Dr. Jason Mireles-James, Professor of Mathematics in the Department of Mathematics and Statistics at Florida Atlantic University, is spending the Fall 2024 semester on sabbatical at the Université de Montréal, where he is a co-organizer for a thematic program titled "Computational Dynamics – Analysis, Topology & Data.” This is a collaborative and interdisciplinary initiative addressing the challenges of identifying dynamical structures in complex nonlinear systems, particularly those that are high-dimensional or poorly resolved. In such intricate settings, computational mathematics emerges as the primary tool for gaining deeper insights and extracting fundamental dynamical features. The thematic program provides a platform for researchers to delve into three core research topics, each contributing to our understanding of nonlinear dynamics and their computational analysis.

The thematic program includes a series of tutorials, lectures and workshops that fuse together analysis, topology and data science. Research topics included for the thematic program consist of Rigorous Computational Differential Equations (R1), and is dedicated to exploring the computational and theoretical challenges associated with rigorously identifying and extracting fundamental dynamical features in finite (high-dimensional) and infinite-dimensional dynamical systems. The second topic is Combinatorial Topological Framework for Nonlinear Dynamics (R2). Here the aim is to develop a combinatorial topological framework for the global analysis of multiparameter systems, enabling researchers to explore and characterize complex nonlinear dynamics. The third, and final, topic is Data-Driven Dynamics, and focuses on building bridges between computational mathematics and data science to develop novel methods for identifying and exploiting models of nonlinear dynamics compatible with time series data. Combining the insights and techniques from R1 and R2, we will aim at enhancing our ability to model nonlinear dynamics from observational data, enabling validation and testing of proposed models.

Through his research, Dr. Mireles-James contributes to the current mathematical literature, seeking a deeper understanding of the important features of nonlinear systems. He enjoys working together with colleagues and students from around the world.