Contact Info
Pure MathematicsUniversity of Waterloo
200 University Avenue West
Waterloo, Ontario, Canada
N2L 3G1
Departmental office: MC 5304
Phone: 519 888 4567 x33484
Fax: 519 725 0160
Email: puremath@uwaterloo.ca
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Brett Nasserden, Department of Pure Mathematics, University of Waterloo
"The valuative tree in action"
To kick off the learning seminar we will investigate how valuative methods can be used to study the dynamics of polynomial endomorphisms of the affine plane. Specifically, we will introduce the valuative tree and related dynamical notions such as the dynamical degree of a morphism. With the preliminaries in place we will sketch why a dominant polynomial endomorphism of the affine plane defined over an algebraically closed field of characteristic zero has a point with a forward dense orbit if it does not preserve a non-constant rational function. This result is known if the base field is uncountable, therefore the arguments presented here will be most interesting to those willing to work over countable algebraically closed fields such as the algebraic closure of the rational numbers.
MC 5479
Departmental office: MC 5304
Phone: 519 888 4567 x33484
Fax: 519 725 0160
Email: puremath@uwaterloo.ca
The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land promised to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is centralized within our Indigenous Initiatives Office.