Series: Mathematics Colloquium

Date: Thursday, February 27, 2003

Time: 4:30 - 5:30 PM

Place: 102 McAllister Building

Host: Luen-Chau Li

Refreshments: 4:00 - 4:30 PM, in 212 McAllister

Speaker: Eyal Markman, University of Massachusetts

Title: Symmetries in Algebraic Geometry

Abstract:

We will survey several examples of hidden symmetries in algebraic
geometry. These will include: (1) Classical results, about line and
vector bundles on a Riemann surface of genus one. (2) The Mckay
correspondence, between representations of a finite subgroup G of
SU(2) and vertices of a Dynkin diagram of type ADE. (3) Symmetries of
the collection of vector bundles on Calabi-Yau varieties
(Fourier-Mukai transformations).  Calabi-Yau varieties are higher
dimensional analogs of a Riemann surface of genus one. They play a
central role in String Theorey.  The last example generalizes the
first two, and has been extensively studied in the context of Mirror
Symmetry.