Mathematics Calendar

Most interesting solutions of string theory are of the form M x C, where M is some D-dimensional non-compact space (e.g. Minkowski or Anti-de Sitter), and C is some (10-D)- or (11-D)-dimensional compact space, known as a compactification. Many interesting questions about string theory then reduce about understanding the properties of the "Kaluza-Klein spectra" of certain differential operators on C. Because these operators often involve a complicated interplay between the p-forms arising in string theory and the metric on C, few general results are known. Generalised geometry is the study of structures on TM + T*M and similar extensions of TM, and naturally "geometrises" the interaction between p-forms and metric in string theory. I will review generalised geometry and show how it allows us to study the Kaluza-Klein spectra for a large class of string theory compactifications.