(Jesse Wolfson) Modern Geometry

One hundred and seventy years ago, the German mathematician Bernhard Riemann submitted a short, 12 page note for his habilitation called "On the hypotheses which lie at the bases of geometry." Where Euclid began by considering constructions at arbitrary scales, Riemann asked what an observer could measure in nearby regions. With this seemingly small shift, Riemann initiated a radical expansion in our conceptions of space, one that set the stage for Einstein's theory of general relativity and all that comes after, and one which continues to lead mathematicians into strange and unfamiliar new worlds. In this talk, using thought experiments, visualizations, and Riemann's original writing, I will try to lead the audience through the doors Riemann opened and into some of these new worlds that mathematicians are still actively exploring and seeking to un-derstand.
Jesse Wolfson is an associate professor of mathematics at the University of California, Irvine. His research focuses on long-standing open problems at the interface of algebra, geometry and topology. His perspective on geometry emerges in part from his long-running exchange with choreographer Reggie Wilson. He also currently serves on the board of directors of Wilson's Fist and Heel Performance Group, an internationally acclaimed Brooklyn based "Post-African neo-hoodoo modern dance company."