Viehweg hyperbolicity predicts that if the fibers of an algebraic family have suitable positivity properties and truly vary, then the base must itself have a certain positivity. I will introduce this circle of ideas, whose origins go back to Beauville’s 1981 work on families of curves. I will also discuss joint work with Sebastian Casalaina-Martin on Viehweg hyperbolicity for Deligne–Mumford stacks. We will focus on the motivation and examples.
Viehweg hyperbolicity and Moduli spaces Sponsored by the Meyer Fund
Thu, Oct. 29 2:30pm (MATH 3…
Functional Analysis
James Woodcock (CU Boulder)
X
We introduce a notion of a graph module which we will use as a unifying framework for the study of the graph algebras and graph groupoids. We will define graph modules and spell out some elementary properties. We will then explain how the Bowen Franks group and the dimension triple can be realized concretely by studying the category of modules over a graph. After this we will generalize this to bimodules and construct a bicategory of graphs and show how this is the category of flow equivalence of graphs. We will give examples and discuss their connection with wrong way maps between graph algebras.
Viehweg hyperbolicity and Moduli spaces