3,243 research outputs found
Categorification of the colored -invariant
We give explicit resolutions of all finite dimensional, simple
-modules. We use these resolutions to categorify the
colored -invariant of framed links via a complex of complexes
of graded -modules.Comment: 39 pages, many figures. Comments welcome
A new way to evaluate MOY graphs
We define a new way to evaluate MOY graphs. We prove that this new evaluation
coincides with the classical evaluation by checking some skein relations. As a
consequence, we prove a formula which relates the and
-evaluations of MOY graphs.Comment: Introduction rewritte
Fourth-order time-stepping for stiff PDEs on the sphere
We present in this paper algorithms for solving stiff PDEs on the unit sphere
with spectral accuracy in space and fourth-order accuracy in time. These are
based on a variant of the double Fourier sphere method in coefficient space
with multiplication matrices that differ from the usual ones, and
implicit-explicit time-stepping schemes. Operating in coefficient space with
these new matrices allows one to use a sparse direct solver, avoids the
coordinate singularity and maintains smoothness at the poles, while
implicit-explicit schemes circumvent severe restrictions on the time-steps due
to stiffness. A comparison is made against exponential integrators and it is
found that implicit-explicit schemes perform best. Implementations in MATLAB
and Chebfun make it possible to compute the solution of many PDEs to high
accuracy in a very convenient fashion
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