## View abstract

### Session II.6 - Computational Algebraic Geometry

Thursday, June 15, 17:00 ~ 17:30

## Hyperplane sections of polytopes

### Chiara Meroni

#### MPI Leipzig, Germany   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloak74d5879072f461d39110d26aabe561d7').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy74d5879072f461d39110d26aabe561d7 = 'ch&#105;&#97;r&#97;_m&#101;r&#111;n&#105;' + '&#64;'; addy74d5879072f461d39110d26aabe561d7 = addy74d5879072f461d39110d26aabe561d7 + 'br&#111;wn' + '&#46;' + '&#101;d&#117;'; var addy_text74d5879072f461d39110d26aabe561d7 = 'ch&#105;&#97;r&#97;_m&#101;r&#111;n&#105;' + '&#64;' + 'br&#111;wn' + '&#46;' + '&#101;d&#117;';document.getElementById('cloak74d5879072f461d39110d26aabe561d7').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy74d5879072f461d39110d26aabe561d7 + '\'>'+addy_text74d5879072f461d39110d26aabe561d7+'<\/a>';

We obtain a parametric, semialgebraic description of properties of the hyperplane sections of a polytope. Using this structure, we provide algorithms for the optimization of several combinatorial and metric properties over all hyperplane slices of a polytope. We report on their computational complexity, and explore some connections to constructions and problems in combinatorics and convex geometry.

Joint work with Marie-Charlotte Brandenburg (Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany) and Jesús A. De Loera (University of California, Davis, USA).