This summer school will offer a hands-on introduction to discriminants, with a view towards modern applications. Discriminants are classical objects in computational algebraic geometry, and their importance is hard to overstate. For any parametrically defined algebraic or geometric problem, the discriminant captures parameter values for which the solution to the problem changes qualitatively.

Starting from the basics of computational algebraic geometry and toric geometry, the school will gently introduce participants to the foundations of discriminants. A particular emphasis will be put on computing discriminants of polynomial systems using computer algebra software. Then, we will dive into three applications of discriminants: algebraic statistics, geometric modeling, and particle physics. Here, discriminants contribute to the study of maximum likelihood estimation, to finding practical parametrizations of geometric objects, and to computations of scattering amplitudes.

We will explain recently discovered unexpected connections between these three applications. In addition to lectures, the summer school will have daily collaborative exercise sessions which will be guided by the teaching assistants and will include software demonstrations.

Registration is closed.

WARNING: Please be wary if a company directly contacts you regarding payment for accommodation in Leipzig: this is fraud / phishing. The communication and organisation of this school is carried out exclusively by staff of the MPI MiS.

Financial support provided by the US National Science Foundation and the academic sponsoring institutions of the Simons Laufer Mathematical Sciences Institute, Berkeley, CA: