General Mathematics Colloquium
Speaker: Prof. Lenny Taelman Title: Arithmetic geometry through point counting sequences
Given a system of polynomial equations with integer coefficients, one can list the number of solutions in integers modulo p, for varying prime numbers p. This gives a sequence of integers, indexed by the prime numbers. These 'point counting sequences' have some beautiful and mysterious properties. In this survey lecture, which is expressly aimed at a non-expert audience, I will give a broad overview of a few of the major theorems and conjectures in arithmetic algebraic geometry, as seen through these point counting sequences.