Cones of locally non-negative polynomials

  • Christoph Schulze (TU Dresden)
E1 05 (Leibniz-Saal)


The study of non-negative polynomials is motivated by the obvious fact that the value at a global minimum of a real polynomial $f$ is the maximal value $c$ such that $f-c$ is globally non-negative. This shows its connection to optimization. Similarly, a local minimum $x_0$ of $f$ induces the polynomial $f-f(x_0)$ which takes value $0$ and is locally non-negative at $x_0$.

I will present results from my PhD thesis on the convex cone of locally non-negative polynomials. We will see geometric interpretations and examples of faces of this cone, some general theory of cones in infinite-dimensional vector spaces and classifications of faces using tools from singularity theory. I will also give a short outlook on an application to sums of squares in real formal power series rings.

Mirke Olschewski

MPI for Mathematics in the Sciences Contact via Mail

Upcoming Events of this Seminar