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.[1]
Biography
editEric 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 his PhD in 1995 from Harvard University with thesis Topics in Probability on Compact Lie Groups under the supervision of Persi Diaconis.[4] 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 2007-2023, 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.[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
edit- 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. S2CID 15326700.
- 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. S2CID 1215697. (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. S2CID 16329605.
- 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. S2CID 14090725.
- 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:quant-ph/9804053. doi:10.1103/PhysRevA.59.1070. ISSN 1050-2947. S2CID 15282650.
- 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. S2CID 17786797.
- 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. S2CID 6115879.
- Rains, E. M.; Sloane, N. J. A. (2002). "Self-Dual Codes". arXiv:math/0208001. Bibcode:2002math......8001R.
{{cite journal}}: 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}}: 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. S2CID 119599225.
- 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. arXiv:1009.0287. doi:10.1090/S0894-0347-2011-00710-8. ISSN 0894-0347.
References
edit- ^ "Eric M. Rains". The Division of Physics, Mathematics and Astronomy, Caltech (caltech.edu).
- ^ "Alum who graduated at age 17 with three degrees returns to CWRU for talk". The Daily, Case Western Reserve University. 16 September 2013.
- ^ a b c "Eric M. Rains, Curriculum Vitae" (PDF). caltech.edu.
- ^ Eric M. Rains at the Mathematics Genealogy Project
- ^ 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.
- ^ 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.
- ^ "New Class of Fellows of the AMS" (PDF). Notices of the AMS. 65 (3): 346–348. March 2018.