John Willard Morgan is an American mathematician, well-known for his contributions to topology and geometry. He is currently the director of the Simons Center for Geometry and Physics at Stony Brook University.

He received his B.A. in 1968 and Ph.D. in 1969, both from Rice University. His Ph.D. thesis, entitled Stable tangential homotopy equivalences, was written under the supervision of Morton L. Curtis. He was an instructor at Princeton University from 1969 to 1972, and an assistant professor at MIT from 1972 to 1974. He has been on the faculty at Columbia University since 1974. In July 2009, he moved to Stony Brook University to become the first director of the Simons Center for Geometry and Physics, a research center devoted to the interface between mathematics and physics.

He is an editor of the Journal of the American Mathematical Society and Geometry and Topology.

OOn April 28th, 2009 he was elected to the National Academy of Sciences.

Interview published at https://www.simonsfoundation.org/john-morgan-interview 

Why is it important to have a center for both geometry and physics under the same roof?

Around the world there are many centers for geometry and centers for physics. Sometimes, like for example at the Institute for Advanced Study, they exist side by side in the same place, but even when they exist in the same place there is usually little organized interaction between the groups. What we are attempting to do here is to create an environment in which geometers and physicists can exchange ideas in a way that enriches both disciplines. The recent interaction has its origin in conversations between Jim Simons and C.N. Yang, here at Stony Brook in the 1960s, concerning the latest developments in physics, gauge theories, and the corresponding mathematical context. But as physics of gauge theories developed and string theory came along, the developments in physics outstripped the available geometry. While these developments give hints about the nature of the geometry that would be needed, what is needed is far too vast, new and different to be developed full-blown out of the hints so far provided by physics. What the nature of this geometry is and how it will be useful in physics are fundamental mysteries in both subjects. Progress toward their resolution will surely have major impacts, some indication of which we can already see. Studying these mysteries – from the mathematical perspective, the physical perspective and the joint perspective – is the focus of the Simons Center for Geometry and Physics.

How will the center create an atmosphere where scientists from both disciplines can collaborate?

We hope to create the collaborative atmosphere in several ways. First of all, the building will have much open, common space with blackboards, chairs and tables to facilitate spontaneous, scientific conversations. As we search for permanent members, post-docs and visitors, we will put real emphasis on a desire for collaboration across the math-physics divide. On the programmatic level, we will be running workshops where the topics will be of interest to both geometers and physicists.

What are some areas of research interest that the center will focus on?

There are many topics that I could list, but I will list the topics of this year’s workshops. The titles of the three workshops planned for the spring are ‘Derived Geometry’, ‘Kahler Geometry and Extemal Metrics’, and ‘String Field Theory’. As the first two names indicate, these topics fit squarely in the area of geometry, but there is a modern twist in the topic inspired by physics, and in particular by string theory, which is one of the most active areas in theoretic high-energy physics. In the study of string theory, the appropriate geometry is not the classical geometry of Gauss and Riemann alluded to before, but rather a more abstract form of geometry ‘derived’ from these classical forms. Ideas from string theory have led to new insights into and new questions about these derived geometries and their relation to classical geometry. These insights have already produced a revolution in how we think about ‘classical geometry’, and there promises to be much more to come. This geometric revolution is providing new impetus for progress in physics. The topic of the last workshop this year is one that belongs more purely to physics: the study of modern string theory.

Contact Information:
5-115  Math Tower
Stony Brook University
Stony Brook, NY 11974-3636
Phone: (631) 632-8298 
Email: jmorgan@math.sunysb.edu