Log schemes, root stacks, and parabolic bundles

Log schemes are an enlargement of the category of schemes that was introduced by Deligne, Faltings, Illusie and Kato, and has applications to moduli theory and deformation problems. Log schemes play a central role in the Gross–Siebert program in mirror symmetry. In this talk I will introduce log schemes and then explain recent work joint with D. Carchedi, S. Scherotzke, and M. Talpo on various aspects of their geometry. I will discuss a comparison result between two different ways of associating to a log scheme its etale homotopy type, respectively via root stacks and the Kato–Nakayama space. Our main result is a new categorified excision result for parabolic sheaves, which relies on the technology of root stacks.