Sampling from the uniform distribution on an algebraic manifold

An algebraic manifold is a submanifold of the smooth locus of some real variety embedded in affine space. We can choose a point on it by first choosing a hyperplane of the right codimension and then choosing one of the intersection points of the plane with the manifold. In this talk, I explain how to do this such that the chosen point is uniformly distributed. I show examples of the corresponding algorithm for sampling in action and highlight a connection to topological data analysis.