Mathematical Sciences Department Colloquium
Speaker: Arnaud Lazarus, MIT
Friday, February 28, 2025
11:00am - 12:00pm
Stratton 202
Upside-Down physics with Floquet theory and model experiments
Abstract: Linear Ordinary Differential Equations (ODEs) with periodic coefficients describe the evolution of physical perturbations in systems whose properties vary periodically in time or space. Those equations explain parametric instabilities in a child swing or the emergence of new exotic quantum states in Floquet systems. They also rationalize the dynamic stabilization of inverted pendulums, the confinement of charged particles in quadrupole ion traps or the physics of (tiny) boats floating upside-down.
We believe the latter regime have been overlooked in Floquet systems and we systematically investigate (theoretically and experimentally) the limit where the periodic modulation to sustain an “upside-down” state is minimal. This approach will lead us to unexpected physical and mathematical territories, that are analog to the basic rules of quantum mechanics. These results could inspire innovative engineering functionalities and provide novel mathematical and numerical tools for the resolution of linear ODEs with periodic coefficients.
Bio: Arnaud Lazarus received a PhD degree in mechanical engineering from Ecole Polytechnique, Palaiseau, France, in 2008. After two post-doctoral years in Paris, he joined the Massachusetts Institute of Technology as an associate postdoctoral researcher from 2010 to 2013. In 2013, he became an associate professor at Sorbonne Université, Paris, France, doing his research at Institut Jean le Rond ∂’Alembert. In 2024, after a one-year sabbatical in Katia Bertoldi’s group within the School of Engineering and Applied Sciences at Harvard he joined the department of Mathematics at MIT, hosted by John W. Bush as an invited associate professor. His current interests include the stability of dynamical systems with a particular interest in Floquet theory and the mechanics of slender elastic structures.