Department of Mathematics
Texas A&M University
College Station, TX 77843-3368

email: paruiz(at)tamu.edu

I am an Associate Professor in the
Department of Mathematics at
Texas A&M (on leave during this AY24/25).
In my research I study random phenomena^{1} that happen in environments with fractal-like features^{2}.
In particular I am interested in how the time evolution of these processes is connected
to the geometry of the environment they take place in.
The mathematics involved in my investigations lie at the crossroads of
Analysis (function spaces, harmonic analysis),
Probability (continuous-time Markov processes, Dirichlet forms, heat kernels)
and Geometry (metric measure theory, fractal geometry).

I find this area of research a truly fascinating one! If you are interested in learning more about it,
feel free to browse through my work, check the TAMU
Fractals Research Team website, or contact me :)

What do I mean by ... ?

An example: imagine a particle to which we apply some heat. Due to the heat the particle starts moving. That movement is random. Einstein made major contributions in finding an equation that would describe that random movement. Mathematicians call it Brownian motion, or Wiener process.

Fractals are more than nice pictures. They serve as mathematical models for highly porous media (sponges, filters) or intricately branching structures (vessels, large networks). One common property is that, if you zoom in a part of a fractal, you will see a similar pattern repeating over and over. If you are into Python, Github has great repositories!