Welcome to SPP 2026
This is the platform of a coordinated research programme in mathematics, funded by the German Research Foundation (DFG). It comprises 80 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.
Latest publications
The heat equation and independence of the spectrum of the Hodge Laplacian on $\ell^p$
Philipp Bartmann, Matthias Keller
We study the heat equation associated to the Hodge Laplacian on simplicial complexes. Using recently developed techniques for magnetic Schrödinger…
Boundary representations of intermediate forms between a regular Dirichlet form and its active main part
Keller, Matthias; Lenz, Daniel; Schmidt, Marcel; Schwarz, Michael; Wirth, Melchior
We characterize all semigroups sandwiched between the semigroup of a Dirichlet form and the semigroup of its active main part. In case the Dirichlet…
Graphs at infinity: Liouville theorems, Recurrence and Characterization of Dirichlet forms
Matthias Keller, Daniel Lenz, Marcel Schmidt
We survey recent results on graphs and their Laplacians related to the behavior of the graph at large. In particular, we focus on Liouville theorems,…
The complex property of the boundary operator on simplicial complexes
Philipp Bartmann, Matthias Keller
We study the complex property $\partial\partial=0$ of the boundary operator $\partial$ on a weighted, infinite, and possibly non-locally finite…