Eric Michael Rains (born 23 August 1973) is an American mathematician specializing in coding theory and special functions, especially applications from and to noncommutative algebraic geometry.

Biography

Eric Rains was 14 when he began classes at Case Western Reserve University in 1987. He graduated with bachelor's degrees in computer science and physics and a master's degree in mathematics at age 17.

By means of a Churchill Scholarship he studied mathematics and physics at the University of Cambridge for the academic year 1991–1992, receiving a Certificate of Advanced Study in Mathematics. He received his PhD in 1995 from Harvard University with thesis Topics in Probability on Compact Lie Groups under the supervision of Persi Diaconis. From 1995 to 1996, Rains worked at the IDA's Center for Communications Research (CCR) in Princeton. From 1996 to 2002 he was a researcher for AT&T Labs. From 2002 to 2003 he returned to the CCR in Princeton. In 2003, Rains became a full professor at the University of California, Davis. From 2007 to 2023, Rains was a full professor at Caltech and served as the Executive Officer of the Caltech Mathematics Department from 2019 to 2022. As of Fall 2023, Rains is a professor emeritus at Caltech, per their website.

In the fall of 2006 he was a visiting professor at the University of Melbourne. He is the co-author with Gabriele Nebe and Neil J. A. Sloane of the 2006 book Self-Dual Codes and Invariant Theory.

In 2007, Rains was a plenary speaker at the Western Sectional meeting of the American Mathematical Society (AMS). In 2010 he was an invited speaker at the International Congress of Mathematicians in Hyderabad. He was elected a Fellow of the AMS in the class of 2018 for "contributions to coding theory, the theory of random matrices, the study of special functions, non-commutative geometry and number theory".

Selected publications

  • Calderbank, A. R.; Rains, E. M.; Shor, P. W.; Sloane, N. J. A. (1997). "Quantum Error Correction and Orthogonal Geometry". Physical Review Letters. 78 (3): 405–408. arXiv:. Bibcode:. doi:. S2CID .
  • Rains, E.M. (1998). . IEEE Transactions on Information Theory. 44: 134–139. doi:. S2CID .
  • Calderbank, A.R.; Rains, E.M.; Shor, P.M.; Sloane, N.J.A. (1998). (PDF). IEEE Transactions on Information Theory. 44 (4): 1369–1387. doi:. S2CID . (This article has over 1200 citations.)
  • Rains, E.M. (1999). "Nonbinary quantum codes". IEEE Transactions on Information Theory. 45 (6): 1827–1832. arXiv:. doi:. S2CID .
  • Rains, E. M. (1999). "Rigorous treatment of distillable entanglement". Physical Review A. 60 (1): 173–178. arXiv:. Bibcode:. doi:. S2CID .
  • Rains, E. M. (1999). "Bound on distillable entanglement". Physical Review A. 60 (1): 179–184. arXiv:. Bibcode:. doi:. S2CID .
  • Bennett, Charles H.; DiVincenzo, David P.; Fuchs, Christopher A.; Mor, Tal; Rains, Eric; Shor, Peter W.; Smolin, John A.; Wootters, William K. (1999). "Quantum nonlocality without entanglement". Physical Review A. 59 (2): 1070–1091. arXiv:. doi:. ISSN . S2CID .
  • Baik, Jinho; Rains, Eric M. (2000). . Journal of Statistical Physics. 100 (3/4): 523–541. doi:. S2CID .
  • Odlyzko, A. M.; Rains, E. M. (2000). . Contemporary Mathematics. 251: 439–452. doi:. ISBN 9780821811481.
  • Rains, E.M. (2001). (PDF). IEEE Transactions on Information Theory. 47 (7): 2921–2933. doi:. S2CID .
  • Rains, E. M.; Sloane, N. J. A. (1998). "Self-Dual Codes". Handbook of Coding Theory. Vol. I. North Holland. pp. 177–294. arXiv:. Bibcode:. ISBN 0444500871.
  • Rains, E. M.; Sloane, N. J. A.; Rains, Eric M.; Svore, Krysta M. (2006). "A logarithmic-depth quantum carry-lookahead adder". Quantum Information & Computation. 6 (4): 351–369. arXiv:. Bibcode:.
  • Borodin, Alexei; Rains, Eric M. (2005). "Eynard–Mehta Theorem, Schur Process, and their Pfaffian Analogs". Journal of Statistical Physics. 121 (3–4): 291–317. arXiv:. Bibcode:. doi:. S2CID .
  • Rains, Eric M. (2010). (PDF). Annals of Mathematics. 171 (1): 169–243. doi:. JSTOR .
  • Poonen, Bjorn; Rains, Eric (2012). . Journal of the American Mathematical Society. 25 (1): 245–269. arXiv:. doi:. ISSN .