# Newton-Okounkov Bodies and Khovanskii Bases

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Revision as of 18:33, 21 December 2016 (edit)Sottile (Talk | contribs) (This page provised more information about the intended minisymposium) ← Previous diff |
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- | '''Newton-Okounkov bodies and Khovanskii Bases''' | + | =='''Overview'''== |

The theory of Newton-Okounkov bodies generalizes that of Newton Polytopes, | The theory of Newton-Okounkov bodies generalizes that of Newton Polytopes, | ||

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community of applied algebraic geometry. | community of applied algebraic geometry. | ||

- | '''Organizer:''' Frank Sottile | ||

- | '''Confirmed Speakers:''' | + | == '''Organizer''' == |

+ | Frank Sottile | ||

+ | |||

+ | == '''Confirmed Speakers''' == | ||

Kiumars Kaveh | Kiumars Kaveh | ||

Frank Sottile | Frank Sottile |

## Revision as of 18:38, 21 December 2016

## **Overview**

The theory of Newton-Okounkov bodies generalizes that of Newton Polytopes, giving a conceptual framework for root counts to systems of functions in terms of volumes and mixed volumes of convex Newton-Okounkov bodies. While the asymptotic definition of these bodies is not particularly constructive, when they admit a Khovanskii basis, they are polyhedral. Having a Khovanskii basis enables other methods based on polyhedra to be used.

While Newton-Okounkov bodies arose to solve questions from pure mathematics they have significant potential in applications. These include providing a foundation for root counts for polynomial systems from applications, the use of these root counts and Khovanskii bases for solving, and a host of algorithmic questions involving computing/determining Newton-Okounkov bodies and Khovanskii bases. The purpose of this minisymposium is to explore some of these opportunities and to advertise this to the wider community of applied algebraic geometry.

## **Organizer**

Frank Sottile

## **Confirmed Speakers**

Kiumars Kaveh

Frank Sottile