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Peter J. Olver

August 29, 2023

Peter John Olver (11 January 1952, Twickenham) is a British-American mathematician working in differential geometry.[1]

Peter John Olver
BornJanuary 11, 1952 (1952-01-11) (age 71)
Middlesex, England
NationalityAmerican (1967)
Alma materBrown University
Harvard University
Known forSymmetry groups of partial differential equations
Scientific career
FieldsMathematics
InstitutionsUniversity of Maryland
University of Minnesota
ThesisSymmetry Groups of Partial Differential Equations (1976)
Doctoral advisorGarrett Birkhoff
Doctoral studentsRui Loja Fernandes

Education and career Edit

After moving to the USA in 1961, Olver obtained a bachelor's degree in Applied Mathematics at Brown University in 1973 and a PhD in Mathematics at Harvard University in 1976. His PhD thesis was entitled "Symmetry Groups of Partial Differential Equations" and has been written under the supervision of Garrett Birkhoff.[2]

He worked as a L.E. Dickson Instructor in Mathematics at University of Chicago (1976-1978) and as a research fellow at University of Oxford (1978-1980). He then moved to University of Minnesota as assistant professor, and he became full professor in the same university in 1985. Between 1992 and 1993 he was professor at University of Maryland.[3]

Olver was member of the board of directors of Foundations of Computational Mathematics from 2002 to 2014.[4][5][6] He was elected fellow of the American Mathematical Society in 2013[7] and of the Society for Industrial and Applied Mathematics in 2014, for "developing new geometric methods for differential equations leading to applications in fluid mechanics, elasticity, quantum mechanics, and image processing."[8] Olver is also member of International Society for the Interaction of Mechanics and Mathematics[9] and an elected fellow of the Institute of Physics.[3]

Research Edit

Olver's primary research fields are differential geometry and mathematical physics. His main interests involve the application of Lie groups and symmetries to the geometry of differential equations,[10][11][12] as well as well the theories of moving frames and Cartan's equivalence method,[13][14] differential invariants[15] and pseudogroups.[16][17]

He has also contributed to various topics in applied mathematics, including image processing and computer vision,[18][19][20] wave and fluid mechanics,[21][22] and elasticity.[23][24]

He has written five books and over 150 research papers in peer-reviewed journals.[25][26] In 2003, Olver was one of the top 234 most cited mathematicians in the world.[1][27] He has supervised 23 PhD students.[2][3]

Books Edit

  • Olver, P. J. (1986), Applications of Lie Groups to Differential Equations, Graduate Texts in Mathematics, vol. 107, Springer, doi:10.1007/978-1-4684-0274-2, ISBN 0387940073
  • Olver, Peter J.; Sattinger, David H., eds. (1990). Solitons in Physics, Mathematics, and Nonlinear Optics. New York, NY: Springer New York. ISBN 978-1-4613-9033-6. OCLC 852788413.
  • Olver, P. J. (1995), Equivalence, Invariants and Symmetry, Cambridge University Press, doi:10.1017/CBO9780511609565, ISBN 0521101042
  • Olver, P. J. (1999), Classical Invariant Theory, Cambridge University Press, doi:10.1017/CBO9780511623660, ISBN 0521558212
  • Olver, Peter J.; Tannenbaum, Allen, eds. (2003). Mathematical methods in computer vision. New York: Springer. ISBN 0-387-00497-1. OCLC 51553365.
  • Olver, P. J. (2014), Introduction to Partial Differential Equations, Undergraduate Texts in Mathematics, Springer, doi:10.1007/978-3-319-02099-0, ISBN 978-3319020983, S2CID 220617008
  • Olver, P. J.; Shakiban, C. (2018), Applied Linear Algebra, Springer, doi:10.1007/978-3-319-91041-3, ISBN 978-0131473829

References Edit

  1. ^ a b "Peter Olver | AMAAZE". amaaze.umn.edu. Retrieved 2021-11-28.
  2. ^ a b Peter Olver at the Mathematics Genealogy Project
  3. ^ a b c Peter J. Olver. "Curriculum Vitae" (PDF). Retrieved 19 June 2017.
  4. ^ "FoCM • Foundations of Computational Mathematics • Governance". focm-society.org. Retrieved 2021-11-28.
  5. ^ "FoCM • Foundations of Computational Mathematics • Governance". focm-society.org. Retrieved 2021-11-28.
  6. ^ "FoCM • Foundations of Computational Mathematics • Governance". focm-society.org. Retrieved 2021-11-28.
  7. ^ AMS. "List of Fellows of the American Mathematical Society". Retrieved 19 June 2017.
  8. ^ "SIAM > Prizes & Recognition > Fellows Program > All SIAM Fellows > Class of 2014". www.siam.org. Retrieved 2021-11-28.
  9. ^ "ISIMM Home Page". isimm.unipg.it. Retrieved 2021-11-28.
  10. ^ Olver, Peter J. (1977-06-01). "Evolution equations possessing infinitely many symmetries". Journal of Mathematical Physics. 18 (6): 1212–1215. Bibcode:1977JMP....18.1212O. doi:10.1063/1.523393. ISSN 0022-2488.
  11. ^ Olver, Peter J.; Rosenau, Philip (1986-02-10). "The construction of special solutions to partial differential equations". Physics Letters A. 114 (3): 107–112. Bibcode:1986PhLA..114..107O. doi:10.1016/0375-9601(86)90534-7. ISSN 0375-9601.
  12. ^ Olver, Peter J.; Rosenau, Philip (1987-04-01). "Group-Invariant Solutions of Differential Equations". SIAM Journal on Applied Mathematics. 47 (2): 263–278. doi:10.1137/0147018. ISSN 0036-1399.
  13. ^ Fels, Mark; Olver, Peter J. (1998-04-01). "Moving Coframes: I. A Practical Algorithm". Acta Applicandae Mathematicae. 51 (2): 161–213. doi:10.1023/A:1005878210297. ISSN 1572-9036. S2CID 6681218.
  14. ^ Fels, Mark; Olver, Peter J. (1999-01-01). "Moving Coframes: II. Regularization and Theoretical Foundations". Acta Applicandae Mathematicae. 55 (2): 127–208. doi:10.1023/A:1006195823000. ISSN 1572-9036. S2CID 826629.
  15. ^ Olver, Peter J. (2007-09-01). "Generating differential invariants". Journal of Mathematical Analysis and Applications. Special issue dedicated to William Ames. 333 (1): 450–471. Bibcode:2007JMAA..333..450O. doi:10.1016/j.jmaa.2006.12.029. ISSN 0022-247X.
  16. ^ Olver, Peter J.; Pohjanpelto, Juha; Valiquette, Francis (2009-07-23). "On the Structure of Lie Pseudo-Groups". SIGMA. Symmetry, Integrability and Geometry: Methods and Applications. 5: 077. arXiv:0907.4086. Bibcode:2009SIGMA...5..077O. doi:10.3842/SIGMA.2009.077. S2CID 1861888.
  17. ^ Olver, Peter J.; Pohjanpelto, Juha (November 2005). "Maurer–Cartan forms and the structure of Lie pseudo-groups". Selecta Mathematica. 11 (1): 99–126. doi:10.1007/s00029-005-0008-7. ISSN 1022-1824. S2CID 14712181.
  18. ^ Kichenassamy, S.; Kumar, A.; Olver, P.; Tannenbaum, A.; Yezzi, A. (1995). "Gradient flows and geometric active contour models". Proceedings of IEEE International Conference on Computer Vision. Cambridge, MA, USA: IEEE Comput. Soc. Press. pp. 810–815. doi:10.1109/ICCV.1995.466855. ISBN 978-0-8186-7042-8. S2CID 10355426.
  19. ^ Kichenassamy, Satyanad; Kumar, Arun; Olver, Peter; Tannenbaum, Allen; Yezzi, Anthony (1996-09-01). "Conformal curvature flows: From phase transitions to active vision". Archive for Rational Mechanics and Analysis. 134 (3): 275–301. Bibcode:1996ArRMA.134..275K. doi:10.1007/BF00379537. ISSN 1432-0673. S2CID 116487549.
  20. ^ Yezzi, A.; Kichenassamy, S.; Kumar, A.; Olver, P.; Tannenbaum, A. (April 1997). "A geometric snake model for segmentation of medical imagery". IEEE Transactions on Medical Imaging. 16 (2): 199–209. doi:10.1109/42.563665. hdl:1853/32559. PMID 9101329. S2CID 6492817.
  21. ^ Olver, Peter J. (January 1979). "Euler operators and conservation laws of the BBM equation". Mathematical Proceedings of the Cambridge Philosophical Society. 85 (1): 143–160. Bibcode:1979MPCPS..85..143O. doi:10.1017/S0305004100055572. ISSN 1469-8064. S2CID 10840014.
  22. ^ Li, Yi A; Olver, Peter J (2000-03-20). "Well-posedness and Blow-up Solutions for an Integrable Nonlinearly Dispersive Model Wave Equation". Journal of Differential Equations. 162 (1): 27–63. Bibcode:2000JDE...162...27L. doi:10.1006/jdeq.1999.3683. ISSN 0022-0396.
  23. ^ Ball, J. M; Currie, J. C; Olver, P. J (1981-04-01). "Null Lagrangians, weak continuity, and variational problems of arbitrary order". Journal of Functional Analysis. 41 (2): 135–174. doi:10.1016/0022-1236(81)90085-9. ISSN 0022-1236.
  24. ^ Olver, Peter J. (1984-06-01). "Conservation laws in elasticity". Archive for Rational Mechanics and Analysis. 85 (2): 111–129. Bibcode:1984ArRMA..85..111O. doi:10.1007/BF00281447. ISSN 1432-0673. S2CID 18746394.
  25. ^ zbMATH. "Olver, Peter J." Retrieved 19 June 2017.
  26. ^ "Peter Olver". scholar.google.com. Retrieved 2021-11-28.
  27. ^ University of Minnesota. "How do we rank?". Retrieved 10 August 2018.

August 29, 2023
peter, olver, peter, john, olver, january, 1952, twickenham, british, american, mathematician, working, differential, geometry, peter, john, olverbornjanuary, 1952, 1952, middlesex, englandnationalityamerican, 1967, alma, materbrown, universityharvard, univers. Peter John Olver 11 January 1952 Twickenham is a British American mathematician working in differential geometry 1 Peter John OlverBornJanuary 11 1952 1952 01 11 age 71 Middlesex EnglandNationalityAmerican 1967 Alma materBrown UniversityHarvard UniversityKnown forSymmetry groups of partial differential equationsScientific careerFieldsMathematicsInstitutionsUniversity of MarylandUniversity of MinnesotaThesisSymmetry Groups of Partial Differential Equations 1976 Doctoral advisorGarrett BirkhoffDoctoral studentsRui Loja Fernandes Contents 1 Education and career 2 Research 3 Books 4 ReferencesEducation and career EditAfter moving to the USA in 1961 Olver obtained a bachelor s degree in Applied Mathematics at Brown University in 1973 and a PhD in Mathematics at Harvard University in 1976 His PhD thesis was entitled Symmetry Groups of Partial Differential Equations and has been written under the supervision of Garrett Birkhoff 2 He worked as a L E Dickson Instructor in Mathematics at University of Chicago 1976 1978 and as a research fellow at University of Oxford 1978 1980 He then moved to University of Minnesota as assistant professor and he became full professor in the same university in 1985 Between 1992 and 1993 he was professor at University of Maryland 3 Olver was member of the board of directors of Foundations of Computational Mathematics from 2002 to 2014 4 5 6 He was elected fellow of the American Mathematical Society in 2013 7 and of the Society for Industrial and Applied Mathematics in 2014 for developing new geometric methods for differential equations leading to applications in fluid mechanics elasticity quantum mechanics and image processing 8 Olver is also member of International Society for the Interaction of Mechanics and Mathematics 9 and an elected fellow of the Institute of Physics 3 Research EditOlver s primary research fields are differential geometry and mathematical physics His main interests involve the application of Lie groups and symmetries to the geometry of differential equations 10 11 12 as well as well the theories of moving frames and Cartan s equivalence method 13 14 differential invariants 15 and pseudogroups 16 17 He has also contributed to various topics in applied mathematics including image processing and computer vision 18 19 20 wave and fluid mechanics 21 22 and elasticity 23 24 He has written five books and over 150 research papers in peer reviewed journals 25 26 In 2003 Olver was one of the top 234 most cited mathematicians in the world 1 27 He has supervised 23 PhD students 2 3 Books EditOlver P J 1986 Applications of Lie Groups to Differential Equations Graduate Texts in Mathematics vol 107 Springer doi 10 1007 978 1 4684 0274 2 ISBN 0387940073 Olver Peter J Sattinger David H eds 1990 Solitons in Physics Mathematics and Nonlinear Optics New York NY Springer New York ISBN 978 1 4613 9033 6 OCLC 852788413 Olver P J 1995 Equivalence Invariants and Symmetry Cambridge University Press doi 10 1017 CBO9780511609565 ISBN 0521101042 Olver P J 1999 Classical Invariant Theory Cambridge University Press doi 10 1017 CBO9780511623660 ISBN 0521558212 Olver Peter J Tannenbaum Allen eds 2003 Mathematical methods in computer vision New York Springer ISBN 0 387 00497 1 OCLC 51553365 Olver P J 2014 Introduction to Partial Differential Equations Undergraduate Texts in Mathematics Springer doi 10 1007 978 3 319 02099 0 ISBN 978 3319020983 S2CID 220617008 Olver P J Shakiban C 2018 Applied Linear Algebra Springer doi 10 1007 978 3 319 91041 3 ISBN 978 0131473829References Edit a b Peter Olver AMAAZE amaaze umn edu Retrieved 2021 11 28 a b Peter Olver at the Mathematics Genealogy Project a b c Peter J Olver Curriculum Vitae PDF Retrieved 19 June 2017 FoCM Foundations of Computational Mathematics Governance focm society org Retrieved 2021 11 28 FoCM Foundations of Computational Mathematics Governance focm society org Retrieved 2021 11 28 FoCM Foundations of Computational Mathematics Governance focm society org Retrieved 2021 11 28 AMS List of Fellows of the American Mathematical Society Retrieved 19 June 2017 SIAM gt Prizes amp Recognition gt Fellows Program gt All SIAM Fellows gt Class of 2014 www siam org Retrieved 2021 11 28 ISIMM Home Page isimm unipg it Retrieved 2021 11 28 Olver Peter J 1977 06 01 Evolution equations possessing infinitely many symmetries Journal of Mathematical Physics 18 6 1212 1215 Bibcode 1977JMP 18 1212O doi 10 1063 1 523393 ISSN 0022 2488 Olver Peter J Rosenau Philip 1986 02 10 The construction of special solutions to partial differential equations Physics Letters A 114 3 107 112 Bibcode 1986PhLA 114 107O doi 10 1016 0375 9601 86 90534 7 ISSN 0375 9601 Olver Peter J Rosenau Philip 1987 04 01 Group Invariant Solutions of Differential Equations SIAM Journal on Applied Mathematics 47 2 263 278 doi 10 1137 0147018 ISSN 0036 1399 Fels Mark Olver Peter J 1998 04 01 Moving Coframes I A Practical Algorithm Acta Applicandae Mathematicae 51 2 161 213 doi 10 1023 A 1005878210297 ISSN 1572 9036 S2CID 6681218 Fels Mark Olver Peter J 1999 01 01 Moving Coframes II Regularization and Theoretical Foundations Acta Applicandae Mathematicae 55 2 127 208 doi 10 1023 A 1006195823000 ISSN 1572 9036 S2CID 826629 Olver Peter J 2007 09 01 Generating differential invariants Journal of Mathematical Analysis and Applications Special issue dedicated to William Ames 333 1 450 471 Bibcode 2007JMAA 333 450O doi 10 1016 j jmaa 2006 12 029 ISSN 0022 247X Olver Peter J Pohjanpelto Juha Valiquette Francis 2009 07 23 On the Structure of Lie Pseudo Groups SIGMA Symmetry Integrability and Geometry Methods and Applications 5 077 arXiv 0907 4086 Bibcode 2009SIGMA 5 077O doi 10 3842 SIGMA 2009 077 S2CID 1861888 Olver Peter J Pohjanpelto Juha November 2005 Maurer Cartan forms and the structure of Lie pseudo groups Selecta Mathematica 11 1 99 126 doi 10 1007 s00029 005 0008 7 ISSN 1022 1824 S2CID 14712181 Kichenassamy S Kumar A Olver P Tannenbaum A Yezzi A 1995 Gradient flows and geometric active contour models Proceedings of IEEE International Conference on Computer Vision Cambridge MA USA IEEE Comput Soc Press pp 810 815 doi 10 1109 ICCV 1995 466855 ISBN 978 0 8186 7042 8 S2CID 10355426 Kichenassamy Satyanad Kumar Arun Olver Peter Tannenbaum Allen Yezzi Anthony 1996 09 01 Conformal curvature flows From phase transitions to active vision Archive for Rational Mechanics and Analysis 134 3 275 301 Bibcode 1996ArRMA 134 275K doi 10 1007 BF00379537 ISSN 1432 0673 S2CID 116487549 Yezzi A Kichenassamy S Kumar A Olver P Tannenbaum A April 1997 A geometric snake model for segmentation of medical imagery IEEE Transactions on Medical Imaging 16 2 199 209 doi 10 1109 42 563665 hdl 1853 32559 PMID 9101329 S2CID 6492817 Olver Peter J January 1979 Euler operators and conservation laws of the BBM equation Mathematical Proceedings of the Cambridge Philosophical Society 85 1 143 160 Bibcode 1979MPCPS 85 143O doi 10 1017 S0305004100055572 ISSN 1469 8064 S2CID 10840014 Li Yi A Olver Peter J 2000 03 20 Well posedness and Blow up Solutions for an Integrable Nonlinearly Dispersive Model Wave Equation Journal of Differential Equations 162 1 27 63 Bibcode 2000JDE 162 27L doi 10 1006 jdeq 1999 3683 ISSN 0022 0396 Ball J M Currie J C Olver P J 1981 04 01 Null Lagrangians weak continuity and variational problems of arbitrary order Journal of Functional Analysis 41 2 135 174 doi 10 1016 0022 1236 81 90085 9 ISSN 0022 1236 Olver Peter J 1984 06 01 Conservation laws in elasticity Archive for Rational Mechanics and Analysis 85 2 111 129 Bibcode 1984ArRMA 85 111O doi 10 1007 BF00281447 ISSN 1432 0673 S2CID 18746394 zbMATH Olver Peter J Retrieved 19 June 2017 Peter Olver scholar google com Retrieved 2021 11 28 University of Minnesota How do we rank Retrieved 10 August 2018 Retrieved from https en wikipedia org w index php title Peter J Olver amp oldid 1170479442, wikipedia, wiki, book, books, library,

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