Abstract: I will discuss applications of algebraic results to combinatorics, focusing in particular on Lefschetz theorem, Decomposition theorem and Hodge Riemann relations. Secondly, I will discuss proving these results combinatorially, using a technique by McMullen and extended by de Cataldo and Migliorini. Finally, I will discuss Lefschetz type theorems beyond positivity.
Recommended prerequisites: basic commutative algebra