# Jim Walsh

- Professor

## Notes

### Jim Walsh publishes

October 2, 2020

Professor of Mathematics Jim Walsh published an article, “A window into the world of KAM theory,” that was the cover article of the October issue of Mathematics Magazine. In this paper, a simple model is used to elucidate the theory that played a key and historic role in mathematical investigations into the stability of the solar system.

### Jim Walsh's Paper Featured as Journal Cover Story

March 30, 2020

Professor of Mathematics Jim Walsh authored "A Discontinuous ODE Model of the Glacial Cycles with Diffusive Heat Transport," with E. Widiasih. The featured paper appeared as the cover story in the open access journal *Mathematics*. The paper concerns a mathematical model of the glacial cycles and, in particular, considers competing climate feedbacks that determine the extent of the ice sheet throughout the glacial-interglacial cycles.

### Jim Walsh Gives Invited Presentation

May 28, 2019

Professor of Mathematics Jim Walsh gave an invited presentation on May 23, 2019 at the biennial SIAM Conference on Applications of Dynamical Systems in Snowbird, Utah. Speaking in the minisymposium "Planetary Motion and its Effects on Climate," Jim presented new research on the mathematical modeling of the glacial cycles. These results were obtained in collaboration with the 2018-19 Department of Mathematics Lenora Lecturer Ester R. Widiasih, associate professor of mathematics at the University of Hawaii.

### Jim Walsh Writes Invited Paper

February 17, 2019

Professor of Mathematics Jim Walsh's invited paper appeared in a Special Issue of the *CODEE Journal* (Consortium for Ordinary Differential Equations Educators), titled "Linking Differential Equations to Social Justice and Environmental Concerns." Walsh's article concerns a conceptual model of the Atlantic Meridional Overturning Circulation, which is an important component of the ocean circulation that has been linked to climate change.

### Jim Walsh Publishes

August 22, 2018

Professor of Mathematics Jim Walsh's paper "Neoproterozoic glacial ages in a nonsmooth conceptual model" has appeared in the *Journal of Physics Communications*. The paper concerns a nonsmooth geometric singular perturbation problem that arises in a mathematical model of the great glacial ages of the Neoproterozoic Era.

### Jim Walsh Speaks at International Conference

June 18, 2018

Professor of Mathematics Jim Walsh gave a talk at the International Conference on Advances in Nonsmooth Dynamics, from June 13-15, 2018 in Bristol, England. Jim spoke about his research in conceptual climate modeling, in which nonsmooth dynamical systems theory plays a major role.

### Jim Walsh Gives Talk

May 1, 2018

Jim Walsh, professor of mathematics, gave a plenary talk at the 20th Annual Chicago Symposium Series on Excellence in Teaching Mathematics and Science: Research and Practice, held April 13 at Northeastern Illinois University/North Park University in Chicago. The symposium series has been convening math and science faculty from the Chicago area for the past twenty years with the goal of improving undergraduate math and science education in and around Chicago. Walsh spoke about his experiences teaching the mathematical modeling of climate.

### Jim Walsh Publishes

October 27, 2017

Jim Walsh, professor of mathematics, published the article "Diffusive Heat Transport in Budyko's Energy Balance Climate Model with a Dynamic Ice Line" in the *Journal Discrete and Continuous Dynamical Systems*—*Series B*. The paper concerns the mathematical analysis of a conceptual climate model that couples surface temperature to a dynamic ice sheet.

### Jim Walsh presents at Society for Industrial and Applied Mathematics conference

November 14, 2016

Professor of Mathematics Jim Walsh gave a mini tutorial titled Conceptual Climate Models at the Society for Industrial and Applied Mathematics conference, Mathematics of Planet Earth Conference held in Philadelphia. SIAM mini tutorials are presented to highlight a future direction or emerging area within applied mathematics. Walsh also co-organized a mini symposium at SIAM MPE16 titled Mathematics and Conceptual Climate Models.

On October 18, Walsh presented his current research in the Mathematics of Climate Seminar in the School of Mathematics at the University of Minnesota. In September, Walsh gave an invited talk in the Department of Mathematics at Boston University on recent work concerning a mathematical model of the glacial cycles.

### Professor of Mathematics Jim Walsh Publishes

May 13, 2016

Professor of Mathematics Jim Walsh served as lead author on the paper “Periodic Orbits for a Discontinuous Vector Field Arising from a Conceptual Model of Glacial Cycles,” which recently appeared in the mathematics journal *Nonlinearity*. The paper was coauthored by Esther Widiasih, Jon Hahn, and Richard McGehee.

Conceptual climate models provide an approach to understanding climate processes through a mathematical analysis of an approximation to reality. Recently, these models have also provided interesting examples of non-smooth dynamical systems. In this paper, Walsh and his coauthors develop a new conceptual model of glacial cycles.

The model, consisting of a system of three ordinary differential equations defining a discontinuous vector field, provides a dynamical systems framework for a mechanism previously shown to play a crucial role in glacial cycle patterns, namely, an increased ice sheet ablation rate during deglaciations. Ad-hoc singular perturbation techniques are used to prove the existence of a large periodic orbit crossing the discontinuity boundary, provided the ice sheet edge moves sufficiently slowly relative to changes in the snow line and temperature.

### Jim Walsh Publishes, Speaks

February 12, 2016

The paper "Climate modeling in differential equations," written by Professor of Mathematics Jim Walsh, appeared recently in the *Journal of Undergraduate Mathematics and Its Applications*. The 38-page "module" recounts Walsh’s efforts in bringing climate modeling into Oberlin's Math 234 Differential Equations course.

Walsh also spoke in January at the annual Joint Meetings of the American Mathematical Society (AMS) and Mathematical Association of America (MAA) in Seattle, describing his new course Math 305 Mathematics of Climate Modeling in the MAA Session Mathematical Modeling in the Undergraduate Classroom.

### Jim Walsh Profiled

December 3, 2015

Professor of Mathematics Jim Walsh was profiled by the Mathematics and Climate Change Research Network (MCRN) about his climate-modeling research. Walsh has been a member of MCRN since 2011, and he currently co-organizes a weekly webinar that focuses on mathematical models arising in the study of paleoclimate.

### Jim Walsh Publishes, Speaks at Workshop

October 6, 2015

The paper “On the Budyko-Sellers energy balance climate model with ice line coupling” by Professor of Mathematics Jim Walsh (lead author) and Christopher Rackauckas ’13 appeared in the September issue of *Discrete and Continuous Dynamical Systems - Series B (DCDS-B)*. The paper presents an analysis of a mathematical model of an ice sheet-surface temperature coupled model. This work was carried out with Rackauckas.

Walsh was also invited to participate in a Mathematics of Planet Earth 2013 workshop held September 30-October 2 at the National Institute of Mathematical and Biological Synthesis in Knoxville, Tennessee. At the workshop, Walsh spoke about the Mathematics and Climate Research Network, an organization funded by an award from the National Science Foundation’s Division of Mathematical Sciences of which he is a member.

### Jim Walsh Gives Talk

March 9, 2015

On March 8, Professor of Mathematics Jim Walsh gave a talk in a special session on conceptual mathematical models in climate science at the 2015 American Mathematical Society Spring Eastern Sectional Meeting at Georgetown University. The talk, "New Budyko-type models of a Slushball Earth," recounted recent work with Christopher Rackauckas '12 in which two new mathematical models were developed that each reproduce ice sheet behavior known to have occurred in the extensive glacial epochs of the Neoproterozoic Era, during which time continental ice sheets flowed into the ocean near the equator.

### Jim Walsh Publishes and Presents

January 29, 2014

Professor of Mathematics Jim Walsh was lead author on the paper “A dynamics approach to a low order climate model,” which appeared recently in the journal *Discrete and Continuous Dynamical Systems Series B*. The paper presented the mathematical analysis of a model focused on the extensive glacial events of the Neoproterozoic Era. Walsh also gave two presentations at the 2014 Joint Mathematics Meeting, held January 15 to 18 in Baltimore. The first talk, given in the AMS Session on Fractal Geometry, Complex Dynamics, and Dynamical Systems, concerned research with Chris Rackauckas ’13 on the Jormungand climate model. The second talk was given in an MAA Session titled Undergraduate Sustainability Experiences in the Introductory Mathematics Classroom.This talk recapped Walsh’s experience incorporating climate modeling into his MATH 234 course.