“The Geometry of the Universe”
In a 1916 paper, Hilbert computed the Euler-Lagrange equation for the integral of the scalar curvature (plus other terms) over a manifold. The resulting equation connects quite beautifully to questions concerning geodesics, minimal surfaces, Ricci and scalar curvature, metric singularities, and geometric flows. Amazingly, this equation, now known as the Einstein equation of general relativity, also replaced Newtonian physics as our current best description of the large-scale structure of the universe by predicting gravitational lensing, black holes, the Big Bang, and quite arguably even the accelerating expansion of the universe - before they were observed. This raises a natural question: What other geometric ideas describe the universe?
Refreshments will be served in the DC Fishbowl (1301) at 3:30 p.m. Everyone is welcome to attend.