# Multivariate Splines and Algebraic Geometry

### From SIAG-AG

Revision as of 03:06, 23 December 2016 (edit)Sottile (Talk | contribs) ← Previous diff |
Revision as of 03:07, 23 December 2016 (edit) (undo)Sottile (Talk | contribs) Next diff → |
||

Line 1: |
Line 1: | ||

+ | =='''Overview'''== | ||

+ | |||

A multivariate spline is a function defined on a domain in $R^d$ with $d>1$ | 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 | that is piecewise a polynomial. These objects from approximation theory | ||

Line 10: |
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) |

## Revision as of 03:07, 23 December 2016

## **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!

## **Organizers**

Michael Di Pasquale (Oklahoma State)

Frank Sottile (Texas A&M)

## **Confirmed Speakers**

Michael Di Pasquale (Oklahoma State)