Professor Sema Salur receives NSF Research Award

Congratulations to Prof. Sema Salur for receiving the National Science Foundation Research Award “Manifolds with Special Holonomy and Applications” (2017-2020).

The unification of the four fundamental forces of nature — electromagnetism, gravity, the strong and weak nuclear forces — is one of the greatest unsolved mysteries of physics. Over the last few decades, M-theory, a “theory of everything,” has emerged as a candidate for such a unification of these forces.

Prof. Salur’s project is about manifolds with special holonomy, which are spaces whose infinitesimal symmetries allow them to play a crucial role in M-theory “compactifications” — that is, they model the tiny “curled up” dimensions lurking at every point of spacetime.

This project will focus in particular on 6-dimensional Calabi-Yau manifolds (which play the analogous role of the curled-up dimensions of superstring theory) and spaces of dimension 7 and 8 whose symmetries fill out the special groups known as G2 and Spin(7), respectively. Despite extensive research on Calabi-Yau manifolds, the geometric properties of G2 and Spin(7) manifolds are not well understood, and the problem of the existence of calibrated (i.e., volume minimizing) submanifolds is still wide open. One goal of this project is to develop techniques that are robust enough to handle these difficult existence questions. Another goal of this project is to study the deformation spaces of calibrated submanifolds, as understanding these spaces will ultimately be useful for M-theory compactifications.

Prof. Salur also believes that manifolds with special holonomy is an excellent topic for graduate research, and intends to continue to supervise PhD students. She also plans to encourage women and members of other under-represented groups to take up graduate study and continue to research careers in differential geometry, through activities that include advising, organizing seminars, special sessions, conference and “Women in Math” workshops.
Prof. Salur earned her Ph.D.from MSU in 2000, under the direction of Gang Tian (MIT), and joined University of Rochester Mathematics Department in 2006. Her research specialty is differential geometry and geometric analysis. Her research has been funded by National Science Foundation grants since 2008: