Simons Grant to Forward Understanding of Semilinear Equations

Professor of Mathematics Alfonso Castro has been awarded a Simons Foundation Collaboration Grant for Mathematicians to support research involving equations fundamental to every area of science.

The five-year, $35,000 grant will fund collaboration, travel and research expenses for Castro’s project, “Solvability of semilinear equations with discrete spectrum.”

“Understanding the temperature distribution in a star, for example, requires balancing heat diffusion, generation and radiation. In recent years, I have fully classified the radial solutions to this problem,” he said. “The fundamental nature of my research allows me to involve mathematics majors interested in differential equations in my research program.”

Research students he has mentored have pursued graduate study and many have gone on to academic careers.

Mississippi State University and the University of Alabama have dedicated their upcoming 9th Differential Equations & Computational Simulations Conference to Castro in celebration of his outstanding contributions to differential equations research.

Castro joined the faculty at Harvey Mudd College in 2003. His research areas include partial differential equations (including semilinear equations with discrete spectrum), variational methods, inverse-function theorems and water waves (solitons). He earned his bachelor’s and master’s degrees in mathematics from the National University of Colombia and his doctorate in mathematics from the University of Cincinnati.

His book, “Ecuaciones semilineales con espectro discreto” (Semilinear equations with discrete spectrum), will be published this fall by the National University of Colombia (NUC). Co-authored with NUC math Professor Jose Caicedo, the book will help prepare scholars interested in researching the solvability of semilinear equations with discrete spectrum. “It is the first of its nature and grew out of several monographs I have written over the last thirty years. Several publishers have shown interest in having it translated into English,” he said.

Established in 1994 by Jim and Marilyn Simons, the Simons Foundation aims to advance the frontiers of research in mathematics and the basic sciences. The goal of its Collaboration Grant for Mathematicians program is to support the “mathematical marketplace” by substantially increasing collaborative contacts in the community of mathematicians working in the United States.