## Welcome to SPP 2026

This is the platform of a coordinated research programme in mathematics, funded by the German Research Foundation (DFG). It comprises 33 research projects in the fields of differential geometry, geometric topology, and global analysis. More than 80 researchers from doctoral to professorial level and based at more than 20 German and Swiss universities are represented in this programme.

## Next Activities

## Latest publications

#### Smoothness and long time existence for solutions of the Cahn-Hilliard equation on manifolds with conical singularities

P. T. P. Lopes, N. Roidos

We consider the Cahn-Hilliard equation on manifolds with conical singularities. For appropriate initial data we show that the solution exists in the...

#### Hilbert schemes, commuting matrices, and hyperkaehler geometry

Roger Bielawski, Carolin Peternell

We represent algebraic curves via commuting matrix polynomials. This allows us to show that the canonical Obata connection on the Hilbert scheme of...

#### Geometry of folded hypercomplex structures

Roger Bielawski, Carolin Peternell

We investigate the geometry of the Kodaira moduli space* M* of sections of a twistor projection, the normal bundle of which is allowed to jump. In...

#### Differential geometry of Hilbert schemes of curves in a projective space

Roger Bielawski, Carolin Peternell

We describe the natural geometry of Hilbert schemes of curves in projective spaces.

## Latest Blog posts

**2019 Christopher Heyde Medal**Three days ago the Australian Academy of Sciences announced the recipients of its 2019 Honorific Awards (Twitter, Webpage). Among them is Professor Geordie Williamson FAA FRS (Wikipedia), Mathematician at the University of Sydney (Homepage), who receives the Christopher Heyde Medal. The Australian Academy of Sciences states: Professor Williamson is a world leader in the field of … Continue reading "2019 Christopher Heyde Medal"

**Global existence for non-linear wave equations**Non-linear wave equations (in 3+1 dimensions) are ubiquitous in physics, playing a vital role in many subfields of it. There are many methods available to show short-time existence of solutions for such equations, but global-in-time existence is a much more subtle problem. In the 1980s Klainermann introduced a so-called null condition on the nonlinearities of … Continue reading "Global existence for non-linear wave equations"

**Ten Years of Polymath**Ten years ago the first Polymath project was launched (link to the original proposal of Timothy Gowers). Polymath can be described as massively collaborative mathematics, i.e., a large groups of mathematicians works on a predefined problem and each member posts his or her (partial) ideas, so that the collective makes progress from each small step … Continue reading "Ten Years of Polymath"