#### Conference abstracts

Session A2 - Computational Algebraic Geometry

July 10, 16:00 ~ 16:25

## Quadratic Persistence and Pythagoras Number of Varieties

### Greg Blekherman

### GeorgiaTech, USA - greg@math.gatech.edu

Let $X \subset \mathbf{P}^n$ be a variety. Quadratic persistence of $X$ is the smallest integer $k$ such that the ideal of projection away from $k$ generic points of $X$ contains no quadrics. I will motivate this definition and explain how quadratic persistence captures some geometric properties of a variety. Finally I will explain how quadratic persistence can be used to provide lower bounds for length of sums of squares decompositions.

Joint work with Rainer Sinn (Georgia Tech), Greg Smith (Queens University) and Mauricio Velasco (Universidad de los Andes).