Jonas Bergström: Moduli spaces of curves and modular forms

In algebraic geometry there is a wish to classify all curves. To this end, the moduli space of curves (actually one space for each positive integer called genus) was created and has since then become a central object of study in algebraic geometry.

In number theory, there is a special kind of very symmetric analytic functions called modular forms. They are arguably also one of the central objects of modern number theory.
These objects are not unrelated. In this talk I will discuss how modular forms turn up in the cohomology (which is an important invariant of a space) of moduli spaces of curves and how one can find information about this relation through counting curves that are defined over finite fields.