Point counting and topology - 1 of 2

Benson Farb

In this first talk I will explain how the machinery of the Weil Conjectures can be used to transfer information back and forth between the topology of a complex algebraic variety and its F_q points. A sample question: How many $F_q$-points does a random smooth cubic surface have? This was recently answered by Ronno Das using his (purely topological) computation of the cohomology of the universal smooth, complex cubic surface. This is part of a much larger circle of fascinating problems, most completely open.   This is the first lecture in a two part series: part 2

https://mathtube.org/lecture/video/point-counting-and-topology-1-2

Mathtube- Workshop on Arithmetic Topology