Gilles Englebert (Oxford) will speak in the differential geometry seminar at 2pm on 30th September, in the Salle des Profs (9th floor of building NO). Gilles’ title is *“Stability of Cayley fibrations and Kovalev-Lefschetz fibrations”* and his abstract is below.

*Motivated by the SYZ conjecture, it is expected that G_2 and Spin(7)-manifolds admit calibrated fibrations as well. One potential way to construct examples is via gluing of complex fibrations, as in the program of Kovalev. For this to succeed we need the fibration property to be stable under deformation of the ambient Spin(7)-structure, with the main difficulty being 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 C^3. As a result we are able to construct Kovalev-Lefschetz fibrations of twisted connected sum G_2 manifolds by coassociative submanifolds.*