This internship focuses on stochastic modeling of plant root hair growth, exploring the mechanochemical couplings between turgor pressure, cell wall rheology, and biochemical remodeling. The project aims to understand how plant cells maintain cell wall integrity under mechanical stress and stochastic secretion, producing oscillatory growth patterns. The intern will develop and analyze stochastic differential equation models, perform numerical simulations, and validate predictions against experimental data. Collaboration with INRAE (Versailles) ensures alignment with biological observations, offering a unique interdisciplinary experience at the intersection of theoretical physics and biophysics.