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		Revision as of 18:38, 21 December 2016 (edit) (undo) Sottile (Talk | contribs) Next 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

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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