## View abstract

#### Conference abstracts

Invited talk

Friday, July 23, 14:45 ~ 15:45 UTC-3

## Characterizations of Nonnegative polynomials on some varieties

### Mauricio Velasco

#### Universidad de los Andes, Colombia   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloak8e23e2dbb0c4849d298acfecd9494c39').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy8e23e2dbb0c4849d298acfecd9494c39 = 'mv&#101;l&#97;sc&#111;' + '&#64;'; addy8e23e2dbb0c4849d298acfecd9494c39 = addy8e23e2dbb0c4849d298acfecd9494c39 + '&#117;n&#105;&#97;nd&#101;s' + '&#46;' + '&#101;d&#117;' + '&#46;' + 'c&#111;'; var addy_text8e23e2dbb0c4849d298acfecd9494c39 = 'mv&#101;l&#97;sc&#111;' + '&#64;' + '&#117;n&#105;&#97;nd&#101;s' + '&#46;' + '&#101;d&#117;' + '&#46;' + 'c&#111;';document.getElementById('cloak8e23e2dbb0c4849d298acfecd9494c39').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy8e23e2dbb0c4849d298acfecd9494c39 + '\'>'+addy_text8e23e2dbb0c4849d298acfecd9494c39+'<\/a>';

In this talk I will describe some recent results on the characterization of those polynomials that are nonnegative on a variety $X$ in $\mathbb{R}^n$. In the first part of the talk I will explain why this is an interesting problem: it turns out to have a wealth of applications ranging from nonconvex optimization to stochastic control. In the second part of the talk I will explain how this problem can be approached on algebraic curves and surfaces.

Joint work with G. Blekherman (GA Tech), R. Sinn (U. Lepizig) and G.G. Smith (Queen's U).