pin symbolizing science and engineering at the annual AAAS meeting in Boston on Feb. 18.