Graduate Lectures (8/12)

11.11.2026

Sebastian Baader

Damaris Meier (ETHZ) and David Loeffler (UniDistance Brig)

The purpose of these traditional lectures is to present recent important developments in mathematics to a large audience of graduate students and young researchers. The lecturers are chosen as experts in their field, with demonstrated pedagogical talent.

Wednesday, 13h15-14-45 Dr. Damaris Meier: Asymptotic Geometry

Abstract: Asymptotic geometry studies the large‑scale structure of metric spaces and has applications in areas such as geometric topology, geometric group theory, and dynamics. The main objects explored in this course are Gromov hyperbolic spaces, which can be viewed as (non‑smooth) generalizations of negatively curved spaces. The asymptotic geometry of a Gromov hyperbolic space is effectively encoded in the metric structure of its boundary at infinity. We will investigate these spaces and their morphisms, and establish embedding and rigidity results.

Wednesday, 15h00-16-30 Prof. Dr. David Loeffler: Modular forms and modular curves

Abstract: Modular forms are a class of complex-analytic functions with many symmetries, which have many rich and surprising connections to number theory: for instance, they are intimately linked with elliptic curves, quadratic forms, representations of Galois groups, and many other important topics.
I will explain the basic theory of modular forms (q-expansions, Hecke operators, etc), assuming only familiarity with elementary algebra and complex analysis, e.g. the residue theorem. Then I will develop the theory of modular curves – the geometric spaces on which modular forms live – and their role as moduli spaces of elliptic curves; here I will assume a little more background in geometry (Riemann surfaces, basics of algebraic varieties). In the final segment of the course, depending on how much time is left and what the audience want to see, I will cover a selection of more advanced topics, potentially including some of the following:
- the Eichler-Shimura congruence relation,
- quaternion algebras and Jacquet-Langlands correspondence,
- connections to representation theory and adèle groups,
- modular symbols and special values of L-functions.

Universität Bern, Room B78, building ExWi, Sidlerstrasse 5