The "Pittsburgh Mathematical Horizons" Public Lecture Series is a newly established annual lecture series made possible by generous funding from the Benter Foundation. It is to feature excellent speakers who can present a topic in modern mathematics of interest to research mathematicians, but at the same time make it accessible to the science-interested public in Pittsburgh and its surroundings.
121 David Lawrence Hall
Abstract or Additional Information
Consider a convex body in 4-dimensional space—perhaps an ellipsoid or a polytope. When we project the convex body onto the six coordinate planes, we obtain six planar shadows whose areas we can measure. This leads to a deceptively simple question: which six numbers can arise as these projection areas?
Behind this concrete geometric problem lies a web of deep mathematics connecting Minkowski's classical work on the isoperimetric problem to recent developments in algebraic geometry. I will trace the path to the answer, revealing the rich mathematical landscape that emerges from this seemingly elementary question.