Mateusz Michalek Title: Complete quadrics: Schubert calculus for Gaussian models and semidefinite programming Abstract: 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.