There is much in life that is inherently complex and worth studying. One of the most powerful ways to study something is to describe it using abstractions of its key properties. Such models are more than toys or predictive black-boxes; they can often elucidate fundamental properties of the object of study. In a similar fashion, sometimes stepping away from one’s technical work and explorations and discussing them in a broader context can be personally illuminating.
This blog will primarily be about my personal forays into Applied Mathematics, and will hopefully be aimed at a general scientific and mathematical audience. I also plan on using it to write expository notes, and discuss recent research in mathematics and its connections with the sciences. Other subjects may be posted about, but I will try and organize everything as clearly as possible.
My name is Andrew Krause. I have B.S. degrees in Mathematics and Computer Science from the New Mexico Institute of Mining and Technology. I recently finished an M.S. degree in Mathematics, specializing in Analysis. I am now attending the University of Oxford as a DPhil student, which is comparable in some ways to a U.S. PhD program.
My research at Tech has mostly been about a particular set of related problems in stochastic dynamical systems. Further information about that can be found here.
My DPhil research is in the general area of biological fluid flow. More specifically, it will involve models of tissue engineered constructs and the role of transport phenomena in the viability of such constructs. More details will be posted later, likely in the form of expository articles.
In general, my research interests are the overlaps of Applied Analysis, particularly PDE and Dynamical Systems, Mathematical Biology, Fluid Dynamics, and related areas of Applied Math. I am also interested in Philosophy, the Foundations of Mathematics, Modern Physics such as Non-equilibrium statistical physics, Theoretical Computer Science, and advances in programming and computation, but these interests are at best hobbies rather than anything directly related to research.