Friday, January 22th at 10:30, Mateusz Michalek (University of Konstanz).

Complete quadrics: Schubert calculus for Gaussian models and semidefinite programming.

Algebraic geometry has made great advances in the last two centuries. A particular role was played by enumerative geometry, where correct setting of moduli spaces found applications beyond mathematics.
In my talk I would like to present a new work on applications of enumerative geometry in algebraic statistics. The main role will be played by the classical variety of complete quadrics and its cohomology ring. However, inspired by algebraic statistics, we will look at it from a different perspective, namely what happens when the dimension of the quadric changes. We will present two theorems, confirming conjectures posed by Nie, Ranestad, Sturmfels and Uhler. Achieving our results would not be possible without the fundamental work of De Concini, Laksov, Lascoux, Pragacz and Procesi. The talk is based on joint works with Manivel, Monin, Seynnaeve, Vodicka and Wisniewski.

The seminar will take place online. Click here for the Zoom link.