Geometry/Topology Seminar
Richard Birkett
UIC
Rational Maps and the Calculus of Blowups
Abstract: A rational map on a (compact) complex curve is always holomorphic.
In two dimensions or more, it is likely that the map has 'indeterminate points' where the map is not continuous; furthermore, subvarieties may get contracted to those of lower dimension. Nevertheless, it still makes sense to iterate rational maps, even though the behaviour of orbits near such singularities is more difficult to understand.
In this talk I will begin by providing a perspective for the analysis and dynamics of curves on surfaces. In the second half, I will expand on a fruitful transformation of the two-dimensional complex rational map into a piecewise-linear map on a non-Archimedean (Berkovich) space. For the applications I will discuss, the latter dynamics mirror those of a one-variable rational map, and return information about the original surface mapping.
Wednesday April 3, 2024 at 3:00 PM in 636 SEO