Videos

How the triangles unfolded: a case study in research illustration

Presenter
August 12, 2025
Abstract
Illustrating a mathematical object can reveal geometric structure in it, and looking for geometric structure in an object can help us illustrate it more revealingly. I saw this cycle play out in recent joint work with Arnaud Maret, where we found geometric realizations for a certain class of surface group representations by studying and expanding on Maret’s pictures of those representations. I’ll trace the evolution of these pictures from their origins in Maret’s sources to their present form, showing how each generation of illustrations informed and inspired the research that led to the next.