The IMA has awarded David F. Anderson, an assistant professor in the Department of Mathematics at the University of Wisconsin, Madison, the inaugural IMA Prize in Mathematics and its Applications. The prize will be given at the opening of the fourth annual Abel Conference on October 31, 2014.

“When I received an email from [IMA Director] Fadil [Santosa] and subsequently spoke with him over the phone, I was shocked and happy. It is an honor to be recognized by your peers, and I am truly grateful,” he said.

Anderson received this recognition for his contributions to numerical methods for stochastic models in biology and to the mathematical theory of biological interaction networks. His work on numerical methods, and, in particular, on how to utilize different mathematical representations to construct and analyze numerical schemes, is changing the landscape of computational systems biology.

“The methods my collaborators and I have developed over the last few years have reduced the time needed to perform certain computational experiments in biology by substantial amounts—sometimes by orders of magnitude,” Anderson explained. “My friends and family often ask if we could just wait for better computers to come along to perform these calculations. The answer is no. Many needed computations in biology are so labor intensive that, even if we assume Moore’s law holds indefinitely, it would take decades to reduce the runtime to something reasonable. Waiting for better computers is simply not feasible and better numerical methods are a must.”

And when it comes to biology, the processes taking place in cells are incredibly complicated, with different constituent parts interacting through a variety of mechanisms. An important question is then: how do the interactions of these individual parts produce the emergent behavior of the entire system? This is where Anderson's work comes in. He and his collaborators model these processes with an object called a “chemical reaction network,” but the networks themselves—and associated mathematical models—are also often extraordinarily complex.

“Numerical simulation is sometimes considered the only way to analyze them,” he noted. “However, hidden within the complexity of a reaction network there are often underlying structures that, if properly quantified, give deep insight into the behavior of the system. Of course, mathematics is great at finding patterns in complexity.”

Many of his theoretical results are aimed at discovering what the possible behaviors of these systems are, based only on easily checked “patterns” in the reaction network itself. This research falls into the field of “chemical reaction network theory,” which has been gaining in popularity over the past few years.

Anderson’s work in biology was not something he expected upon entering graduate school. He credits his graduate advisor, Michael Reed of Duke University, for convincing him that the mathematical questions related to biology are hard, interesting, and really important.

“One of the first questions he asked me as a grad student was, ‘How can the cell carry on its functions in such a noisy environment?’ It was a great question that sparked my interest,” Anderson added.

His other Ph.D. advisor at Duke was Jonathan Mattingly, who introduced Anderson to the fields of probability, stochastic processes, and numerical methods. These subjects have remained important aspects of his research. But Anderson goes back to his undergraduate years to credit professor Roberto Triggiani of the University of Virginia with setting him on the path of studying mathematics, in part due to the many conversations they had about the subject.

An important and influential mentor includes his postdoc advisor, and current colleague, Tom Kurtz of the University of Wisconsin, Madison.

“I cannot overstate the influence that Tom has had on my career. Not only did he introduced me to the jump processes I now study in much of my work, but many of my results build upon, in one way or another, his research over the past few decades,” Anderson said. “Moreover, he has been a mentor in the truest sense of the word. I look back at the decision to move to Wisconsin to work with Tom as one of the best decisions of my life.”

In 2016, Anderson will spend the spring semester at the Newton Institute in Cambridge to work with collaborators on numerical methods. But until then, he will continue to enjoy the problems he has been working on for the last few years.

“I have wonderfully supportive colleagues at the University of Wisconsin and beyond, and I hope to continue to contribute to the field,” he said.

The IMA Prize in Mathematics and its Applications is awarded annually to a mathematical scientist who is within 10 years of having received his or her Ph.D. degree. The award recognizes an individual who has made a transformative impact on the mathematical sciences and their applications. The prize can recognize either a single notable achievement or acknowledge a body of work. The prize consists of a certificate and a cash award of $3,000. Funding for the IMA Prize in Mathematics and its Applications is made possible by generous donations of friends of the IMA.