Multivariate Splines and Algebraic Geometry

From SIAG-AG

(Difference between revisions)
Jump to: navigation, search
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''')
 
(7 intermediate revisions not shown.)
Line 1: Line 1:
-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
Line 9: Line 12:
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)

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)

Views
Personal tools