Geometry and Analysis Seminar

Please note unusual day and room. 

Motivated by the SYZ conjecture, it is expected that $G_2$ and Spin(7)-manifolds also admit calibrated fibrations. One potential way to construct examples is via gluing of complex fibrations, as in the program of Kovalev. For this to succeed we need that the fibration property is stable under deformation of the ambient Spin(7)-structure. Here the main difficulty lies in the analysis of the singular fibres. In this talk I will present a stability result for fibrations with conically singular Cayleys modeled on the complex cone $\{x^2 + y^2 + z^2 = 0\}$ in ${\mathbb C}^3$.