## The UW Sage Seminar Schedule

The seminar meets at 5pm in Communications B027.

Monday, October 15, 2007:

TITLE: Introduction to Abelian Varieties TIME: 5-6pm on Monday, October 15, 2007 LOCATION: B027 in the Communications building SPEAKER: Robert Miller Abstract: What the heck is an abelian variety? Elliptic curves are the 1-dimensional abelian varieties. What are they in general? Maybe something like an abelian group and an algebraic variety? A complex torus is a complex manifold which is diffeomorphic to an n-torus. All such structures can be obtained as a quotient of CC^n by a lattice, and this procedure gives us a compact complex manifold. For n=1, this is an elliptic curve. For n >= 1, any variety structure on a complex torus must be unique, and Riemann proved that there is such a variety structure if and only if the torus can be embedded in complex projective space. More specifically, CC^n/L is an abelian variety if and only if there is a positive definite Hermitian form whose imaginary part takes integral values on L. After defining abelian varieties as above, William Stein will give an example or two in Sage.

Monday, October 22, 2007:

Monday, October 29, 2007:

Monday, November 5, 2007:

Monday, November 12, 2007: (no seminar -- Sage Days 6)

Monday, November 19, 2007:

Monday, November 26, 2007:

Monday, December 3, 2007: