# May Prize Spotlight: Margaret Beck and Philip Holmes

Congratulations to these two members of the SIAM community, who were recently awarded the J. D. Crawford Prize and the Jürgen Moser Lecture.

## Margaret Beck - J. D. Crawford Prize

The SIAM Activity Group on Dynamical Systems (SIAG/DS) awards the J. D. Crawford Prize every two years to an individual for recent outstanding work on a topic in nonlinear science, as evidenced by a publication in English in a peer-reviewed journal. The term “nonlinear science” is used in the spirit of the SIAM Activity Group on Dynamical Systems conferences. Specifically, it includes dynamical systems theory and its applications as well as experiments, computations, and simulations.

Beck is an associate professor in the Department of Mathematics and Statistics at Boston University. As an undergraduate at Colorado College, she earned her BA in mathematics and spent much of her non-mathematical time on the soccer field and in the darkroom. She completed her PhD in mathematics at Boston University in 2006. After spending three years in postdoctoral positions, traveling among the University of Surrey, the Mathematical Sciences Research Institute (MSRI), and Brown University, she returned to Boston University as an assistant professor in 2009.

**Q:** *Why are you excited to be awarded the J. D. Crawford Prize?*

**A:** I am honored to receive this prize, particularly because previous recipients include mathematicians whose work I greatly admire!

**Q:** *Could you tell us a bit about the research that won you the prize?*

**A:** My work is focused on understanding the long-time behavior of solutions to PDEs, typically ones that can be viewed as infinite-dimensional dynamical systems. Often I approach this by considering coherent structures in the model and analyzing their stability, meaning whether or not small perturbations of the state remain small as it evolves over time. Stable perturbations typically correspond to physically observable phenomena. Recently I've been particularly interested in spectral stability, which amounts to analyzing the spectra of linear differential operators, and how this can be connected with a topological invariant known as the Maslov index. This has been particularly fun for me, because I've been able to learn about and use ideas from several different areas within mathematics: dynamics, topology, and symplectic geometry.

**Q:** *What does your research mean to the public?*

**A:** I hope that my work will contribute to the repository of mathematical tools that other researchers can use to understand specific models of interest in a variety of applications.

**Q:** *What does participation in SIAM mean to you?*

**A:** SIAM has been very important to me. My first SIAM conference was the 2003 SIAM Conference on Applications of Dynamical Systems (DS03). Directly due to my positive experience at the 2004 SIAM Conference in Nonlinear Waves and Coherent Structures (NW04), I became excited about and committed to a career in mathematics.

## Philip Holmes - Jürgen Moser Lecture

The SIAM Activity Group on Dynamical Systems (SIAG/DS) awards the Jürgen Moser Lecture prize every two years to an individual who has made distinguished contributions to nonlinear science. The term “nonlinear science” is used in the spirit of the SIAM Activity Group on Dynamical Systems conferences. Specifically, it includes dynamical systems theory and its applications as well as experiments, computations, and simulations. The 2019 award of the Jürgen Moser Lecture recognizes Holmes for his fundamental contributions both to the mathematical theory of dynamical systems and to a broad range of applications in physics, optics, neuroscience, and engineering.

**Q:**** ***Why are you excited to be awarded the Jürgen Moser Lecture?*

**A:** I am honored to receive the Jürgen Moser Lecture prize, especially because the distinguished former winners span my scientific interests and they have encouraged me, wittingly or not, to follow in their paths. I hope that my lecture at DS19 conveyed the fun I've found discovering areas in science where dynamical systems theory can create new descriptions, predictions, and deeper understanding.

**Q:**** ***Could you tell us a bit about the research that won you the prize?*

**A:** The citation, composed by the kind colleagues who nominated me, mentions "... contributions both to the mathematical theory of dynamical systems and to ... applications in physics, optics, neuroscience, and engineering." Here is what set me on this path. While finishing a thesis on vibration transmission in structures in 1973-4, I was lucky to discover papers and books on bifurcation theory. Then, working with an old analog computer, I found chaotic oscillations in a simple mathematical model. These events prompted a wonderful journey through classical and fluid mechanics and into the neuromechanics of locomotion and the neuroscience of decision making. Throughout, I was fortunate to advise terrific students and postdocs, and in return, to be advised by them.

**Q:** *What does your research mean to the public?*

**A: **I hope to have contributed to the modeling, analysis, and understanding of bodies, both inanimate and animate, in motion and in thought. More technically, my research and that of my students, postdocs and colleagues aims to help solve some of the mysteries remaining in dynamics, biomechanics and neuroscience. For example, we have worked on the general question of how action potentials (electrical impulses emitted by neurons) give rise to behavior. In the case of locomotion, we study how control signals from the brain interact with pattern-generating neural circuits in the thoraxes of insects. Through the study of such simpler model organisms, we hope to contribute to improving the treatment of paralysis. We have also investigated neural mechanisms in human and non-human primates that integrate visual evidence, and proposed optimal strategies for decision making in response to environmental cues.

**Q:** *What does being a SIAM member mean to you?*

**A: **The society forms a delightfully diverse community of scholars and creators. I have benefited greatly from SIAM's meetings, publications and workshops, which encompass the mathematical sciences, connect with all other fields of science, and even go beyond them.