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Christoph Schulze (TU Dresden): Cones of locally non-negative polynomials

Ort: MPI für Mathematik in den Naturwissenschaften Leipzig, Inselstr. 22, 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.

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Beginn: July 30, 2021, 11 a.m.

Ende: July 30, 2021, noon