Extra Seminar - Dr. A.M. von Pippich (Darmstadt, Germany)

Title:             Modular forms: geometric, arithmetic, and analytic aspects

ABSTRACT:

Modular forms are fundamental objects appearing in many areas of mathematics,

one of the most prominent example being the proof of Fermat’s last

theorem. In our talk, we will first provide a collection of motivating questions

arising from the geometric, arithmetic, and analytic theory of modular forms,

which are related to our research. In the second part of our talk, we will give a

more detailed overview on our work on the arithmetic Riemann–Roch theorem

leading, in particular, to an explicit formula for a special value of the Selberg

zeta function for the modular group. This result nicely reflects the interplay

between the various views on modular forms.