Title: “Fractals, Recursion, Paradoxes, and Applications”
Humans are capable of designing the most amazing objects and pieces of engineering using rather simple (and often boring) lines, curves, and, for the most part, regular geometrical shapes. These shapes, however, are rarely useful in describing objects and phenomena that are ubiquitous in nature such as plants, clouds, snowflakes, or turbulent flows. Fractals and their mathematical properties allow us to model, reproduce, and understand these objects that surround us. In this talk, we will explore some of the properties of fractals, how to generate them, some mathematical ideas they illustrate, and discover how they show up where we least expect them in our daily lives.
Jorge Balbás grew up in Madrid, Spain. He moved to the US in 1992 for professional flight training. While working as a commercial pilot and flight instructor in Southern California, he enrolled in Mt. San Antonio College and later transferred to UCLA, where he obtained a Bachelor’s and a Master’s degree in Applied Mathematics at in 2000, and a PhD in Mathematics in 2004. He spent the next three years at the University of Michigan in Ann Arbor as a post-doc, and returned to Southern California in 2007 to join the mathematics department at California State University, Northridge, where he is currently an Associate Professor. Balbás’ is currently serving as Associate Director at the Institute for Pure and Applied Mathematics (IPAM at UCLA). His research is in Scientific Computing and Numerical Analysis. His work focuses in the development of numerical methods for solving PDEs and the simulation of physical phenomena such as astrophysical flows (e.g., MHD) and shallow-water flows along channels. He also has an interest in image processing and heuristic optimization algorithms for scheduling and timetabling problems.