Past

One natural question in interpolation theory is: given a finite set of points

in R^n, what is the least degree of polynomials on R^n needed to induce every

function from the points to R? It turns out that this "interpolation degree" is

closely related to a fundamental measure of complexity in algebraic geometry

called Castelnuovo-Mumford regularity. I'll explain these ideas a new

application to projections of varieties.

In this talk we shall be looking at recent and forthcoming developments in the widely used LAPACK and ScaLAPACK numerical linear algebra libraries.

Improvements include the following: Faster algorithms, better numerical methods, memory hierarchy optimizations, parallelism, and automatic performance tuning to accommodate new architectures; more accurate algorithms, and the use of extra precision; expanded functionality, including updating and downdating and new eigenproblems; putting more of LAPACK into ScaLAPACK; and improved ease of use with friendlier interfaces in multiple languages. To accomplish these goals we are also relying on better software engineering techniques and contributions from collaborators at many institutions.

After an overview, this talk will highlight new more accurate algorithms; faster algorithms, including those for pivoted Cholesky and updating of factorizations; and hybrid data formats.

This is joint work with Jim Demmel, Jack Dongarra and the LAPACK/ScaLAPACK team.

http://www.maths.ox.ac.uk/oxmos/meetings/2007-03-13_workshop.pdf

This talk will discuss recent work on 3-phase junctions (electrolyte wedges)

in porous electrodes, including nonlinear reaction kinetics. Recent work on

reaction route representations (Kirchoff graphs) will also be discussed.