## View abstract

### Session II.3 - Real-Number Complexity

Thursday, June 15, 14:30 ~ 15:00

## The Wonderful Geometry of the Vandermonde map

### Cordian Riener

#### UiT The Arctic University of Norway, Norway   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloakb1d78f34e1c9328eed66bc1e747d602b').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addyb1d78f34e1c9328eed66bc1e747d602b = 'c&#111;rd&#105;&#97;n.r&#105;&#101;n&#101;r' + '&#64;'; addyb1d78f34e1c9328eed66bc1e747d602b = addyb1d78f34e1c9328eed66bc1e747d602b + '&#117;&#105;t' + '&#46;' + 'n&#111;'; var addy_textb1d78f34e1c9328eed66bc1e747d602b = 'c&#111;rd&#105;&#97;n.r&#105;&#101;n&#101;r' + '&#64;' + '&#117;&#105;t' + '&#46;' + 'n&#111;';document.getElementById('cloakb1d78f34e1c9328eed66bc1e747d602b').innerHTML += '<a ' + path + '\'' + prefix + ':' + addyb1d78f34e1c9328eed66bc1e747d602b + '\'>'+addy_textb1d78f34e1c9328eed66bc1e747d602b+'<\/a>';

The Vandermonde map is the polynomial map given by the power-sum polynomials. We study the geometry of the image of the nonnegative orthant under under this map and focus on the limit as the number of variables approaches infinity. We will show, the geometry of this limit is the key to new undecidability results in nonnegativity of symmetric polynomials and deciding validity of trace inequalities in linear algebra.

Joint work with Jose Acevedo (Georgia Institute of Technology, USA), Grigoriy Blekherman (Georgia Institute of Technology, USA) and Sebastian Debus (Otto-von-Guericke-University Magdeburg, Germany).