The main research interests of Robert C. Penner are moduli spaces and their applications to physics and biology; geometry, especially in its confluences with theoretical physics, specifically 2d and 3d quantum gravity, and with theoretical biology, notably structural biology and macromolecules; string theory – and attempt to reconcile the theories of quantum gravity and quantum mechanics with general relativity; theoretical high-energy physics and mathematical physics, particularly quantum physics; low-dimensional topology.

Robert Penner wrote an article in which he explains how curiosity and a little help from friends have led to his COVID initiative.