DATE:

Friday, October 27, 2023

TIME:

3:30 PM

LOCATION:

GMCS 314

SPEAKER:

Ricardo Carretero-González, Mathematics and Statistics, San Diego State University

ABSTRACT:

In this talk we describe techniques for the dynamical reduction of localized structures (such as solitons, kinks, filaments, vortices, and vortex rings) in nonlinear spatio-temporal systems. The central idea is use mathematical reductions to accurately describe these complex spatio-temporal structures with lower-dimensional models that are more easily tackled, both mathematically and computationally. In turn, the reduced models allow for an unprecedented description of the statics, stability, dynamics, and interactions of these structures. After showcasing the success of this reduction methodology in a wide range of situations, we will focus on the interesting case of vortices in complex fields bearing applications to condensed matter physics, nonlinear optics, and superfluids. In particular, motivated by recent experiments studying vortex dynamics in Bose-Einstein condensates (the coldest form of matter in the Universe), we show that considering these vortices as quasi-particles allows for a full understanding of their dynamics, stability, and bifurcations. We will also explore some extensions of the quasi-particle approach for 3D vortex rings which are formed when a vortex filament (a “twister”) is looped back onto itself creating a close ring that carries vorticity.

Bio: Prof. Ricardo Carretero holds a Summa Cum Laude B.Sc. from the Universidad Nacional Autónoma de México, UNAM (1992) and a Ph.D. in Applied Mathematics and Computation from Queen Mary College, University of London, UK (1997). He was a post-doctoral fellow at the Centre for Nonlinear Dynamics, University College London, UK and a Pacific Institute for the Mathematical Sciences Postdoctoral Research Fellow at Simon Fraser University and University of British Columbia, Vancouver, Canada. He is currently a Professor of Mathematics at San Diego State University (SDSU) where his multidisciplinary research has been supported by NSF grants since 2005. His research focuses on spatio-temporal dynamical systems, nonlinear waves and their applications. He has published some 140 manuscripts, two books and one textbook. He is the co-founder and co-director of the Nonlinear Dynamical Systems (NLDS) group at SDSU. He is an active advocate of the dissemination of science and he continuously delivers engaging presentations at local high schools and science festivals.

HOST:

Parag Katira

VIDEO: