Event

Talk
Exceptional Lie groups and algebraic geometry
Prof. Dr. Igor Dolgachev
25 Oct 2011, 16:00 – 17:00

Title: Exceptional Lie groups and algebraic geometry.

Abstract: Does Nature use Exceptional Lie groups to express its laws of physics? This question is left to physicists to decide. However, their ubiqueness in many areas of mathematics has no doubts. In my talk I will discuss some examples of appearance of exceptional groups in classical and modern algebraic geometry. For example, the complex Lie group of type E_6 was constructed by E. Cartan as the group of linear symmetries of a certain homogeneous cubic form in 27 variables corresponding to 27 lines on a nonsingular cubic surface in three-dimensional projective space. A similar construction of the group of type E_7 involves a quartic homogeneous form in 28 variables corresponding to bitangents of a plane quartic curve. Another examples are the McKay correspondence for finite subgroups of SU(2) and the conjectural existence of the Holy Grail family of Calabi-Yau manifolds parameterized by a Hermitian symmetric space of
type E_7

Related to:

• Igor Dolgachev