Colloquia

Mathematical Modeling of Energy Consumption in the Acute Inflammatory Response

Abstract:

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

Abstract:

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.

Quantitative Mostow Rigidity

Abstract:

Hyperbolic space is the classical non-Euclidean space introduced by Lobachevksy, Bolyai and Gauss, in which the sum of the angles of a triangle is less than \pi. Hyperbolic n-manifolds are spaces that have the local geometry of hyperbolic n-space. The study of these spaces, besides being natural from the viewpoint of classical geometry, has important connections with differential geometry, algebraic geometry, complex analysis, number theory and topology.

Data-driven decision-making facing complex data environment

In this talk, we present the key challenges in data-driven decision-making when faced with a complex data environment. Traditionally, most data-driven decision-support tools are developed in a static fashion, meaning they consider a set of fixed, well-structured data to derive inferences or decisions. Nevertheless, even though these decision-making tools are rigorous and mathematically sound, they have not often been effective due to the dynamic nature and underlying complexity of the data in practice.