Multivariate Splines and Algebraic Geometry

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Revision as of 03:03, 23 December 2016 (edit) Sottile (Talk | contribs) (New page: The focus of the proposed minisymposium is on problems in approximation theory that may be studied using techniques from commutative algebra and algebraic geometry. Research interests of...) ← Previous diff		Current revision (22:43, 24 December 2016) (edit) (undo) Sottile (Talk | contribs) (→'''Confirmed Speakers''')
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-	The focus of the proposed minisymposium is on problems in approximation theory	+	=='''Overview'''==
-	that may be studied using techniques from commutative algebra and algebraic	+
		+	A multivariate spline is a function defined on a domain in $R^d$ with $d>1$
		+	that is piecewise a polynomial. These objects from approximation theory
		+	may be studied using techniques from commutative algebra and algebraic
	geometry. Research interests of the participants relevant to the minisymposium		geometry. Research interests of the participants relevant to the minisymposium
	fall broadly under multivariate spline theory, interpolation, and geometric		fall broadly under multivariate spline theory, interpolation, and geometric
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	space of piecewise cubics on a planar triangulation (especially relevant for		space of piecewise cubics on a planar triangulation (especially relevant for
	applications) is still unknown in general!		applications) is still unknown in general!
		+
		+	== '''Organizers''' ==
		+	Michael Di Pasquale (Oklahoma State)
		+
		+	Frank Sottile (Texas A&M)
		+
		+	== '''Confirmed Speakers''' ==
		+
		+	Michael Di Pasquale (Oklahoma State)
		+
		+	Bernard Mourrain (INRIA Sophia-Antipolis)
		+
		+	Tatyana Sorokina (Towson University)
		+
		+	Peter F. Stiller (Texas A&M)
		+
		+	Frank Sottile (Texas A&M)
		+
		+	Nelly Villamizar (RICAM Linz)
		+
		+	'''Likely Speakers'''
		+
		+	Oleg Davydov (Universitaet Giessen)
		+
		+	Bert Juettler (Johannes Kepler Universitaet, Linz)
		+
		+	Hendrik Speleers (Universita di Roma 2)
		+
		+	Julianna Tymoczko (Smith College)

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Current revision

[edit] Overview

A multivariate spline is a function defined on a domain in $R^d$ with $d>1$ that is piecewise a polynomial. These objects from approximation theory may be studied using techniques from commutative algebra and algebraic geometry. Research interests of the participants relevant to the minisymposium fall broadly under multivariate spline theory, interpolation, and geometric modeling. For instance, a main problem of interest is to study the Hilbert function and algebraic structure of the spline module; recently there have been several advances on this front using notions from algebraic geometry. Nevertheless this problem remains elusive in low degree; the dimension of the space of piecewise cubics on a planar triangulation (especially relevant for applications) is still unknown in general!

[edit] Organizers

Michael Di Pasquale (Oklahoma State)

Frank Sottile (Texas A&M)

[edit] Confirmed Speakers

Michael Di Pasquale (Oklahoma State)

Bernard Mourrain (INRIA Sophia-Antipolis)

Tatyana Sorokina (Towson University)

Peter F. Stiller (Texas A&M)

Frank Sottile (Texas A&M)

Nelly Villamizar (RICAM Linz)

Likely Speakers

Oleg Davydov (Universitaet Giessen)

Bert Juettler (Johannes Kepler Universitaet, Linz)

Hendrik Speleers (Universita di Roma 2)

Julianna Tymoczko (Smith College)