Patricia Alonso Ruiz

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 phenomena¹ that happen in environments with fractal-like features².
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 :)

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What do I mean by ... ?

Random phenomena

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

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!