Arithmetic circuits and algebraic geometry
The goal of this talk is to show that natural questions in complexity theory raise very natural questions in algebraic geometry.
More precisely, we will show how to adapt an approach introduced by Landsberg and Ottaviani, called Young Flattening, to questions about arithmetic circuits. We will show that this approach generalizes the method of shifted partial derivatives introduced by Kayal to show lower bounds for shallow circuits.
We will also show how one can calculate shifted partial derivatives of the permanent using methods from homological algebra, namely by calculating a minimal free resolution of an ideal generated by partial derivatives.
I will not assume any previous knowledge about arithmetic circuits.
Joint work with J.M. Landsberg, H Schenck, J Weyman.