Simon K. Donaldson, Ph.D.Stony Brook University and Imperial College London
Mathematics and Physical Sciences lectures are open to the public and are held at the Gerald D. Fischbach Auditorium at the Simons Foundation headquarters in New York City. Tea is served prior to each lecture.
The study of differential geometric structures on manifolds has evolved from elementary geometry and calculus to the more complex structures prominent in current research. Work in this area of research has led to significant advances in theoretical physics.
In this lecture, Simon K. Donaldson will explain some basic concepts in modern differential geometry and their historical development. He will discuss connections with analysis of complex variables and illustrate how fundamental existence questions lead to nonlinear partial differential equations. The central section of the talk will discuss four-dimensional K3 surfaces. Donaldson will discuss the special solutions of Einstein’s equation on such surfaces, connected to the quaternions. He will outline some of the analytical techniques used to establish the existence of these. He will also sketch some related questions in higher dimensions which are the scene for much current research activity.