Biography:Eric M. Rains
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
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 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
- 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. doi:10.1103/PhysRevLett.78.405. Bibcode: 1997PhRvL..78..405C.
- Rains, E.M. (1998). "Shadow bounds for self-dual codes". IEEE Transactions on Information Theory 44: 134–139. doi:10.1109/18.651000. https://resolver.caltech.edu/CaltechAUTHORS:20170927-074638028.
- Calderbank, A.R.; Rains, E.M.; Shor, P.M.; Sloane, N.J.A. (1998). "Quantum error correction via codes over GF(4)". IEEE Transactions on Information Theory 44 (4): 1369–1387. doi:10.1109/18.681315. https://authors.library.caltech.edu/81821/1/00681315.pdf. (This article has over 1200 citations.)
- Rains, E.M. (1999). "Nonbinary quantum codes". IEEE Transactions on Information Theory 45 (6): 1827–1832. doi:10.1109/18.782103.
- Rains, E. M. (1999). "Rigorous treatment of distillable entanglement". Physical Review A 60 (1): 173–178. doi:10.1103/PhysRevA.60.173. Bibcode: 1999PhRvA..60..173R.
- Rains, E. M. (1999). "Bound on distillable entanglement". Physical Review A 60 (1): 179–184. doi:10.1103/PhysRevA.60.179. Bibcode: 1999PhRvA..60..179R.
- 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. https://authors.library.caltech.edu/82254/.
- 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. https://books.google.com/books?id=P08bCAAAQBAJ&pg=PA439.
- Rains, E.M. (2001). "A semidefinite program for distillable entanglement". IEEE Transactions on Information Theory 47 (7): 2921–2933. doi:10.1109/18.959270. https://authors.library.caltech.edu/81816/1/00959270.pdf.
- Rains, E. M.; Sloane, N. J. A. (2002). Self-Dual Codes. Bibcode: 2002math......8001R.
- Rains, E. M.; Sloane, N. J. A.; Rains, Eric M.; Svore, Krysta M. (2004). A logarithmic-depth quantum carry-lookahead adder. Bibcode: 2004quant.ph..6142D.
- Borodin, Alexei; Rains, Eric M. (2005). "Eynard–Mehta Theorem, Schur Process, and their Pfaffian Analogs". Journal of Statistical Physics 121 (3–4): 291–317. doi:10.1007/s10955-005-7583-z. Bibcode: 2005JSP...121..291B.
- Rains, Eric M. (2010). "Transformations of elliptic hypergeometric integrals". Annals of Mathematics 171 (1): 169–243. doi:10.4007/annals.2010.171.169. https://authors.library.caltech.edu/18651/3/0309252.pdf.
- 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
- ↑ "Eric M. Rains". http://pma.caltech.edu/people/eric-m-rains.
- ↑ "Alum who graduated at age 17 with three degrees returns to CWRU for talk". 16 September 2013. https://thedaily.case.edu/alum-who-graduated-at-age-17-with-three-degrees-returns-to-cwru-for-talk/.
- ↑ 3.0 3.1 3.2 "Eric M. Rains, Curriculum Vitae". http://www.math.caltech.edu/people/cvRains.pdf.
- ↑ 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. https://books.google.com/books?id=x2NU9hSl0m4C.
- ↑ Rains, Eric M. (2011). "Elliptic Analogues of the Macdonald and Koornwinder Polynomials". Proceedings of the International Congress of Mathematicians 2010 (ICM 2010). 4. pp. 2530–2554. doi:10.1142/9789814324359_0157. ISBN 978-981-4324-30-4.
- ↑ "New Class of Fellows of the AMS". Notices of the AMS 65 (3): 346–348. March 2018. http://ams.org/profession/ams-fellows/Fell-list-2018.pdf.
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