Seminar

We develop and analyze a splitting method for fluid-poroelastic structure interaction. The fluid is described using the Stokes equations and the poroelastic structure is described using the Biot equations. The transmission conditions on the interface are mass conservation, balance of stresses, and the Beavers-Joseph-Saffman condition. The splitting method involves single and decoupled Stokes and Biot solves at each time step. The subdomain problems use Robin boundary conditions on the interface, which are obtained from the transmission conditions.

This talk focuses on the computation of a certain birational invariant, denoted as β. The core of this work involves analysing the filtration by order of vanishing of global sections of line bundles over a variety. We address this problem for certain Schubert subvarieties of a Grassmannian by using the Borel-Weil-Bott theorem. 

Let C+ be a curve of genus at least 2 embedded in its Jacobian and let C- = {-c : c in C+} be the negative embedding. The Ceresa cycle [C+] - [C-] is the simplest example of an algebraic cycle which is trivial in homology but (generally) non-trivial modulo algebraic equivalence. Hyperelliptic curves have trivial Ceresa class, but only recently examples of non-hyperelliptic curves with torsion Ceresa cycle were found.