Eric M. Rains

Eric Michael Rains (born 23 August 1973) is an American mathematician specializing in coding theory and special functions.[1]

Biography

Eric Rains was 14 when he began classes in 1987. He left Case Western Reserve University with bachelor's degrees in computer science and physics and a master's degree in mathematics—at age 17.[2]

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.[3] He received in 1995 his Ph.D. from Harvard University with thesis Topics in Probability on Compact Lie Groups under the supervision of Persi Diaconis.[4] Rains worked from 1995 to 1996 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 worked at the CCR in Princeton. Rains was from 2003 to 2007 a full professor at the University of California, Davis and is since 2007 a full professor at Caltech. In the fall of 2006 he was a visiting professor at the University of Melbourne.[3] He is the co-author with Gabriele Nebe and Neil J. A. Sloane of the 2006 book Self-Dual Codes and Invariant Theory.[5]

In 2007, Rains was a plenary speaker at the Western Sectional meeting of the American Mathematical Society (AMS).[3] In 2010 he was an invited speaker at the International Congress of Mathematicians in Hyderabad.[6] 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."[7]

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:quant-ph/9605005. Bibcode:1997PhRvL..78..405C. doi:10.1103/PhysRevLett.78.405.
  • Rains, E.M. (1998). "Shadow bounds for self-dual codes". IEEE Transactions on Information Theory. 44: 134–139. doi:10.1109/18.651000. S2CID 32909885.
  • Calderbank, A.R.; Rains, E.M.; Shor, P.M.; Sloane, N.J.A. (1998). "Quantum error correction via codes over GF(4)" (PDF). IEEE Transactions on Information Theory. 44 (4): 1369–1387. doi:10.1109/18.681315. (This article has over 1200 citations.)
  • Rains, E.M. (1999). "Nonbinary quantum codes". IEEE Transactions on Information Theory. 45 (6): 1827–1832. arXiv:quant-ph/9703048. doi:10.1109/18.782103. S2CID 1738302.
  • Rains, E. M. (1999). "Rigorous treatment of distillable entanglement". Physical Review A. 60 (1): 173–178. arXiv:quant-ph/9809078. Bibcode:1999PhRvA..60..173R. doi:10.1103/PhysRevA.60.173.
  • Rains, E. M. (1999). "Bound on distillable entanglement". Physical Review A. 60 (1): 179–184. arXiv:quant-ph/9809082. Bibcode:1999PhRvA..60..179R. doi:10.1103/PhysRevA.60.179.
  • 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. doi:10.1103/PhysRevA.59.1070. ISSN 1050-2947.
  • Baik, Jinho; Rains, Eric M. (2000). "Limiting distributions for a polynuclear growth model with external sources". Journal of Statistical Physics. 100 (3/4): 523–541. doi:10.1023/A:1018615306992.
  • Odlyzko, A. M.; Rains, E. M. (2000). "On longest increasing subsequences in random permutations". Contemporary Mathematics. 251: 439–452. doi:10.1090/conm/251/03886. ISBN 9780821811481.
  • Rains, E.M. (2001). "A semidefinite program for distillable entanglement" (PDF). IEEE Transactions on Information Theory. 47 (7): 2921–2933. doi:10.1109/18.959270.
  • Rains, E. M.; Sloane, N. J. A. (2002). "Self-Dual Codes". arXiv:math/0208001. Bibcode:2002math......8001R. Cite journal requires |journal= (help)
  • Rains, E. M.; Sloane, N. J. A.; Rains, Eric M.; Svore, Krysta M. (2004). "A logarithmic-depth quantum carry-lookahead adder". arXiv:quant-ph/0406142. Bibcode:2004quant.ph..6142D. Cite journal requires |journal= (help)
  • 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:math-ph/0409059. Bibcode:2005JSP...121..291B. doi:10.1007/s10955-005-7583-z.
  • Rains, Eric M. (2010). "Transformations of elliptic hypergeometric integrals" (PDF). Annals of Mathematics. 171 (1): 169–243. doi:10.4007/annals.2010.171.169. JSTOR 27799200.
  • Poonen, Bjorn; Rains, Eric (2012). "Random maximal isotropic subspaces and Selmer groups". Journal of the American Mathematical Society. 25 (1): 245–269. doi:10.1090/S0894-0347-2011-00710-8. ISSN 0894-0347.

References
  1. "Eric M. Rains". The Division of Physics, Mathematics and Astronomy, Caltech (caltech.edu).
  2. "Alum who graduated at age 17 with three degrees returns to CWRU for talk". The Daily, Case Western Reserve University. 16 September 2013.
  3. "Eric M. Rains, Curriculum Vitae" (PDF). caltech.edu.
  4. Eric M. Rains at the Mathematics Genealogy Project
  5. Gabriele Nebe; Eric M. Rains; Neil J. A. Sloane (20 May 2006). Self-Dual Codes and Invariant Theory. Springer Science & Business Media. ISBN 978-3-540-30731-0.
  6. Rains, Eric M. (2011). "Elliptic Analogues of the Macdonald and Koornwinder Polynomials". Proceedings of the International Congress of Mathematicians 2010 (ICM 2010). vol. 4. pp. 2530–2554. doi:10.1142/9789814324359_0157. ISBN 978-981-4324-30-4.
  7. "New Class of Fellows of the AMS" (PDF). Notices of the AMS. 65 (3): 346–348. March 2018.
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