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.