| Computation of numerical solutions to
the optimal transport problem of the type $ determinant(\nabla^2\phi)=V $
with $\nabla\phi:R^n -> P$ diffeomorphism where P is a convex body (second boundary value problem) for $n=2$ using balanced metrics. The user can choose P and the measure V. |
[ZIP] The code written in C++ uses PlotUtils library. |
| Computation of the Weil-Petersson metric
on the moduli space of Quintics threefolds in CP^4. This
is based on my collaboration with S. Lukic, see the paper. Note
that the program also computes the Kähler Ricci flat
metric on these manifolds. |
[ZIP] Code in C++. |
| Computation of extremal Kahler metrics
over any toric smooth surface. This is based on the work of R.
Bunch and S.K.Donaldson. |
[ZIP] Code in C++. See README file. |
| Computation of the Kahler-Ricci flat
metric for the K3 surface given as the double cover of the
projective plane along the Fermat sextic curve. This is
related to the work of
S.K. Donaldson about nu-balanced metrics. |
[ZIP] Code in C++, using Newmat library. See README and INSTALL file. |
| Computation of the Kahler-Einstein
metric for the projective plane blown up at 3
points, i.e 3rd del Pezzo surface. An animated file showing the evolution of the scalar curvature of the computed metric (at each step of the iteration) can be downloaded here. We used this program to draw geodesics on this manifold, with a metric very close to the Kahler-Einstein metric, showing they form an integrable system. |
[ZIP] Code in C++ using PlotUtils library. See README and INSTALL file. [ZIP] Code in C++ using PlotUtils library. |
| Evaluation of the Bergman kernel over
CP1 vanishing on 1,2, or 3 points. It uses MathGl3d
library. Related to the following preprint. |
[NB] Code in Mathematica |
| For educational purpose: Newton's method
in dimension 1 and higher dimensions. Applications to the
dynamics of z --> z +z^2 on the complex plane. This a
work of my former B.Sc students. |
[ZIP] The PDF file contains a Maple code. |
| Computation of the Relative
Donaldson-Futaki invariant for a projective bundle over a
curve |
[ZIP] Code in Maple |
