# Newton-Okounkov Bodies and Khovanskii Bases

### From SIAG-AG

Revision as of 17:59, 27 January 2017 (edit)Sottile (Talk | contribs) (→'''Confirmed Speakers''') ← Previous diff |
Revision as of 17:02, 30 January 2017 (edit) (undo)Sottile (Talk | contribs) (→'''Confirmed Speakers''') Next diff → |
||

Line 36: |
Line 36: | ||

Fatemeh Mohammadi Technische Universitaet Berlin | Fatemeh Mohammadi Technische Universitaet Berlin | ||

- | Frank Sottile Texas A&M University | + | Frank Sottile Texas A&M University "Newton-Okounkov Bodies and Khovanskii Bases for Applications" |

## Revision as of 17:02, 30 January 2017

## **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**

Hiraku Abe McMaster University

Lara Bossinger Universitaet Koeln

Daniel Corey Yale University

Kiumars Kaveh University of Pittsburgh

Chris Manon George Mason University

Fatemeh Mohammadi Technische Universitaet Berlin

Frank Sottile Texas A&M University "Newton-Okounkov Bodies and Khovanskii Bases for Applications"