Algebraic Geometry Working Seminar

Tuesday, October 4, 2022 12:30 pm - 12:30 pm EDT (GMT -04:00)

Changho Han, Department of Pure Mathematics, University of Waterloo

“Periods I: Elliptic Curves and Hodge Theory”

This is the first talk in the series of two talks with the goal of introducing a method of
parametrizing isomorphism classes of certain varieties using analytic techniques; even if it’s
analytic, this particular construction (of using ”periods”) plays key roles in algebraic side of
algebraic geometry and number theory as well. In this first talk, I will showcase the standard
construction for elliptic curves, as a differential geometric consequence that any elliptic curve
(as a complex manifold) is a quotient of complex plane; the result is the famous quotient of the
upper half-plane by SL(2,Z). Then I will re-interpret this construction in terms of cohomologies,
leading to the Hodge theory. This viewpoint will play a key role in the next talk when we look
at K3 surfaces.

MC 5403

Zoom information:
Meeting ID: 817 1030 9714; Passcode: 063438