Counting Number Fields

Abstract: We will discuss some recent techniques that have been successful in counting a variety of objects in number theory. Our main focus will be on counting low degree number fields, following the inspirational work of Bhargava. We will see many areas of mathematics come together in this story.

Cut finite element methods for complex multi-physics problems

Many advanced computational problems in engineering and biology require the numerical solution of multidomain, multidimension, multiphysics and multimaterial problems with interfaces. When the interface geometry is highly complex or evolving in time, the generation of conforming meshes may become prohibitively expensive, thereby severely limiting the scope of conventional discretization methods.
In this talk we focus on recent, so-called cut finite element methods (CutFEM)