Geometric Dynamical Systems: Manifolds and Stability Part I

04 May 2016 | Presentations | Contributor(s): Laura Slivinski

This is the first part of a series of dynamical systems lectures on the center, stable and unstable manifold theorems. This short lecture series was part of the MCRN Mathematics of Climate Modelling Course taught at the University of North Carolina by Chris Jones in 2013. This course was a...

Chaotic Dynamical Systems: the Horseshoe Map

04 May 2016 | Presentations | Contributor(s): Laura Slivinski

This is the second part of a series of lectures on chaotic dynamics, and focuses on the Horseshoe Map. This short lecture series was part of the MCRN Mathematics of Climate Modelling Course taught at the University of North Carolina by Chris Jones in 2013. This course was a second year graduate...

Chaotic Dynamical Systems: the Bernoulli Shift

04 May 2016 | Presentations | Contributor(s): Laura Slivinski

This is the first part of a series of lectures on chaotic dynamics, and focuses on the Bernoulli shift. This short lecture series was part of the MCRN Mathematics of Climate Modelling Course taught at the University of North Carolina by Chris Jones in 2013. This course was a second year...

Geometric Dynamical Systems: Manifolds and Stability Part III

04 May 2016 | Presentations | Contributor(s): Laura Slivinski

This is the final part of a series of dynamical systems lectures on the center, stable and unstable manifold theorems. This is background lecture 3.1C for the Mathematics of Climate Modelling course.

Geometric Dynamical Systems: Manifolds and Stability Part II

04 May 2016 | Presentations | Contributor(s): Laura Slivinski

This is the second part of a series of dynamical systems lectures on the center, stable and unstable manifold theorems. This is background lecture 3.1B for the Mathematics of Climate Modelling course.

Deriving the SWM Lecture 3: Barotropic Vorticity Equations

04 May 2016 | Presentations | Contributor(s): Laura Slivinski

This lecture develops the barotropic vorticity equations for the shallow water model.  This is background lecture 2.1C in the Mathematics of Climate Modelling course.

Deriving the SWM Lecture 2: Stream Functions for Velocity Fields

04 May 2016 | Presentations | Contributor(s): Laura Slivinski

This lecture develops the formulation of the stream function for the velocity field of the shallow water equation.  his is the second in a series of short lectures on deriving the shallow water model, given by Chris Jones in 2013. 

Deriving the SWM Lecture 1: Conservation of Potential Vorticity

04 May 2016 | Presentations | Contributor(s): Laura Slivinski

This lecture develops the conservation equation for potential vorticity in the shallow water model.

Vegetation patterns in mathematical models, and vegetation patterns in Horn of Africa

21 Apr 2016 | Presentations

Visually striking large-scale spatial patterns of vegetation have been observed in semi-arid regions in the Americas, Africa and Australia. These have led to suggestions by theoretical ecologists that certain characteristics of the patterns may serve as early-warning signs of desertification....

New averaging results motivated by climate models: fat tails, oscillations, and tipping

10 Dec 2015 | Presentations

We review recent results where new averaging approaches are developed and applied in the context of systems with multiple time scales and fat tails  and in non-autonomous multiple scale systems with oscillatory forcing.  These types of systems appear in a variety of higher dimensional...

Where's the Math in Climate Science?

09 Nov 2015 | Presentations | Contributor(s): Laura Slivinski

Abstract: Climate science is dominated by the use of large-scale models, of which there are only 30 or so around the world. It might then seem that the need for mathematics is limited to areas that directly support the operation of such models. I will explain, by digging into the way the models...

Tipping points and power cuts

18 Jun 2015 | Presentations

Who, or what, will tip the big climate models?

18 Jun 2015 | Presentations

ICMS Tipping Points: Fundamentals and Applications

13 Jun 2015 | Workshops

Objectives: This workshop (September, 2013) brings together mathematicians and statisticians, whose research expertise is relevant to investigating threshold behaviour in complex environmental systems, with the climate scientists and ecologists who exploit mathematical modelling in their research...

Midwest Mathematics and Climate Conference - Day 2 Afternoon Session

12 May 2015 | Presentations | Contributor(s): Laura Slivinski

Charles Jackson, University of Texas, AustinDual-state Behavior of the Community Climate System ModelIce age climate between 80,000 and 11,000 years ago experienced abrupt (< 10 year) global-scale climate transitions every few thousand years. Evidence and theory suggests such behavior may be...

Midwest Mathematics and Climate Conference - Day 2 Afternoon Session

12 May 2015 | Presentations

Charles Jackson, University of Texas, AustinDual-state Behavior of the Community Climate System ModelIce age climate between 80,000 and 11,000 years ago experienced abrupt (< 10 year) global-scale climate transitions every few thousand years. Evidence and theory suggests such behavior may be...

Midwest Mathematics and Climate Conference - Day 3 Afternoon Session

12 May 2015 | Presentations | Contributor(s): Laura Slivinski

Mary Silber, Northwestern UniversityPattern Formation in the Drylands: Self Organization in Semi-Arid EcosystemsMuch of our understanding of spontaneous pattern formation in spatially extended systems was developed in the “wetlands" of fluid mechanics. That setting allowed...

Midwest Mathematics and Climate Conference

12 May 2015 | Workshops | Contributor(s): Laura Slivinski

The conference is sponsored by the National Science Foundation, Institute of Mathematics and Its Applications, the Office of Research,College of Liberal Arts and Sciences, and the Department of Mathematics, Department of Geography/Atmospheric Science Program, and The...

Midwest Mathematics and Climate Conference

12 May 2015 | Workshops

The conference is sponsored by the National Science Foundation, Institute of Mathematics and Its Applications, the Office of Research,College of Liberal Arts and Sciences, and the Department of Mathematics, Department of Geography/Atmospheric Science Program, and The...

Introduction to the Mathematics of Climate at UMN - Lecture 23

12 May 2015 | Presentations | Contributor(s): Laura Slivinski

This is lecture 23 in the series "Introduction to the Mathematics of Climate" offered at the University of Minnesota in 2014 with the support of MCRN and The Institute for Mathematics and its Applications.