Conference abstracts

Session S10 - Homological Methods

July 28, 15:00 ~ 15:30

## Nearest Points on Toric Varieties

### UC Berkeley, USA   -   bernd@berkeley.edu

We determine the Euclidean distance degree of a projective toric variety. This extends the formula of Matsui and Takeuchi for the degree of the $A$-discriminant in terms of Euler obstructions. The primary goal of the project is the development of reliable algorithmic tools for computing the points on a real toric variety that are closest to a given data point. In this lecture we emphasise the role played by characteristic classes such as the Chern-Mather class.

Joint work with Martin Helmer (UC Berkeley, USA).