Daniel Thompson, assistant professor, mathematics, has been granted a five-year, $445,000 NSF CAREER Award for his project, Entropy in dynamics: connections with geometry, algebraic numbers, and bioscience.

The CAREER award is the top award given by the National Science Foundation to support the work of junior faculty members. Those selected exemplify the role of teacher-scholars through outstanding research, excellent teaching and the integration of education and research within the context of their organization's mission.

This is the second CAREER Award for ASC researchers in less than two months. Chemist Hannah Shafaat received a CAREER award in January.

Thompson’s award will support his core research program in pure mathematics, and allow him to develop connections in the applied setting of bioinformatics.

It also enhances his outreach in mathematics and STEM education for K-12 students from under-represented groups.

Thompson’s main research area lies at the intersection of ergodic theory and dynamical systems — “two sides of the same coin,” he said.

“Essentially, my field is the study of systems that change over time — you take a point in the system and you want to say something about where it will go when you let time evolve. This kind of setup arises in all sorts of mathematical and applied settings, and there’s a fascinating interplay between concrete problems from the natural sciences and the abstract mathematical theory.

“In some situations, the abstract probabilistic point of view is most effective, and that’s what we call ergodic theory. That’s where the majority of my research lives, but I’m also fascinated and inspired by the applied side of the theory.

“My work — and more generally the entropy theory of dynamical systems — might best be characterized as being about detecting — and quantifying — the unpredictable. Entropy is a number which tells you how much complexity is in the system, and for chaotic systems where you can’t hope to say much about the behavior of individual points, there’s still an amazingly powerful mathematical theory to describe the system as a whole based on the entropy, and related concepts.

“The challenge in my field is to understand high dimensional systems, where things are even more complicated, and I’m particularly motivated by some high dimensional chaotic systems that arise naturally in geometry.”

Now, Thompson is working to implement his theoretical research in the applied setting of bioinformatics at the NSF-funded Mathematical Biosciences Institute (MBI). MBI researchers apply diverse mathematical skills to find solutions to problems in the biological and health sciences. “That’s one of the main aspects of this grant,” he said, “I’m always looking to relate my work to other areas. I can bring my training in pure math to bear on interpreting complexity and say something real about issues in bioinformatics. The connection is that a big complicated data set can look quite a lot like a chaotic dynamical system.

“The thing about basic research is that you are developing this foundation, building this world, and you’re free from worrying too much about anything practical, and then you hear about problems in biology dealing with big data sets — and you realize that you have all these tools from the pure theory that can be adapted to measure those complexities.

“That’s the interplay between pure and applied mathematics — sometimes the applied problems motivate the theory, and sometimes the theory gives you a new tool for the applied problems.”

Thompson is based at the MBI this semester to interact with other MBI researchers, and to develop this line of research.

“The MBI is a really great resource, and it’s one of the things that sets Ohio State apart. Literally hundreds of interdisciplinary researchers visit the MBI every year from all around the world, so we’re hearing about all the latest research, and we’ve got a great forum to interact with researchers from other disciplines.”

Outreach is another area that concerns Thompson, particularly developing programs for mathematics and STEM education for K-12 students from under-represented groups. In summer 2013, together with his colleagues John Johnson and Adriana Dawes, he began work with Ohio State’s Young Scholars Program to develop and deliver the mathematical content for the 'Building Mathematical Capacity Summer Experience' summer camp for rising 10th graders.

“The Summer Experience was all about giving the students a positive impression of mathematics — we designed workshops on number theory, mathematical biology and the mathematics of voting, and the students worked in groups on a project of their choice.

“We had groups working on cryptography, game theory, the mathematics of basketball and using data about the movies to predict how successful a new release will be. One group worked out a formula for how fast the venom of a Komodo dragon will kill you based on estimating the volume of blood in your body! It was great to see the students getting excited about their projects, and I hope that experience has stayed with them.

“The program I’m setting up now has a different flavor — we’re focusing on college-readiness in mathematics for the 12^th grade Young Scholars. We’re setting up a year round math enrichment program to get their math skills where they need to be to succeed at Ohio State.

“These are very intelligent students, and it seems to me that if you make sure they know what they need to do, and give them a path to doing that, you’re going to see a big improvement in their math outcomes.

“They’ll be working on educational software on iPads, which will pinpoint exactly what math skills they need to improve, and the iPad-based training will be supplemented with individualized mentoring. The CAREER award is funding the software licenses for this program, so it’s giving these plans a huge boost."

Thompson completed his PhD in mathematics at the University of Warwick in the UK in 2009, then was a Chowla Research Assistant Professor at Penn State for three years before coming to Ohio State, autumn, 2012.

Thompson looked at several schools, but said, “Ohio State’s math department is really first-class — and not just in one area, but is strong across an incredible range of areas. The number of Sloan Fellows and NSF Career Award winners speaks to its national reputation and support of young mathematicians.

“Also, as a musician who played upright bass and bass guitar in bands pretty much continuously since high school, I found Columbus’s thriving local music scene appealing. There are some really excellent singer-songwriters and instrumentalists in town, and I’ve had some great experiences sitting in with a number of local bands. There’s just a lot going on here, and it’s been great to be a part of that.”

—Sandi Rutkowski