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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There are strong analogies between the problem of finding fixed points for group actions on a manifold, finding sections of a fibration of topological spaces, and finding solutions of systems of polynomial equations. In particular, every fibration over a curve whose fibers are path connected admits a section, as does every fibration over a surface whose fibers are simply connected. There are algebro-geometric analogues of path connected and simply connected: ”rationally connected” and ”rationally simply connected” complex projective manifolds. Work of Graber, Harris and myself and of de Jong, He and myself establishes analogues of the fibration result in algebraic geometry. Chenyang Xu and I combined this with beautiful work of H ́el`ene Esnault to explain several classical results in number theory (over global function fields): the Tsen-Lang theorem, a theorem of Brauer-Hasse- Noether, and the split case of a theorem of Harder on Serre’s ”Conjecture II”.
Refreshments will be served in MC 5046 at 3:30 p.m. Everyone is welcome to attend.
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 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 Indigenous Initiatives Office.