##
Research

My area of research is superstring theory, a theory that purports to give us a quantum theory of gravity as well as a unified theory of all forces and all matter. As such, superstring theory has the potential to realize Einstein's long sought dream of a single, all encompassing, theory of the universe. One of the strangest features of superstring theory is that it requires the universe to have more than three spatial dimensions. Much of my research has focused on the physical implications and mathematical properties of these extra dimensions --- studies that collectively go under the heading "quantum geometry".

Quantum geometry differs in substantial ways from the classical geometry underlying general relativity. For instance, topology change (the "tearing" of space) is a sensible feature of quantum geometry even though, from a classical perspective, it involves singularities. As another example, two different classical spacetime geometries can give rise to identical physical implications, again at odds with conclusions based on classical general relativity.

Superstring theory is most relevant under extreme physical conditions such as those that existed at the time of the big bang. Recently, we have formed a new institute at Columbia called ISCAP (Institute for Strings, Cosmology, and Astroparticle Physics) dedicated to understanding the interface of superstring theory and cosmology. One primary focus of ISCAP is the search for subtle signatures of string theory that may be imprinted in the precision cosmological data that will be collected through a variety of experiments over the next decade.

##
Education

Ph.D., Oxford University, 1987

##
Publications

A current list of publications can be found here: INSPIRE