DMV Topic day “Riemann’s mathematical legacy”

September 18, 2026

To mark the 200th anniversary of Bernhard Riemann's birth, his alma mater, the Georg August-Universität Göttingen, and the German Mathematical Society (DMV) organize the DMV Topic Day "Riemann's legacy". We discuss recent developments in some of the areas which Riemann has started and shaped.

Speakers:

- Valentin Blomer (Bonn)
- Esther Cabezas Rivas (València)
- Gerhard Huisken (Tübingen)
- Jonathan Keating (Oxford)
- Hee Oh (Yale)
- David Rowe (Mainz)

Program:

The scientific program will start in the morning and will finish early afternoon.
There will be the opportunity of contributions by registered participants in a poster session.

Lectures:

Valentin Bloomer Zeta functions and reciprocity
Riemann started the systematic investigation of the zeta function outside the region of absolute convergence and linked its analytic properties to number theoretic statements. In addition to the classical zeta function, there is a large collection of natural families of Dirichlet series that share similar properties, such as an Euler product and a functional equation. I will describe unexpected reciprocity phenomena between families of zeta functions along with some applications.

Esther Cabezas Rivas Constrained Extrinsic Flows in Riemannian manifolds
Volume-preserving curvature flows deform hypersurfaces toward canonical shapes while preserving enclosed volume or other integral quantities. Their nonlocal terms create difficulties that depend strongly on the ambient geometry and the initial hypersurface. After briefly reviewing classical results in space forms, I will present three recent developments. The first concerns constrained curvature flows of closed curves on pinched Hadamard surfaces, providing a first treatment of variable ambient curvature and requiring comparison arguments adapted to nonconstant negative curvature. The second uses a preserved notion of horospherical convexity in the sphere for a quermassintegral-preserving mean curvature flow. This removes the need to move the reference centre and yields global existence and smooth convergence to a geodesic sphere. The third establishes stability of geodesic spheres under volume-preserving mean curvature flow from hypersurfaces that are geometrically C1-close to a geodesic sphere of an ambient space form, without convexity, mean convexity, or initial curvature bounds. Alexandrov reflection and maximum-principle estimates give global curvature control, eventual convexity, and exponential convergence.

Gerhard Huisken Riemannian Geometry and Geometric evolution Equations
An important question in Riemannian geometry concerns the influence of pointwise curvature bounds on the global shape of a Riemannian manifold. Starting from a short review of classical results in this direction the lecture describes how geometric evolution equations such as Ricci flow and mean curvature flow during the last few decades have led to new answers based on a combination of analytic and geometric techniques.

Jonathan Keating The zeta function post-Riemann
I will discuss some of the things we have discovered about the zeta function since Riemann's death that I suspect he might have found interesting. In several cases, I will highlight connections with Physics.

Hee Oh Circles on the Riemann sphere: Dynamics and Rigidity
One of Bernhard Riemann’s great legacies is the geometric approach to complex analysis through Riemann surfaces. The simplest compact example is the Riemann sphere. Beautiful fractal configurations on this sphere, including Apollonian and Sierpiński-type circle packings, provide a bridge between classical geometry and modern dynamics. Starting from four natural questions about circle packings, I will show how viewing the Riemann sphere as the boundary at infinity of hyperbolic three-space leads directly into dynamics and rigidity in spaces of infinite volume.

David Rowe On the Origins of Riemann’s Hypothesis
In this talk I pick up a thread in the story concerning Riemann’s relationship with Gauss. In 1849, Gauss replied to a letter he received from his former student Franz Encke, professor of astronomy in Berlin. This letter later came to light as an important source of information about Gauss’s nearly lifelong interest in finding a law for the asymptotic
distribution of the prime numbers. Little is known about when Riemann first became interested in this question, though he did leave hints in his famous note from 1859 indicating he was aware that Gauss and Dirichlet had worked on this problem. As it happened, Riemann discussed these matters with Kronecker and Weierstrass when he visited with them in Berlin in 1859. As I recently discovered, Riemann told them at that time about Gauss’s letter to Encke from ten years earlier. Here we will discuss this new finding and other unpublished documents relating to Riemann’s paper and his famous hypothesis concerning the zeros of the zetafunction.

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