Mathematical Biology seminar Amir Arzani University of Utah "Dynamical systems theory in medicine and biology: flow topology and data-driven model discovery" Monday, October 26, 2026 12-1pm in ST E1105 I will discuss two applications of dynamical systems theory in mathematical biology. First, I will discuss how dynamical systems theory could be used to better understand biotransport problems governed by advection-dominated and singularly perturbed advection-diffusion partial differential equations (PDEs). I will introduce the concept of wall shear stress (WSS) topology (stable/unstable manifolds) and demonstrate how these surface manifolds govern near-wall biotransport in major forms of cardiovascular disease. In the second part of the talk, I will discuss how we can use some of the building blocks of neural networks, such as ADAM optimization and the PyTorch language, to discover dynamical systems models from trajectory data. I introduce ADAM-SINDy, a sparse identification framework that uses ADAM optimization for data-driven discovery of nonlinear dynamical systems. Unlike traditional sparse identification of nonlinear dynamics (SINDy), which often depends on prior knowledge of nonlinear parameters, ADAM-SINDy efficiently and accurately identifies them through a flexible global optimization scheme. Multiple examples, including cancer systems biology, will be presented.