### Mathematics Colloquium

# Ludwig Arnold

### (Universitat Bremen)

## "Zeros of Random Polynomials"

** Date: ** |
Mon, November 13, 2017 |

** Time: ** |
15:45 |

** Place: ** |
Lecture Hall, Research I |

**Abstract:** We consider the zeros of polynomials with random variables as coefficients. First we treat the number and location of real zeros and present a famous result of Marc Kac (1943). Then we prove that under mild conditions the distribution of the complex zeros tends to the uniform distribution on the unit circle. The Rice formula and its application will also be presented. We discuss the connection with random power series, their analytic continuability, Lyapunov indices, and the basic property of temperedness of a random variable with respect to a dynamical system. Recent results beyond the classical case will also be mentioned. We finish with a little curiosity.

*The colloquium is preceded by tea from 15:15 in the Resnikoff Mathematics Common Room, Research I, 127.*