The climate is changing due to the heat trapping caused by the rapid increase in greenhouse gases, mainly carbon dioxide, in the atmosphere. One way to state the issue is that we cannot, as a species, adapt to the new conditions quickly enough. This is an example of rate-induced tipping for which the mathematics has been developed over the past ten years. Tipping is usually associated with the possibility, and fear, of abrupt shifts in a climate subsystem. There are many such examples: Greenland ice sheet loss, break-off of Antarctic ice-sheets, boreal forest dieback, permafrost loss etc. These tipping scenarios are mostly viewed in terms of bifurcation-based tipping, but it may be that rate-induced tipping is the most relevant for exactly the reason that parameters effecting these shifts are changing more rapidly than the ability of the system to adjust. These rate-induced shifts may also be abrupt, but the driver is quite different. I will discuss the dynamical systems behind rate-induced tipping, which has been developed over the past ten years, open questions, applications to climate related systems and interesting new directions in which noise and rate change are working together.

Christopher K.R.T. Jones is currently a domain scientist in the Renaissance Computing Institute at the University of North Carolina at Chapel Hill and research professor in Mathematics. He received his Ph.D. in Mathematics from the University of Wisconsin-Madison in 1979, and, prior to being Bill Guthridge Distinguished Professor of Mathematics at UNC, he was a Professor of Applied Mathematics at Brown for thirteen years. The main thrust of his research is the use of dynamical systems as a tool for solving problems that originate in applications; in particular, the use of dynamical systems methods in the study of nonlinear wave motion in neuroscience and optics, ocean dynamics and, more recently, climate. His recent work has included contributions to the area of Data Assimilation, with a particular focus on assimilating data in ocean and sea-ice models. He is currently Director of the Mathematics and Climate Research Network. He is a Fellow of the Society of Industrial and Applied Mathematics and won the inaugural prize of the SIAM Activity Group on the Mathematics for Planet Earth in 2020.