Sylvester Gallai Theorem for higher degree curves

Abstract: The celebrated Sylvester Gallai theorem concerns line point configurations of real lines. I will show how using methods of algebraic geometry this statement can be generalized for curves of degree 2. Then I will discuss some applications and possible generalizations. Line point configurations have appeared recently in commutative algebra in connection to the containment problem and in algebraic geometry in connection with the Bounded Negativity Conjecture.