The model-theoretic construction of the binding group in the presence of internality has proven to be one of the most important group existence theorems. It saw numerous applications, including those in differential Galois theory, envisaged by Poizat, and pursued by Pillay in his generalisation of the strongly normal theory of Kolchin.
We show how to view the binding group construction as an instance of Janelidze's categorical Galois theory. This allows us to apply it in areas beyond model theory, for example to the scheme-theoretic treatment of Pillay's differential Galois theory.
We will discuss connections with Hrushovski’s work on groupoids.
In this talk, we study the numerical approximation of the stochastic heat equation on the sphere driven by an additive Lévy process. For this, we first prove new regularity results for the solution of the stochastic heat equation under different regularity assumptions on the initial value and driving Lévy process. In these settings, we perform a spectral approximation based on the truncation of the series expansion with respect to the real-valued spherical harmonic functions. Further, we apply a forward resp. backward Euler-Maruyama scheme for the temporal approximation. We prove strong and weak convergence rates for the introduced approximation scheme and present numerical simulations that confirm our theoretical results.
This is joint work with Annika Lang and Andrea Papini.