This talk will introduce an overview of some of the most important concepts and ideas from geometry and topology and then describe the recent interplay between these mathematical subjects and high energy theoretical physics, interactions that have been of a fundamentally different nature from earlier ones.
From the time of Newton through the middle of the 19th century, physics and the analytic/geometric side of mathematics were one discipline — natural philosophy. During the 19th century, the subjects began to separate as analysis required a more logically rigorous foundation. This separation accelerated with the introduction of modern geometry and topology around 1850, with its need for a similar rigor. In the early 20th century, there were some spectacular convergences of the two subjects, but overall their trajectories since 1850 have taken them ever farther apart. The last 40 years have witnessed renewed, robust interactions between geometry/topology and physics that have resulted in great advances in both disciplines.
John Morgan is a professor of mathematics and founding director of the Simons Center for Geometry and Physics at Stony Brook University. His work is in the areas of geometry and topology. He has concentrated study of manifolds and smooth algebraic varieties. His most recent works include books, jointly with Gang Tian, explaining in detail the proof of the Poincaré conjecture and the geometrization conjecture, both of which concern the nature of three-dimensional spaces.
Morgan received his Ph.D. from Rice University in 1969. He was an instructor at Princeton from 1969 to 1972, an assistant professor at MIT from 1972 to 1974, and an associate professor and then professor at Columbia University from 1974 to 2009. In 2009, he joined Stony Brook University as Simons Center for Geometry and Physics Director. His awards include the Levi L. Conant Prize of the American Mathematical Society (AMS) in 2009. He is a member of the AMS, an AMS Fellow (2013), and a member of the U.S. National Academy of Sciences.