Quick Facts
Biography
Catherine A. Roberts (born Feb.5, 1965 in Boston, Massachusetts) is an American applied mathematician, the Executive Director of the American Mathematical Society, and a professor of mathematics at the College of the Holy Cross.
Education
Roberts graduated, magna cum laude, from Bowdoin College in 1987 with an A.B. in Mathematics & Art History and a teacher certification in math. She graduated from Northwestern University in 1992 with a Ph.D in Applied Mathematics & Engineering Sciences.
Professional career
Roberts was an assistant professor of mathematics at the University of Rhode Island from 1992-1995. She then was appointed an assistant professor at Northern Arizona University from 1995-1998 and from 1998-2001 she worked as an associate professor at that same University. Roberts was appointed an associate professor at the College of the Holy Cross from 2001-2013 and a full professor from 2013 to the present time, also at the College of the Holy Cross. From 2004-2016 she served as the Editor-in-Chief of the Natural Resource Modeling journal. Roberts is the Executive Director of the American Mathematical Society, having been appointed in 2016.
Research
Roberts' research focused on the analysis of nonlinear Volterra integral equations that arise in studies involving diffusive media as well as the mathematical modeling of interactions between humans and their natural environment. The objective of these studies is to investigate the phenomena of explosion, quenching, and anomalous diffusion within a diffusive medium in the context of nonlinear Volterra integral equations. These problems are characterized by spatially localized nonlinearities, distinguishing them from the work of earlier researchers. Such nonlinearities are motivated, for example, by applications where the event occurs within a very confined area (e.g., flooding events in porous media, internal electrode energy stimulation on a heated surface).
These phenomena are of wide importance in applications. Studies of explosion have been conducted on theoretical models that are originally presented as nonlinear partial differential equations. Unlike previous studies, which have required a smoothness property for spatially dependent nonlinearities, this research replaces such requirements by strongly localized behavior. In this case, conversion of the theoretical models from partial differential equations to integral equations represents a very effective format for the analysis. This reformulation permits a more direct and efficient inquiry into the challenging scenario of spatially localized nonlinear behavior.
Her work with interactions between humans and their natural environment sought to characterize complex human-environment interactions in a recreational setting. Specifically, the research studied problems related to human decision-making and how it influences the routing of recreational white water rafting traffic on rivers. This research developed traffic models that simulate the responses of humans to an ever-changing natural environment. Roberts developed the Grand Canyon River Trip Simulator. This model uses artificial intelligence and statistical techniques to capture the unique nature of this interaction.
Service
- Association for Women in Mathematics-Executive Committee, Member-at-Large (2002-2006)
- Regional Environmental Council of Central Massachusetts-Board of Directors (2004-2007)
- Resource Modeling Association-Board of Directors (2002-2016)
- River Management Society-Vice-President, Northeast Chapter (2006-2008)
- Rocky Mountain Math Consortium-Board of Directors (1998-2001)
- Society for Industrial and Applied Mathematics-Scientific Advisory Board, SIAM Activity Group on Mathematics of Planet Earth (2014-2017)
Personal life
Roberts was born in 1965 in Boston, Massachusetts. Her family subsequently moved to Cape Cod, Massachusetts where her father opened a law practice and her mother became an important civic leader and social advocate in the community. Roberts enjoyed a happy childhood growing up with her 3 sisters. She loved her childhood of swimming in the ocean and the ponds of Cape Cod. Roberts met her spouse while living in Chatham and attending high school. Roberts' spouse is a chemistry professor at Worcester Polytechnic Institute. She and her husband have two sons both currently attending colleges.
Publications
Publications – Volterra Integral Equations
| 1. | Volterra Equations that Model Explosion in a Diffusive Medium, C. A. Roberts, D. G. Lassiegne and W. E. Olmstead, J. Integral Eqns. Appl., Vol. 5, No. 4, 1993, 531-546. |
| 2. | Explosion in a Diffusive Strip Due to a Concentrated Nonlinear Source, W. E. Olmstead and C. A. Roberts, Methods Appl. Analysis, Vol. 1, No. 4, 1994, 434-445. |
| 3. | Quenching for the Heat Equation with a Non-local Nonlinearity, W. E. Olmstead and C. A. Roberts, in Nonlinear Problems in Applied Math, eds. Angell et. al., SIAM, 1995, 199-205. |
| 4. | Growth Rates of Blow-up Solutions for Nonlinear Volterra Equations, C. A. Roberts and W. E. Olmstead, Quart. Appl. Mathematics, Vol. 54, No.1, 1996, 153-160. |
| 5. | Coupled Volterra Equations with Blow-up Solutions, W. E. Olmstead, C. A. Roberts and K. Deng, J. Integral Eqns. Applications, Vol. 7, No. 4, 1995, 499-516. |
| 6. | Explosion in a Diffusive Strip Due to a Source with Local and Non-local Features, W. E. Olmstead and C. A. Roberts, Methods Appl. Analysis, Vol. 3, No. 3, 1996, 345-357. |
| 7. | The one-dimensional Heat Equation with a Non-local Initial Condition, W. E. Olmstead and C. A. Roberts, Applied Math Letter., Vol. 10, No.3, 1997, 89-94. |
| 8. | Characterizing the Blow-up Solutions for Nonlinear Volterra Integral Equations, C. A. Roberts, Nonlinear Analysis, Proc. of Second World Congress of Nonlinear Analysts (WCNA96), Vol. 30, No. 2, 1997, 923-933. |
| 9. | Quenching for a Diffusive Equation with a Concentrated Singularity, K. Deng and C. A. Roberts, Differential and Integral Equations, Vol. 10, No. 2, 1997, 369-379. |
| 10. | Analysis of Explosion for Nonlinear Volterra Equations, C. A. Roberts, J. Comput. Appl. Math., Vol. 97, 1998, 153-166. |
| 11. | Local and Non-local Boundary Quenching, C. A. Roberts and W. E. Olmstead, Math. Meth. Appl. Sci., Vol. 22, 1999, 1465-1484. |
| 12. | A Method to Determine Growth Rates of Nonlinear Volterra Equations, C. A. Roberts, in Volterra Equations & Applications, eds. Corduneanu/Sandberg, Gordon & Breach, UK, 2000, 427-431. |
| 13. | A Critical Speed for Quenching, W. E. Olmstead and C. A. Roberts, in Advances in Quenching, Dynam. Contin. Discrete Impulsive Systems, Series A: Math Anal, 8, 2001, 77-89. |
| 14. | A Quenching Problem for the Heat Equation, C. M. Kirk and C. A. Roberts, J. Int. Eqns. Appl., Vol. 14, No. 1, 2002, 1-20. |
| 15. | A Review of Quenching Results in the Context of Nonlinear Volterra Equations, C. M. Kirk and C. A. Roberts, Dynamics of Continuous, Discrete and Impulsive Systems, Series A: Math Anal, Vol. 10, 2003, 343-356. |
| 16. | Blow-up Solutions to a System of Nonlinear Volterra Equations, W. Mydlarczyk, W. Okrasiński and C. A. Roberts, J. Math Anal. Appl., Vol. 301, 2005, 208-218. |
| 17. | Recent Results on Blow-up and Quenching for Nonlinear Volterra Equations, C. A. Roberts, J. Comput. Appl. Math., Vol. 205, No. 2, 15 Aug 2007, 736-743. |
| 18. | Thermal Blow-up in a Subdiffusive Medium, W. E. Olmstead and Catherine A. Roberts, SIAM Journal on Applied Mathematics, Vol. 69, No. 2, 2009, 514-523. |
| 19. | Blow-up in a Subdiffusive Medium of Infinite Extent, Catherine A. Roberts and W. E. Olmstead, Fract. Calc. Appl. Anal. Vol. 12, No. 2, 2009, 179-194. |
| 20. | Dimensional Influence on Blow-Up in a Superdiffusive Medium, W. E. Olmstead and Catherine A. Roberts, SIAM Journal on Applied Mathematics, Vol. 70, No. 5, 2010, 1678-1690. |
| 21. | Blow-up in a Subdiffusive Medium with Advection, W. E. Olmstead, C. M. Kirk and C. A. Roberts, Discrete and Continuous Dynamical Systems, Vol. 28, No. 4, 2010, 1655-1667. |
| 22. | A System of Nonlinear Volterra Equations with Blow-up Solutions, C. M. Kirk, W. E. Olmstead and C. A. Roberts, J. Int. Eqns. Appl., Vol. 25, No. 3, 2013, 377-393. |
Publications – Environmental Modeling
| 1. | Evaluation of river beach carrying capacity information utilized by the Grand Canyon River Trip Simulator: Analysis and recommendations for future study, G. O’Brien and C. A. Roberts, Grand Canyon Science Center (CA8210-99-002), Final Report. May 1, 1999, 17 pp. |
| 2. | Intelligent Agent Modeling for Simulating and Evaluating River Trip Scheduling Scenarios for the Grand Canyon National Park, H. R. Gimblett, C. A. Roberts, T. Daniel, M. Mitner, S. Cherry, D. Kilbourne, M. Ratliff, D. Stallman, R. Bogle, J. Bieri in Integrating GIS and Agent based modeling techniques for Understanding Social and Ecological Processes, ed. H. R. Gimblett, Oxford Press, 2000, 245-275. |
| 3. | Computer Simulation for Rafting Traffic on the Colorado River, C. A. Roberts and H. R. Gimblett, Proc. 5th Conf. Research on Colorado Plateau USGS, 2001, 19-30. |
| 4. | Impacts of Low Flow Rates on Recreational Rafting Traffic on the Colorado River in Grand Canyon National Park, C. A. Roberts and J. A. Bieri, Bureau of Reclamation, Grand Canyon Monitoring and Research Center, Final Report. May 15, 2001, 18 pp. |
| 5. | Modeling Complex Human-Environment Interactions: The Grand Canyon River Trip Simulator, C. A. Roberts, D. Stallman and J. A. Bieri, J. Ecological Modeling, Vol. 153, Issue 2, 2002,181-196. |
| 6. | Environmental Mathematical Modeling: The Grand Canyon. Math Horizons, Sept 2007, 10 - 13. |
| 7. | Impacts of Low Flow Rates on Recreational Rafting Traffic on the Colorado River in Grand Canyon National Park, Roberts, C. and Bieri, J. published in Synopsis of Studies Completed in Association with the Low Steady Summer Flow Experimental Release from Glen Canyon Dan in WY2000, edited by B. E. Ralston and G. L. Waring, U.S. Department of Interior and U.S. Geological Survey, July 24, 2008, 58-61. |
| 8. | River Support Flows in Two Directions, C. A. Roberts, power-point presentation & speaker notes in Proceedings of the 2008 River Management Society Symposium, 2008. (http://www.river-management.org/pdfs/Symposiums/2008sympo/Catherine%20Roberts/Roberts2008.pdf) |
| 9. | Author’s Commentary for MCM Problem B: Camping Along the Big Long River, C. A. Roberts, The UMAP Journal: Undergraduate Mathematics and Its Applications, V. 33, No. 3, 253 -257, 2012. |
Publications – Mathematics Education Research
| 1. | How to Get Started with Group Activities, C. A. Roberts, Creative Math Teaching, Vol. 1, No. 1, 1994. |
| 2. | Group Testing, C. A. Roberts, in Assessment Practices in Undergraduate Mathematics, eds. B. Gold, S. Keith and W. Marion, MAA Notes, Mathematical Association of America, Washington DC, 1999, 137-139. |
| 3. | A Liberal Arts Course Linking Art, Art History, Mathematics and Chemistry, C. Kelley, A. Jordan and C. A. Roberts, J. Clg. Sci. Teaching, Vol. 31, 2001, 162-166. |
| 4. | Perspectives on Modeling Applications in a Service-Learning Framework, C. A. Roberts, in Mathematics in Service to the Community: Concepts and Models for Service-Learning in the Mathematical Sciences, edited by Charles R. Hadlock, MAA Notes #66, Mathematical Association of America, Washington DC, 2005. |