# Bernd Sturmfels: The Euclidean Distance Degree

Bernd Sturmfels, UC Berleley and MPI Bonn

**Time: ** Wed 2013-10-09 14.15 - 16.15

**Location: ** Room B2

## Schedule

14:15-15:00: Precolloquium for PhD and master students by Erik Aas (Room B2)

15:15-16:15: Colloquium lecture by Christoph Berndt Sturmfels (Room B2)

16:15-17:00: Coffee and SMC social get-together.

## Abstract (Colloquium)

The nearest point map of a real algebraic variety with respect to Euclidean distance is an algebraic function. The Euclidean distance degree is the number of critical points of this optimization problem. We focus on varieties seen in engineering applications, and we discuss exact computational methods. Our running example is the Eckart-Young Theorem which states that the nearest point map for low rank matrices is given by the singular value decomposition. This is joint work with Jan Draisma, Emil Horobet, Giorgio Ottaviani, Rekha Thomas.