John McCarthy reflects on his longtime collaboration with fellow mathematician Jim Agler.
By Claire Navarro
John McCarthy, chair of mathematics and the Spencer T. Olin Professor in Arts & Sciences, remembers the first time he became interested in free analysis, a rapidly developing area of modern mathematics which studies function theory in free noncommutative variables.
“Jim Agler and I were at a conference in Banff when we heard Victor Vinnikov give a talk on free analysis,” McCarthy recalls. “It sounded interesting, and perhaps would help us solve a problem we were stuck on, so we decided to try to understand it. It turned into a very enjoyable project.”
It seems fitting that McCarthy and Agler together discovered a curiosity for free analysis. The two mathematicians began collaborating more than 25 years ago, and their joint efforts have resulted in some thirty coauthored papers. One of these articles, “Global Holomorphic Functions in Several Noncommuting Variables,” recently earned McCarthy and Agler the 2016 G. de B. Robinson Award.
McCarthy notes that collaboration played a vital role in both this recent achievement and his career more broadly. “Creating mathematics is inherently frustrating – you are constantly trying to come up with new ideas, and even when you do, most of the time they don't pan out,” he says. “Having a collaborator you can share your insights with, even if ultimately they don't get you very far, makes it much easier to keep going.”
Creating mathematics is inherently frustrating ... Having a collaborator you can share your insights with, even if ultimately they don't get you very far, makes it much easier to keep going.”
Luckily, Agler, a professor at the University of California, San Diego, shares a common outlook and mathematical interests. Both he and McCarthy are well-known specialists in multivariate complex analysis and operator theory.
“Jim has been the most important person in my professional life,” says McCarthy. “I met him by chance 25 years ago, and we hit it off. Before I had children, I would spend large chunks of time in San Diego, and we would sit outside at cafes and do mathematics all day. It was very intense, and very exciting as we made new discoveries.”
The Canadian Mathematical Society, which grants the G de. B. Robinson Award in recognition of an outstanding paper contributed to the Canadian Journal of Mathematics, recently recognized one of the results of this long-term friendship and pooling of intellectual resources.
The prize-winning article is “without doubt is one of the most influential papers in the area,” according to the selection committee. “The article’s nomination for the Robinson Prize was enthusiastically supported by the CMS Editorial Board due to its novelty, originality and introduction of important techniques leading to pioneering results.”
We would sit outside at cafes and do mathematics all day. It was very intense, and very exciting as we made new discoveries.”
“It was very kind of the Canadian Mathematical Society to give us this award,” McCarthy says. His interest in free analysis now also includes collaborators here at WashU; he and fellow professor Xiang Tang hosted a seminar on free analysis. “It was attended by analysts, algebraists and geometers - that was very exciting,” McCarthy says.
Owing to time, geography, and family life, over the years McCarthy’s and Agler’s partnership has shifted from sunny Californian cafes to Skype, but they continue to work together toward mathematical discoveries.
“It is nice to know that at least one other person in the world cares about your lemma*,” McCarthy says.
*As all dictionaries and mathematical collaborators know, a lemma is a subsidiary or intermediate theorem in an argument or proof.