Mattia Talpo (UBC)
Infinite root stacks of log schemes
I will talk about the notion of "infinite root stack" of a logarithmic scheme, introduced by myself and Angelo Vistoli as part of my PhD thesis. It is a "limit" version of the generalization to log schemes of the stack of roots of a divisor on a variety, and we show, among other things, that its "bare" geometry closely reflects the "log" geometry of the base log scheme. After giving some motivation, I will briefly define log schemes and describe this infinite root construction. I will then state the results we get about it, and their relevance to log geometry, also in view of (hopefully) upcoming applications.
Nathan Ilten (SFU)
Frobenius Splittings of Varieties with Diagonalizable Group Action
The property of an algebraic variety being Frobenius split has many strong consequences, including the vanishing of the higher cohomology of any ample line bundle. While normal toric varieties are always Frobenius split, varieties with more general torus actions need not be. In this talk, I will relate the existence of a Frobenius splitting for a normal variety with diagonalizable group action to the existence of a Frobenius splitting for a suitable quotient. Applications include a classification of Frobenius split complexity-one T-varieties, as well as a better understanding of Frobenius splitting properties of toric vector bundles. This is joint work with Piotr Achinger and Hendrik Suess.
Bianca Viray (UW)