The unexpected existence of aperiodic tilings, although not Berger's explicit construction of them, follows from another result proved by Berger: that the so-called domino problem is undecidable, disproving a conjecture of Hao Wang, Berger's advisor. The result is analogous to a 1962 construction used by Kahr, Moore, and Wang, to show that a more constrained version of the domino problem was undecidable.[2]
Berger's work on tiling was published as "The Undecidability of the Domino Problem" in the Memoirs of the AMS in 1966.[4] This paper is essentially a reprint of Berger's 1964 dissertation at Harvard University.[5]
In 2009, a paper by Berger and other Lincoln Laboratories researchers, "Wafer-scale 3D integration of InGaAs image sensors with Si readout circuits", won the best paper award at the IEEE International 3D System Integration Conference (3DIC).[6] In 2010, a CMOSinfrared imaging device with an analog-to-digital converter in each pixel, coinvented by Berger, was one of R&D Magazine's R&D 100 Award recipients.[7]
Referencesedit
^Darling, David J. (2004). The universal book of mathematics: from Abracadabra to Zeno's paradoxes. John Wiley and Sons. pp. 18–. ISBN978-0-471-27047-8. Retrieved 29 September 2011.
^Author biography from Raffel, J. I.; Mann, J. R.; Berger, R.; Soares, A. M.; Gilbert, S. (1989), (PDF), The Lincoln Laboratory Journal, 2 (1): 63–76, Bibcode:1989LLabJ...2...63R, archived from the original (PDF) on 2012-05-21, retrieved 2011-09-30.
^Awards and Recognition, Lincoln Laboratory Annual Report 2010, p. 50, retrieved 2011-09-30.
^MIT Lincoln Laboratory receives five R&D 100 Awards, Lincoln Laboratory, retrieved 2011-09-30.
January 01, 1970
robert, berger, mathematician, other, people, with, same, name, robert, berger, robert, berger, born, 1938, applied, mathematician, known, discovering, first, aperiodic, tiling, using, distinct, tile, shapes, contents, contributions, tiling, theory, education,. For other people with the same name see Robert Berger Robert Berger born 1938 is an applied mathematician known for discovering the first aperiodic tiling 1 using a set of 20 426 distinct tile shapes Contents 1 Contributions to tiling theory 2 Education and career 3 Publications 4 ReferencesContributions to tiling theory editThe unexpected existence of aperiodic tilings although not Berger s explicit construction of them follows from another result proved by Berger that the so called domino problem is undecidable disproving a conjecture of Hao Wang Berger s advisor The result is analogous to a 1962 construction used by Kahr Moore and Wang to show that a more constrained version of the domino problem was undecidable 2 Education and career editBerger did his undergraduate studies at Rensselaer Polytechnic Institute and studied applied physics at Harvard earning a master s degree before shifting to applied mathematics for his doctorate Along with Hao Wang Berger s other two doctoral committee members were Patrick Carl Fischer and Marvin Minsky Later he has worked in the Digital Integrated Circuits Group of the Lincoln Laboratory 3 Publications editBerger s work on tiling was published as The Undecidability of the Domino Problem in the Memoirs of the AMS in 1966 4 This paper is essentially a reprint of Berger s 1964 dissertation at Harvard University 5 In 2009 a paper by Berger and other Lincoln Laboratories researchers Wafer scale 3D integration of InGaAs image sensors with Si readout circuits won the best paper award at the IEEE International 3D System Integration Conference 3DIC 6 In 2010 a CMOS infrared imaging device with an analog to digital converter in each pixel coinvented by Berger was one of R amp D Magazine s R amp D 100 Award recipients 7 References edit Darling David J 2004 The universal book of mathematics from Abracadabra to Zeno s paradoxes John Wiley and Sons pp 18 ISBN 978 0 471 27047 8 Retrieved 29 September 2011 Buchi J R The undecidability of the domino problem Mathematical Reviews 36 49 MR 0216954 Author biography from Raffel J I Mann J R Berger R Soares A M Gilbert S 1989 A generic architecture for wafer scale neuromorphic systems PDF The Lincoln Laboratory Journal 2 1 63 76 Bibcode 1989LLabJ 2 63R archived from the original PDF on 2012 05 21 retrieved 2011 09 30 Berger Robert 1966 The Undecidability of the Domino Problem Memoirs of the American Mathematical Society 66 66 72 pp doi 10 1090 memo 0066 Robert Berger at the Mathematics Genealogy Project Awards and Recognition Lincoln Laboratory Annual Report 2010 p 50 retrieved 2011 09 30 MIT Lincoln Laboratory receives five R amp D 100 Awards Lincoln Laboratory retrieved 2011 09 30 Retrieved from https en wikipedia org w index php title Robert Berger mathematician amp oldid 1222190543, wikipedia, wiki, book, books, library,
