Motivic zeta functions for degenerating Calabi-Yau varieties

Zeta functions are historically important objects in mathematics, and continue to motivate a wealth of work in research today. Zeta functions often arise at the crossroads between different mathematical fields, such as analysis, number theory and algebraic geometry. This talk will mainly focus on so-called "motivic zeta functions", which are of a more geometric nature. These objects can be attached to degenerating families of Calabi-Yau varieties, and provide an interesting link between arithmetic and geometric aspects of such varieties. I will give an intuitive introduction to some of the key properties of motivic zeta functions, and mention a few influential open questions. I will also present some of my own results, both old and new, in this area.