Welcome to Ian Ruau's Webpage

Mathematics PhD Student
Auburn University
College of Sciences and Mathematics (COSAM)
Department of Mathematics and Statistics
Parker Hall 144 B
Auburn, Alabama 36849
Email: ianruau@auburn.edu
LinkedIn: Link to LinkedIn

• About Me
  • CV
• Research Overview
• Projects
• Teaching
  • In the United States
  • In Argentina

I am a graduate student at Auburn University pursuing a PhD in Mathematics. My interest is on partial differential equations (PDEs), dynamical systems, stochastic PDEs, programming, data science and financial mathematics. My advisors are Dr. Wenxian Shen and Dr. Le Chen. We work on deterministic and stochastic chemotaxis models.

Before coming to Auburn, I got my B.Ed. in Mathematics in December 2015 at the National University of Mar del Plata and started teaching at a high school and at the College of Engineering of that same university. I got my BS. in Mathematics at the National University of Mar del Plata in August 2020.

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• Chemotaxis Simulation CLI Tool (Python) GitHub Page of the Project
  • Python project as part of my ongoing research that simulates a chemotaxis process from a parabollic-elliptic system of differential equations.
  • Central differences and the Runge-Kutta numerical method were used to improve the accuracy of the simulations while ghost points were used to treat the Neumann boundary conditions accurately.
  • The simulations match theoretical results previously known, and we expect to find new properties of the solutions in our ongoing research.
• Simulations on Some Surface Growth Models (Python) GitHub Page of the Project
  • Project developed for the Applied Stochastic Processes course to simulate a ballistic deposition model.
  • We could corroborate through our simulations that the growth model belongs to the universality class such as the one exhibit by the fluctuations of the KPZ equation. Indeed, different ballistic depositions of tetrominoes led to the same universality class of fluctuations.
  • Although the empirical results corresponded with the expected behaviour, we could not provide a theoretical proof of the specific region where the fluctuation behaved as the ones of the KPZ equation due to the randomness of the fluctuation paths.
• Chicken Behaviour via Markov Chains (Python)
  • Project developed for the Applied Stochastic Processes course to analize the behaviour of chickens from a real dataset provided by a Poultry Sciences graduate student.
  • By analizing the behavioral data we were able to identify the significant and often ocurring sequential behavioral patterns which led us to find the stationary distribution of the Markov chain associated to the chickens' actions.
• Problems of the Sturm-Liouville type associated with Lacunary Series tetrominoes: Thesis for the B. S. in Mathematics in which a self-adjoint Sturm-Liouville problem contains a coefficient whose Fourier series is a lacunary sequence.
  • We proved that the solution of the Sturm-Liouville problem has equally spaced Fourier coefficients given by the lacunary sequence of the problem.