Eric M. Rains
{{short description|American mathematician}}
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.{{cite web|title= Eric M. Rains|website=The Division of Physics, Mathematics and Astronomy, Caltech (caltech.edu)|url=http://pma.caltech.edu/people/eric-m-rains}}
== 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.{{cite web|title=Alum who graduated at age 17 with three degrees returns to CWRU for talk|date=16 September 2013|website=The Daily, Case Western Reserve University|url=https://thedaily.case.edu/alum-who-graduated-at-age-17-with-three-degrees-returns-to-cwru-for-talk/}}
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.{{cite web|title=Eric M. Rains, Curriculum Vitae|website=caltech.edu|url=http://www.math.caltech.edu/people/cvRains.pdf}} He received his PhD in 1995 from Harvard University with thesis Topics in Probability on Compact Lie Groups under the supervision of Persi Diaconis.{{MathGenealogy|id=53493}} 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. He is the co-author with Gabriele Nebe and Neil J. A. Sloane of the 2006 book Self-Dual Codes and Invariant Theory.{{cite book|author1=Gabriele Nebe|author2=Eric M. Rains|author3=Neil J. A. Sloane|title=Self-Dual Codes and Invariant Theory|url=https://books.google.com/books?id=x2NU9hSl0m4C|date=20 May 2006|publisher=Springer Science & Business Media|isbn=978-3-540-30731-0}}
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.{{cite book|doi=10.1142/9789814324359_0157|chapter=Elliptic Analogues of the Macdonald and Koornwinder Polynomials|title=Proceedings of the International Congress of Mathematicians 2010 (ICM 2010)|volume=4|pages=2530–2554|year=2011|last1=Rains|first1=Eric M.|isbn=978-981-4324-30-4}} 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".{{cite journal|title=New Class of Fellows of the AMS|journal=Notices of the AMS|date=March 2018|volume=65|number=3|pages=346–348|url=http://ams.org/profession/ams-fellows/Fell-list-2018.pdf}}
Selected publications
- {{cite journal|doi=10.1103/PhysRevLett.78.405|title=Quantum Error Correction and Orthogonal Geometry|journal=Physical Review Letters|volume=78|issue=3|pages=405–408|year=1997|last1=Calderbank|first1=A. R.|last2=Rains|first2=E. M.|last3=Shor|first3=P. W.|last4=Sloane|first4=N. J. A.|bibcode=1997PhRvL..78..405C|arxiv=quant-ph/9605005|s2cid=15326700}}
- {{cite journal|doi=10.1109/18.651000|title=Shadow bounds for self-dual codes|journal=IEEE Transactions on Information Theory|volume=44|pages=134–139|year=1998|last1=Rains|first1=E.M.|s2cid=32909885|url=https://resolver.caltech.edu/CaltechAUTHORS:20170927-074638028}}
- {{cite journal|doi=10.1109/18.681315|title=Quantum error correction via codes over GF(4)|journal=IEEE Transactions on Information Theory|volume=44|issue=4|pages=1369–1387|year=1998|last1=Calderbank|first1=A.R.|last2=Rains|first2=E.M.|last3=Shor|first3=P.M.|last4=Sloane|first4=N.J.A.|s2cid=1215697|url=https://authors.library.caltech.edu/81821/1/00681315.pdf}} (This article has over 1200 citations.)
- {{cite journal|doi=10.1109/18.782103|title=Nonbinary quantum codes|journal=IEEE Transactions on Information Theory|volume=45|issue=6|pages=1827–1832|year=1999|last1=Rains|first1=E.M.|s2cid=1738302|arxiv=quant-ph/9703048}}
- {{cite journal|doi=10.1103/PhysRevA.60.173|title=Rigorous treatment of distillable entanglement|journal=Physical Review A|volume=60|issue=1|pages=173–178|year=1999|last1=Rains|first1=E. M.|bibcode=1999PhRvA..60..173R|arxiv=quant-ph/9809078|s2cid=16329605}}
- {{cite journal|doi=10.1103/PhysRevA.60.179|title=Bound on distillable entanglement|journal=Physical Review A|volume=60|issue=1|pages=179–184|year=1999|last1=Rains|first1=E. M.|bibcode=1999PhRvA..60..179R|arxiv=quant-ph/9809082|s2cid=14090725}}
- {{cite journal|last1=Bennett|first1=Charles H.|last2=DiVincenzo|first2=David P.|last3=Fuchs|first3=Christopher A.|last4=Mor|first4=Tal|last5=Rains|first5=Eric|last6=Shor|first6=Peter W.|last7=Smolin|first7=John A.|last8=Wootters|first8=William K.|title=Quantum nonlocality without entanglement|journal=Physical Review A|volume=59|issue=2|year=1999|pages=1070–1091|issn=1050-2947|doi=10.1103/PhysRevA.59.1070|arxiv=quant-ph/9804053|s2cid=15282650}}
- {{cite journal|doi=10.1023/A:1018615306992|year=2000|last1=Baik|first1=Jinho|title=Limiting distributions for a polynuclear growth model with external sources|journal=Journal of Statistical Physics|volume=100|issue=3/4|pages=523–541|last2=Rains|first2=Eric M.|s2cid=17786797|url=https://authors.library.caltech.edu/82254/ }}
- {{cite journal|author=Odlyzko, A. M.|author2=Rains, E. M.|title=On longest increasing subsequences in random permutations|journal=Contemporary Mathematics|volume=251|year=2000|pages=439–452|doi=10.1090/conm/251/03886|isbn=9780821811481|url=https://books.google.com/books?id=P08bCAAAQBAJ&pg=PA439}}
- {{cite journal|doi=10.1109/18.959270|title=A semidefinite program for distillable entanglement|journal=IEEE Transactions on Information Theory|volume=47|issue=7|pages=2921–2933|year=2001|last1=Rains|first1=E.M.|s2cid=6115879|url=https://authors.library.caltech.edu/81816/1/00959270.pdf}}
- {{cite encyclopedia|arxiv = math/0208001|last1 = Rains|first1 = E. M.|title = Self-Dual Codes|last2 = Sloane|first2 = N. J. A.|encyclopedia=Handbook of Coding Theory|year = 1998|pages=177-294|volume=I|publisher=North Holland|ISBN=0444500871|bibcode = 2002math......8001R}}
- {{cite journal|arxiv = quant-ph/0406142|last1 = Rains|first1 = E. M.|title = A logarithmic-depth quantum carry-lookahead adder|last2 = Sloane|first2 = N. J. A.|last3 = Rains|first3 = Eric M.|last4 = Svore|first4 = Krysta M.|author4-link= Krysta Svore |year = 2006|bibcode = 2004quant.ph..6142D|journal=Quantum Information & Computation|volume=6|issue=4|pages=351-369}}
- {{cite journal|doi=10.1007/s10955-005-7583-z|title=Eynard–Mehta Theorem, Schur Process, and their Pfaffian Analogs|journal=Journal of Statistical Physics|volume=121|issue=3–4|pages=291–317|year=2005|last1=Borodin|first1=Alexei|last2=Rains|first2=Eric M.|bibcode=2005JSP...121..291B|arxiv=math-ph/0409059|s2cid=119599225}}
- {{cite journal|jstor=27799200|title=Transformations of elliptic hypergeometric integrals|journal=Annals of Mathematics|volume=171|issue=1|pages=169–243|last1=Rains|first1=Eric M.|year=2010|doi=10.4007/annals.2010.171.169|url=https://authors.library.caltech.edu/18651/3/0309252.pdf|doi-access=free}}
- {{cite journal|last1=Poonen|first1=Bjorn|last2=Rains|first2=Eric|title=Random maximal isotropic subspaces and Selmer groups|journal=Journal of the American Mathematical Society|volume=25|issue=1|year=2012|pages=245–269|issn=0894-0347|doi=10.1090/S0894-0347-2011-00710-8|doi-access=free|arxiv=1009.0287}}
References
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Category:20th-century American mathematicians
Category:21st-century American mathematicians
Category:Case Western Reserve University alumni
Category:Alumni of the University of Cambridge
Category:Harvard University alumni
Category:Fellows of the American Mathematical Society