Peter J. Olver

Peter John Olver
Born	January 11, 1952 (1952-01-11) (age 73) Middlesex, England
Alma mater	Brown University Harvard University
Known for	Symmetry groups of partial differential equations
Spouse	Chehrzad Shakiban
Scientific career
Fields	Mathematics
Institutions	University of Maryland University of Minnesota
Thesis	Symmetry Groups of Partial Differential Equations  (1976)
Doctoral advisor	Garrett Birkhoff
Doctoral students	Rui Loja Fernandes

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

Education and career

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 was 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

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]} , quasi-exact solvability ^[23] and elasticity. ^{[24] [25]}

He has written five books and over 150 research papers in peer-reviewed journals. ^{[26] [27]} In 2003, Olver was one of the top 234 most cited mathematicians in the world. ^{[1] [28]} He has supervised 23 PhD students. ^{[2] [3]}

Personal life

Olver married Iranian mathematician Chehrzad Shakiban in 1976. ^[29]

Books

• 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

1. "Peter Olver | AMAAZE". amaaze.umn.edu. Retrieved 2021-11-28.
2. Peter Olver at the Mathematics Genealogy Project
3. 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". Archived from the original on 25 August 2018. 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. Archived from the original on 2022-02-03. 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. González-López, Artemio; Kamran, Niky; Olver, Peter J. (1994), "Quasi-exact solvability", Lie algebras, cohomology, and new applications to quantum mechanics (Springfield, MO, 1992), Contemp. Math., vol. 160, Providence, RI: Amer. Math. Soc., pp. 113–140
24. 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.
25. 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.
26. zbMATH. "Olver, Peter J." Retrieved 19 June 2017.
27. "Peter Olver". scholar.google.com. Retrieved 2021-11-28.
28. University of Minnesota. "How do we rank?" . Retrieved 10 August 2018.
29. Riddle, Larry (July 2, 2024). "Chehrzad Shakiban". Biographies of Women Mathematicians. Agnes Scott College.