Newton-Okounkov Bodies and Khovanskii Bases

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	Kiumars Kaveh University of Pittsburgh		Kiumars Kaveh University of Pittsburgh
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		+	Chris Manon George Mason University
	Frank Sottile Texas A&M University		Frank Sottile Texas A&M University

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Revision as of 03:36, 22 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

Lara Bossinger Universitaet Koeln

Kiumars Kaveh University of Pittsburgh

Chris Manon George Mason University

Frank Sottile Texas A&M University