Rafael Herrera, Assistant Professor of Mathematics at the College of Staten Island, was named a Guggenheim Fellow in the 2002 competition.
Herrera’s research will be in the “Classification Problems in Riemannian Geometry of Manifolds with Special Structures.”
In his classic work, Euclid focused on the geometry of the (flat) plane. The study of curved surfaces like those of a sphere or a doughnut, flowered in the late 19th century, thanks to mathematicians such as the German-born J. C. F. Gauss and G. F. B. Riemann. Their revolutionary ideas and use of calculus to study the geometry of surfaces created the field of Differential Geometry and laid the mathematical foundation for the development of theories such as the theory of relativity. Their studies led to the definition and study of abstract multidimensional spaces or n-dimensional Riemannian manifolds.
Herrera, working in the realm of abstraction, studies multidimensional spaces, which under certain circumstances are related to physical models of the world. His objective during his Guggenheim research will be to achieve the classification of the positive quaternion-Kähler manifolds, which form a family of Riemannian manifolds with special structures.
Herrera earned a BSc in Mathematics from the National University of Mexico in 1993. He graduated with Honors, and was a recipient of the prestigious and competitive Gabino Barreda Medal for the highest grade average among the 130,000 undergraduate students in the University.
In 1993, Herrera received a full scholarship to attend Oxford University, UK, where he entered the PhD program in Mathematics. Herrera became a Junior Research Fellow at Worcester College, Oxford, from 1996-1998 by successfully competing against 300 other scholars in the Arts and Sciences.
Upon graduating from Oxford in 1997, Herrera became a Gibbs Instructor (an endowed position for promising young mathematicians) at Yale University in 1998-2000, teaching undergraduate as well as graduate courses on Complex manifolds and Riemannian manifolds with special holonomy.
Before joining CSI, Herrera was a Visiting Professor at the University of California at Riverside, teaching Differential and Integral Calculus of one and several variables, Linear Algebra, Differential Equations and Differential Geometry.
Concomitantly, Herrera was the Director of Upper Elementary School Mathematics Institute for teachers of Coachella Valley Unified School District, a K-12 outreach project funded by the California Department of Education through the University of California where he endeavored to raise the educational standards of current teachers.
In addition to his recent Guggenheim, Herrera is working on a joint project funded by the National Science Foundation in association with Professor Yat-Sun Poon, the Primary Researcher at the University of California at Riverside.