Finite Element Discretizations for Incompressible Flow on Split Meshes

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Mathematical Modeling of Energy Consumption in the Acute Inflammatory Response


When a pathogen enters the human body, an acute inflammatory response is activated to eliminate the intruder. However, in some patients an extreme response of the immune system may occur which can lead to tissue damage, organ failure, and eventually death. This overwhelming reaction of the immune system is called sepsis.

Unirationality of Low Degree Hypersurfaces


There are several notions which define classes of projective varieties which are close to projective space: unirationality, rationality, stable rationality, etc.  I will discuss what is known about some of these notions for hypersurfaces. The focus of my talk will be on unirationality of hypersurfaces and how spaces of linear subvarieties can be used to show low degree hypersurfaces are unirational.

This is based on joint work with Eric Riedl.

The isometric embedding of abstract surfaces in the 3-dim Euclidean space

A surface in the 3-dim Euclidean space can be viewed as the image of a map from a planar domain to the 3-dim Euclidean space, at least locally. The standard metric in the Euclidean space induces a metric on the surface, which allows us to compute the lengths of curves on the surface and to compute the distance of any two points on the surface. For example, the distance of two points on a sphere is the length of the small arc on the great circle through these two points.