#### Christoph Schulze (TU Dresden)

## Cones of locally non-negative polynomials

**Programm / Abstract:**

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.

**Zeit:**

am Freitag den 30. Juli 2021 um 11:00

**Ort:**

MPI fur Mathematik in den Naturwissenschaften Leipzig

Inselstr. 22

04103 Leipzig

E1 05 (Leibniz-Saal) 1. Etage

*eingetragen von Saskia Gutzschebauch(Saskia.Gutzschebauch@mis.mpg.de, 0341 9959 50)*

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