Master thesis

Here is a link  to my master thesis about Kähler-Einstein metric on toric Fano manifolds and connections to optimal transport. In the image below you see the moment polytope of the complex projective plane, together with the Euclidean square grid. Inside the polytop is the image of the grid under the moment map associated to the Kähler-Einstein metric in logarithmic coordinates. This moment map is also the optimal transport map mapping the Kähler-Einstein volume form to the uniform measure on the polytope. The pear-shaped curves are isocurves of the Kähler-Einstein (Fubini-Study) metric potential. This is also the Kantorovich potential of the optimal transport problem.