Contact Info
Pure MathematicsUniversity of Waterloo
200 University Avenue West
Waterloo, Ontario, Canada
N2L 3G1
Departmental office: MC 5304
Phone: 519 888 4567 x43484
Fax: 519 725 0160
Email: puremath@uwaterloo.ca
Anthony McCormick, Department of Pure Mathematics, University of Waterloo
“The Frobenius Theorem for Supermanifolds Part 2”
We will begin with some basic theory of locally ringed spaces with examples from both differential and algebraic geometry. After introducing the notion of a functor of points we will see a duality between geometric and algebraic objects through the adjunction between the global sections functor and Spec, as well as Milnors exercise in differential geometry. This will motivate the definition of a supermanifold and allow us to better understand the nature of morphisms between them. Using all of this formalism we will then give several examples of supermanifolds, construct the reduced manifold associated to a supermanifold and prove the Frobenius theorem in this more general context.
MC 5501
Departmental office: MC 5304
Phone: 519 888 4567 x43484
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 granted 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 Office of Indigenous Relations.