Georgia Institute of Technology College of Sciences

In this talk, we will study random dynamical systems of smooth surface diffeomorphisms. Aaron Brown and Federico Rodriguez Hertz showed that, in this setting, hyperbolic stationary measures have the SRB property, except when certain obstructions occur. Here, the SRB property essentially means that the measure is absolutely continuous along certain “nice” curves (unstable manifolds). In this talk, we want to understand conditions that guarantee that SRB stationary measures are absolutely continuous with respect to the Lebesgue measure of the ambient space.

Ice sheets are fascinating dynamical systems that flow, fracture and melt on a wide range of time scales, presenting a range of challenging prediction problems with important implications for how coastal communities plan for sea level rise. In this talk, I will introduce a few outstanding problems concerning the evolution of Earth’s ice sheets under climate change.

Travelling pulses and waves are a rich subset of feasible patterns in reaction-diffusion systems. Many have investigated their existence, stability, and other properties, but what happens if the deterministic dynamics is affected by random occurrences? How does the interplay between diffusion and noise influence the velocity, curvature, and stability of multidimensional patterns?

Abstract: Classifying the invariant measures for a given dynamical system represents a fundamental challenge.

Link: https://gatech.zoom.us/j/91390791493?pwd=QnpaWHNEOHZTVXlZSXFkYTJ0b0Q0UT09

Link: https://gatech.zoom.us/j/91390791493?pwd=QnpaWHNEOHZTVXlZSXFkYTJ0b0Q0UT09

Link: https://gatech.zoom.us/j/91390791493?pwd=QnpaWHNEOHZTVXlZSXFkYTJ0b0Q0UT09