Eric M. Rains

Eric Michael Rains (born August 23, 1973) is an American mathematician and professor emeritus of mathematics at the California Institute of Technology. His research includes special functions, especially applications from and to noncommutative algebraic geometry, as well as earlier work in random matrix theory, coding theory, lattices, and quantum information theory.

Education and career

Rains began classes at Case Western Reserve University in 1987, when he was 14 years old. He graduated from Case Western Reserve at age 17 with bachelor's degrees in computer science and physics and a master's degree in mathematics. His first peer-reviewed journal article, written with Case Western Reserve physicists Robert Brown and Cyrus Taylor, appeared in 1991.

From 1995 to 1996, Rains worked at the Institute for Defense Analyses' Center for Communications Research in Princeton. He was a researcher at AT&T Labs from 1996 to 2002, returned to the Center for Communications Research from 2002 to 2003, and became a professor at the University of California, Davis in 2003. He joined Caltech as professor in 2007, served as executive officer of the Caltech mathematics department from 2019 to 2022, and became professor emeritus in 2023. With Bjorn Poonen, he developed a model for the distribution of p-Selmer groups of elliptic curves, later generalized by other researchers.

Awards and honors

Churchill Scholarship, 1991-1992 Fellow of the American Mathematical Society, class of 2018, for contributions to coding theory, random matrices, special functions, noncommutative geometry, and number theory

Selected publications