Abstract: Recently, there has been great progress in understanding rank-one rigidity phenomena in dynamics. “Rank-one” rigidity refers the rigidity of a single diffeomorphism or flow rather than the rigidity of a bigger group action. Rank one rigidity in dynamics has close ties to geometric rigidity problems in negative and non-positive curvature such as marked length spectrum rigidity and boundary rigidity and makes use of a variety of methods, such as microlocal analysis, coarse geometry, and KAM theory. This workshop will bring together researchers working on rank-one problems from a variety of points of view to discuss recent work and the future directions and challenges in the field.
This workshop will also feature a 2-day special session in honor of Keith Burns’ 70th birthday.
Speaker: Ruth Chapman (London School of Economics, UK) - When: Tue, October 20, 2026 - 3:30pm Where: Kirwan Hall 3206
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Abstract: A non-autonomous system can undergo a rapid change of state inresponse to a small or slow change in forcing, due to the presence of nonlinear
processes that give rise to critical transitions or tipping points. Such transitions are
thought possible in various subsystems (tipping elements) of the Earth’s climate
system. The Atlantic Meridional Overturning Circulation (AMOC) is considered one
such tipping element where models of varying complexity have shown the potential
for bi-stability and tipping. I will present a conceptual model of the AMOC which can
be used to investigate tipping mechanisms. We utilise an Ordered Line Integral
Method (OLIM, Cameron et al 2012) to approximate the Quasipotential of this low-
order system and explore noise tipping paths. We are working to extend this method
for 3 dimensional systems with anisotropic noise to investigate the role of additional
ocean basins in the tipping of this circulation. This work is supported by a SIAM
postdoctoral support grant.