Cooperation between mathematicians and physicists has recently intensified to levels not seen since Einstein's days nearly a century ago. The cooperation, and the enthusiasm, center on the project of developing string theory, and its current extension known as M-theory, into a "Theory of Everything". This is expected to be a unified theory reconciling the two great twentieth-century physical ideas of relativity and quantum field theory, and explaining all the observed forces and elementary particles. The new enthusiasm is based, to a large extent, on the tremendous progress made in recent years in our understanding of non-perturbative aspects of strings and their dualities. The parts of string theory which are already understood depend in a very essential way on new and emerging mathematical machinery. They have profound applications to a wide range of physical theories, from elementary particles to cosmology. Ideas arising from string theory have also radically transformed the areas of mathematics with which they came in contact, including such central branches of mathematics as algebraic geometry and topology. The two disciplines of mathematics and physics, while retaining their separate motivations and powerful technologies, have revitalized and transformed each other to an amazing extent.
Over the past few years, the University of Pennsylvania has emerged as home to one of the most active and successful interdisciplinary Math/Physics research groups in the country. This group has a strong and cohesive research program aimed at understanding the mathematical structures underlying string theory, and applying them to some of the most fundamental problems of particle physics and cosmology. The group draws on the human capital available in both the mathematics and physics departments at Penn, as well as on its strong connections with leading researchers at Princeton University, the Institute for Advanced Study, Rutgers University, and further afield. The Penn Math/Physics research group has, in addition to research, developed a very successful seminar, runs a wide ranging visitor program, trains graduate students in interdisciplinary Math/Physics research and has developed an integrated network of graduate courses. It has also had significant national impact through a series of conferences at Penn and a month long Math/Physics workshop organized at the Institute for Theoretical Physics in Santa Barbara. Research achievements of the group on the physics side include contributions to field theory and string dualities, exhibiting standard model particle physics vacua in strings and M-theory, brane-world scenarios and a new cosmological theory. On the math side, they include the understanding of moduli of principal bundles on elliptic fibrations as well as recent advances in gerbe theory.
The Math/Physics research group at Penn is continuing to focus on specific, fundamental research problems in the mathematical structure of string theory, as well on the application of mathematical string theory to elementary particle physics and cosmological theories. In the process of pursuing these research goals, we are attempting to develop Penn into a leading center for cooperation and intellectual exchange between mathematicians and physicists.