Course Title: Geometry and complexity theory
This will cover central problems in theoretical computer science from
a geometric perspective. Topics in computer science: the complexity of
matrix multiplication, both upper and lower bounds, Valiant's conjecture
on permanent v. determinant and variants, the problem of explicitness:
how to find hay in a haystack. Geometry that will be covered: rank
and border rank of tensors, basic representation theory and algebraic
geometry. I will follow http://www.math.tamu.edu/~jml/simonsclass.pdf,
which will be rewritten in more polished form over the summer.
Background required: a strong background in linear algebra.
Some experience with algebraic geometry and/or representation
theory would be helpful but is not required.