## 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

Monday, October 20, 2014 — 4:00 PM EDT

A celebrated theorem of Mazur asserts that the order of the torsion part of the Mordell-Weil group of an elliptic curve over Q is absolutely bounded; it is conjectured that the same is true for abelian varieties over number fields, though very little progress has been made towards a proof. We explain how the natural geometric analog where Q is replaced by the function field of a complex curve— dubbed the geometric torsion conjecture—is equivalent to the nonexistence of low genus curves in congruence towers of Siegel modular varieties. In joint work with B. Bakker we prove the geometric torsion conjecture in the special case of abelian varieties with real multiplication. In fact, we present a general method for ruling out low genus curves in quotients of locally symmetric spaces, by using hyperbolic geometry to produce bounds on Seshadri constant. This method moreover allows us to prove a geometric analogue of another famous problem, namely the Frey-Mazur conjecture, asserting that isogeny classes of elliptic curves E over function fields of complex curves are classified by the associated torsion group schemes E[n] for a fixed n.

Refreshments will be served in MC 5046 at 3:00 p.m. Everyone is welcome to attend.

Location

M3 - Mathematics 3

3103

200 University Avenue West

Waterloo, ON N2L 3G1

Canada

200 University Avenue West

Waterloo, ON N2L 3G1

Canada

University 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

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1

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.