Roger Casals Gutierrez, assistant professor in the Department of Mathematics, has been named a 2020 Sloan Research Fellow by the Alfred P. Sloan Foundation.
Sloan Research Fellowships, worth $75,000 over two years, are given to outstanding young researchers in mathematics, chemistry, computer science, economics, computational and evolutionary molecular biology, neuroscience, ocean sciences, or physics.
This is Casals’ second prestigious award in a month, the first coming from the National Science Foundation: $450,000 over five years. It’s a CAREER award from the NSF’s Faculty Early Career Development Program, supporting junior faculty who perform outstanding research, are excellent educators and integrate outreach in their work.
Casals works in an area of mathematics called contact geometry, which deals with shapes formed by rays of light bouncing off other objects. If you’ve noticed a bright curved pattern in your morning coffee cup, that is an object called a caustic that is described by contact geometry.
Contact geometry originated in control systems, where the goal is to manage complex processes with a small number of controls. It turns out to have connections in many other areas, from optics and string theory to liquid crystals. Sunlight playing on waves creates caustics, and so does the path of a car reversing into a parking space.
Casals has developed mathematical tools to describe the caustics formed by particular interactions, proving new results in geometry and connecting them to other fields.
He earned his doctorate in geometry and topology at the Institute of Mathematical Sciences in Madrid and worked at the Massachusetts Institute of Technology and University College London before joining UC Davis in 2018.