LECTURE SERIES ANNOUNCEMENT  "Inclusionexclusion in topology and (kind(s) of) arithmeticā€¯ The first talk will cover all the prerequisites. The other talks should be accessible to anyone who knows cohomology and has heard of spectral sequences. 3:30  4:30 pm, Seminar Hall Points and lines on cubic surfaces Ronno Das University of Chicago. 290819 Abstract The CayleySalmon theorem states that every smooth cubic surface in CP^3 has exactly 27 lines. Their proof is that marking a line on each cubic surface produces a 27sheeted cover of the space M of smooth cubic surfaces. Similarly, marking a point produces a 'universal family' of cubic surfaces over M. One difficulty in understanding these spaces is that they are complements of incredibly singular `discriminant' hypersurfaces. I will explain how to compute the rational cohomology of these spaces. I'll also explain how these purely topological theorems have purely arithmetic consequences: the average smooth cubic surface over a finite field F_q contains 1 line and q^2 + q + 1 points.
