On this page I will keep a running list of current projects to make it easier to follow the larger narrative. My interests range from stochastic analysis and high-performance computing to developmental biology and climate modeling. So here's a little taste of what's going on:
DifferentialEquations.jl is a Julia package for solving various types of differential equations. My goal is to provide an easy interface in Julia for solving many of the most common nonlinear ordinary and partial differential equations (and their stochastic variants).
High Order Numerical Methods for Stochastic (Partial) Differential Equations
This is one of the projects that I am doing for my thesis. More details will come when the results are closer to publication, but I will be documenting the implementing and performance of the codes here to both show researchers how to use the MATLAB/Julia code and help explain why it works.
Theoretical/Systems Developmental Biology
My research focuses on the application of stochastic analysis to the understanding of biological organisms. For that reason, and because I simply love science, I tend to keep up on systems biology, bioinformatics, and developmental biology literature that is "interesting for noise reasons". This could either be because it is an interesting system/results to think about, or simply the results are fun random noise in the scientific literature. Whatever it is, that's why I am sharing it.
I don't want to put a category on this because all too often the math I need to use comes from way out of nowhere. Stochastic/functional analysis will be everywhere, but I keep being surprised how much (algebraic) geometry, nonstandard analysis, and commutative algebra shows up. Also, one of my little tricks is to bring in machine learning and computer algebra systems to solve / approximate hard problems.
High Performance Computing in the New Age
When I first started programming, I did freelance web development to earn money in college. If there's one thing I learned from that job, it's just about every programming language and model (web development was all over the place before node.js). I am now using the experience to jump into the new age of high performance computing. I am starting to use Julia. I have a Xeon Phi and Nvidia cards for CUDA on my workstation. And I am sharing all of the tools I am using to tear down brick walls I am banging my head on to make these things work.
The inevitable randomness. It will show up on here. Embrace it.