Title: Lines in a cubic surface
Abstract: Given a surface in 3 dimensional space defined by a polynomials equation f(x,y,z)=0, one can ask how many lines lie completely inside the surface. When degree of f is different from 3, one should expect either 0 or infinitely many lines. Only for cubic surfaces (i.e. deg(f)=3) should one expect a finite number. In this talk, I will explain these expectations and give a proof that every smooth cubic surface over the complex numbers contains exactly 27 lines.
