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.
2026 Projection areas of 4-dimensional shapes
June Huh
Princeton University
April 17, 2026, 3:30pm, 125 Frick Fine Arts Building (tbc)
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.
2025 Patterns in the primes
James A. Maynard
University of Oxford
March 21, 2025, 3:30pm, 125 Frick Fine Arts Building
How often do two prime numbers differ by exactly 2? This simple (and famous) question is unsolved despite mathematicians working on it for over 100 years. Moreover, basic questions like this about prime numbers turn out to lie at the heart of many important real-world questions. For example, it turns out that the security of internet communication (which we rely on whenever we buy something online) is related to basic questions about patterns in prime numbers which we don't know how to solve!
I'll talk about why prime numbers are so special to mathematicians, how important questions in both pure mathematics and the real world turn out to be connected to primes, and how we are making progress towards solving these famous problems which have been studied for hundreds of years.