Geometry of numbers in infinite rank and diophantine applications
Resumo: I will explain how basic geometric constructions in arithmetic geometry related to integral points or periods involve natural analogues of lattices in infinite rank. I will sketch the basic setup that makes it possible to do geometry of numbers in that setting, thus providing a rough analogue in diophantine geometry for the theory of quasi-coherent sheaves. I will sketch basic applications to integral points on affine varieties. This is joint work with Jean-Benoît Bost.
On the impact of diffusion ratio on vanishing viscosity solutions of Riemann problems for chemical flooding models
Resumo: We will discuss the vanishing viscosity solutions for a chemical flooding model. The model originates from oil industry and describes a process of injection of water with solvent into the oil in a porous media. We describe situations with unique and non-unique vanishing viscosity solutions to the Riemann problem. Typical examples are the polymer flooding and surfactant flooding. The google-Meet link of the lecture is posted in fluid.impa.br .