Smoothing toroidal crossing varieties

Friedman and Kawamata-Namikawa studied smoothability of normal crossing Calabi-Yau varieties. I present the proof of a very general smoothing result that also works for toroidal crossing spaces and therefore also generalizes work by Gross and Siebert. The key technologies are the construction of log structures, a proof of a degeneration of the log Hodge to de Rham spectral sequence as well as L-infinity-deformation theory. This is a joint project with Simon Felten and Matej Filip.