Geometry of Light

Have you ever mused over the cusp of light in your morning coffee cup, or eyed the highlight on a polished cue ball? What you were observing was an optical phenomenon called a caustic.

Caustics are patterns that emerge from the reflection of light rays off surfaces — like the sparkle of sunlight on Lake Spafford in the UC Davis Arboretum. The mathematics that explains caustics is called contact geometry. That’s the specialty of Roger Casals, an assistant professor in the Department of Mathematics. Casals was recently awarded both a Sloan Research Fellowship and a National Science Foundation Faculty Early Career Development award to support his work.

Ducks swim in the UC Davis Arboretum Waterway.

Contact geometry has connections to string theory, which seeks to explain all fundamental particles and forces in the universe as tiny, vibrating, one-dimensional strings.

So the next time you gaze into your morning coffee, you’re connecting with the basic mathematics of the universe.

Adapted from a story by Andy Fell, UC Davis Strategic Communications.