DCSS 2020

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Cornell Dynamics and Climate Summer School:
Nonsmooth and Multivalued Dynamics in Conceptual Climate Models
July 14 - 24, 2020

*This is not to be confused with the Cornell Probability Summer School (CPSS). CDSS is a separate event and focuses on entirely different subject material.

We are in the early stages of planning and more information will be posted as it comes available.

Inquiries can be sent to dcss_cu-math@cornell.edu.

The Cornell Dynamics and Climate Summer School focuses on the interrelated topics of conceptual climate models and nonsmooth / multivalued dynamical systems. Participants - graduate students, postdocs, and junior faculty - will delve into the following topics through a series of lectures and informal discussions:

  1. conceptual models of planetary climate, including the Budyko energy balance model and its extensions.
  2. mathematical frameworks for nonsmooth and multivalued dynamics, including Filippov systems and combinatorial/algebraic topological approaches to nonlinear dynamics.

Details on each topic follow:

(1) Conceptual climate models sit opposite the complexity spectrum from computationally massive general circulation models that inform IPCC reports on climate change. Though they sacrifice details, conceptual models based on mass and/or energy balance offer mechanistic clarity and analytic tractability. They pose an invitation to the climate-curious mathematician to engage with a timely topic that brings its own collection of mathematical questions.

(2) One such question involves the nonsmooth features that arise frequently in conceptual climate models. For instance, surface reflectivity jumps when one crosses the line between ocean and sea ice. Abrupt boundary transitions occur when northern and southern ice lines join at the equator or retreat completely to their respective poles. In addition, density-triggered mixing between ocean layers and flip-flops between glacial and interglacial planetary regimes may occur. Discontinuous and merely continuous vector fields can offer physically accurate or simplified descriptions of such phenomena, despite lacking traditional results of existence and uniqueness of solutions. We’ll explore how one can nonetheless conceive of solutions mathematically.

Multivalued dynamics offer a framework for nonsmooth systems, as well as systems with uncertainty. For example, in the nonsmooth systems x’=sqrt(x) and x’=sgn(x), nonunique trajectories depart from the origin at arbitrary times; solutions to the latter may depart in either direction. Uncertainty stemming from sparse data or anticipated climate mitigation actions can also give rise to multiple possible trajectories. Multivalued dynamical systems bundle nonunique or uncertain trajectories together; analyzing their behaviors reveals possible outcomes. 

ACKNOWLEDGEMENTS

This meeting is partially supported by a grant from the National Science Foundation.

Thanks also to the staff at the Cornell Department of Mathematics for handling much of the organization of the meeting.

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