Computing the homology of semialgebraic sets is a central problem in computational real algebraic geometry. However, as of today, all symbolic algorithms for this problem require still time that is doubly exponential with respect to the number of variables. The latter is so although the size of the Betti numbers is known to be singly exponential in the number of variables. In this talk, we show how numerical computation (in combination with topological data analysis) can lead to algorithms that are singly exponential in the number of variables with high probability. This improves the state of the art of computation for a big proportion of the possible inputs.

This is joint work with Peter Bürgisser and Felipe Cucker.

Meeting ID: 941 1780 2328
Passcode: 107634