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Jürg Peter Buser

January 01, 1970

Jürg Peter Buser, known as Peter Buser, (born 27 February 1946 in Basel) is a Swiss mathematician, specializing in differential geometry and global analysis.

Education and career edit

Buser received his doctorate in 1976 from the University of Basel with advisor Heinz Huber and thesis Untersuchungen über den ersten Eigenwert des Laplaceoperators auf kompakten Flächen (Studies on the first eigenvalue of the Laplace operator on compact surfaces).[1] As a post-doctoral student he was at the University of Bonn, the University of Minnesota. and the State University of New York at Stony Brook, before he habilitated at the University of Bonn with a thesis on the length spectrum of Riemann surfaces.

Buser is known for his construction of curved isospectral surfaces (published in 1986 and 1988). His 1988 construction led to a negative solution to Mark Kac's famous 1966 problem Can one hear the shape of a drum?. The negative solution was published in 1992 by Scott Wolpert, David Webb and Carolyn S. Gordon.[2][3] The Cheeger-Buser inequality [de] is named after him and Jeff Cheeger.

He has been a professor at the École Polytechnique Fédérale de Lausanne (EPFL) since 1982. From 2004 to 2005 he was president of the Swiss Mathematical Society. In 2003 he was made an honorary doctor of the University of Helsinki.

Selected publications edit

  • Buser, Peter (1978). "Über eine Ungleichung von Cheeger". Mathematische Zeitschrift. 158 (3): 245–252. doi:10.1007/BF01214795.
  • "On Cheeger's inequality  ". Geometry of the Laplace Operator. Proceedings of Symposia in Pure Mathematics. Vol. 36. American Mathematical Society. 1980. pp. 29–78. doi:10.1090/pspum/036. ISBN 9780821814390.
  • with Hermann Karcher: Buser, Peter; Karcher, Hermann (1981). "The bieberbach case in gromov's almost flat manifold theorem". Global Differential Geometry and Global Analysis. Lecture Notes in Mathematics. Vol. 838. pp. 82–93. doi:10.1007/BFb0088844. ISBN 978-3-540-10285-4. ISSN 0075-8434.
  • with Hermann Karcher: Gromov`s almost flat manifolds, Astérisque 1981, Nr. 81, p. 148
  • "A note on the isoperimetric constant." In Annales scientifiques de l'École Normale Supérieure, vol. 15, no. 2, 1982, pp. 213-230.
  • "On the bipartition of graphs." Discrete Applied Mathematics 9, no. 1 (1984): 105–109.
  • Isospectral Riemann Surfaces, Annales Institut Fourier (Grenoble), vol. 36, 1986, pp. 167–192
  • Cayley graphs and planar isospectral domains, in Toshikazu Sunada (ed.), Geometry and Analysis on Manifolds, Springer Verlag, Lecture Notes in Mathematics, vol. 1339, 1988, pp. 64–77 doi:10.1007/BFb0083047
  • Geometry and Spectra of Compact Riemann Surfaces, Birkhäuser 1992;[4][5] 2010 pbk reprint
  • with John Horton Conway, Peter Doyle, and Klaus-Dieter Semmler: Buser, Peter; Conway, John; Doyle, Peter; Semmler, Klaus-Dieter (1994). "Some planar isospectral domains" (PDF). International Mathematics Research Notices. 1994 (9): 391–400. doi:10.1155/S1073792894000437.
  • with Peter Sarnak: Buser, P.; Sarnak, P. (1994). "On the period matrix of a Riemann surface of large genus (with an Appendix by J.H. Conway and N.J.A. Sloane)". Inventiones Mathematicae. 117 (1): 27–56. Bibcode:1994InMat.117...27B. doi:10.1007/BF01232233. ISSN 0020-9910. S2CID 116904696.
  • with Mika Seppälä: Buser, Peter; Seppälä, Mika (2003). "Triangulations and homology of Riemann surfaces". Proceedings of the American Mathematical Society. 131 (2): 425–432. doi:10.1090/S0002-9939-02-06470-5. ISSN 0002-9939.

References edit

  1. ^ Jürg Peter Buser at the Mathematics Genealogy Project
  2. ^ Gordon, Carolyn; Webb, David L.; Wolpert, Scott (1992). "One Cannot Hear the Shape of a Drum". Bulletin of the American Mathematical Society. 27 (1): 134–139. arXiv:math/9207215. doi:10.1090/S0273-0979-1992-00289-6. ISSN 0273-0979.
  3. ^ Barry Cipra: You can't always hear the shape of a drum , in What´s happening in the Mathematical Sciences , volume 1, American Mathematical Society 1993, p. 15
  4. ^ Patterson, S. J. (1994). "Book Review: Geometry and spectra of compact Riemann surfaces". Bulletin of the American Mathematical Society. 30 (1): 143–145. doi:10.1090/S0273-0979-1994-00448-3. ISSN 0273-0979.
  5. ^ Berg, Michael (13 May 2011). "Review of Geometry and Spectra of Compact Riemann Surfaces". MAA Reviews, Mathematical Association of America.

External links edit

  • Homepage at EPFL

January 01, 1970
jürg, peter, buser, known, peter, buser, born, february, 1946, basel, swiss, mathematician, specializing, differential, geometry, global, analysis, contents, education, career, selected, publications, references, external, linkseducation, career, editbuser, re. Jurg Peter Buser known as Peter Buser born 27 February 1946 in Basel is a Swiss mathematician specializing in differential geometry and global analysis Contents 1 Education and career 2 Selected publications 3 References 4 External linksEducation and career editBuser received his doctorate in 1976 from the University of Basel with advisor Heinz Huber and thesis Untersuchungen uber den ersten Eigenwert des Laplaceoperators auf kompakten Flachen Studies on the first eigenvalue of the Laplace operator on compact surfaces 1 As a post doctoral student he was at the University of Bonn the University of Minnesota and the State University of New York at Stony Brook before he habilitated at the University of Bonn with a thesis on the length spectrum of Riemann surfaces Buser is known for his construction of curved isospectral surfaces published in 1986 and 1988 His 1988 construction led to a negative solution to Mark Kac s famous 1966 problem Can one hear the shape of a drum The negative solution was published in 1992 by Scott Wolpert David Webb and Carolyn S Gordon 2 3 The Cheeger Buser inequality de is named after him and Jeff Cheeger He has been a professor at the Ecole Polytechnique Federale de Lausanne EPFL since 1982 From 2004 to 2005 he was president of the Swiss Mathematical Society In 2003 he was made an honorary doctor of the University of Helsinki Selected publications editBuser Peter 1978 Uber eine Ungleichung von Cheeger Mathematische Zeitschrift 158 3 245 252 doi 10 1007 BF01214795 On Cheeger s inequality l 1 h 2 4 displaystyle lambda 1 geq h 2 4 nbsp Geometry of the Laplace Operator Proceedings of Symposia in Pure Mathematics Vol 36 American Mathematical Society 1980 pp 29 78 doi 10 1090 pspum 036 ISBN 9780821814390 with Hermann Karcher Buser Peter Karcher Hermann 1981 The bieberbach case in gromov s almost flat manifold theorem Global Differential Geometry and Global Analysis Lecture Notes in Mathematics Vol 838 pp 82 93 doi 10 1007 BFb0088844 ISBN 978 3 540 10285 4 ISSN 0075 8434 with Hermann Karcher Gromov s almost flat manifolds Asterisque 1981 Nr 81 p 148 A note on the isoperimetric constant In Annales scientifiques de l Ecole Normale Superieure vol 15 no 2 1982 pp 213 230 On the bipartition of graphs Discrete Applied Mathematics 9 no 1 1984 105 109 Isospectral Riemann Surfaces Annales Institut Fourier Grenoble vol 36 1986 pp 167 192 Cayley graphs and planar isospectral domains in Toshikazu Sunada ed Geometry and Analysis on Manifolds Springer Verlag Lecture Notes in Mathematics vol 1339 1988 pp 64 77 doi 10 1007 BFb0083047 Geometry and Spectra of Compact Riemann Surfaces Birkhauser 1992 4 5 2010 pbk reprint with John Horton Conway Peter Doyle and Klaus Dieter Semmler Buser Peter Conway John Doyle Peter Semmler Klaus Dieter 1994 Some planar isospectral domains PDF International Mathematics Research Notices 1994 9 391 400 doi 10 1155 S1073792894000437 with Peter Sarnak Buser P Sarnak P 1994 On the period matrix of a Riemann surface of large genus with an Appendix by J H Conway and N J A Sloane Inventiones Mathematicae 117 1 27 56 Bibcode 1994InMat 117 27B doi 10 1007 BF01232233 ISSN 0020 9910 S2CID 116904696 with Mika Seppala Buser Peter Seppala Mika 2003 Triangulations and homology of Riemann surfaces Proceedings of the American Mathematical Society 131 2 425 432 doi 10 1090 S0002 9939 02 06470 5 ISSN 0002 9939 References edit Jurg Peter Buser at the Mathematics Genealogy Project Gordon Carolyn Webb David L Wolpert Scott 1992 One Cannot Hear the Shape of a Drum Bulletin of the American Mathematical Society 27 1 134 139 arXiv math 9207215 doi 10 1090 S0273 0979 1992 00289 6 ISSN 0273 0979 Barry Cipra You can t always hear the shape of a drum in What s happening in the Mathematical Sciences volume 1 American Mathematical Society 1993 p 15 Patterson S J 1994 Book Review Geometry and spectra of compact Riemann surfaces Bulletin of the American Mathematical Society 30 1 143 145 doi 10 1090 S0273 0979 1994 00448 3 ISSN 0273 0979 Berg Michael 13 May 2011 Review of Geometry and Spectra of Compact Riemann Surfaces MAA Reviews Mathematical Association of America External links editHomepage at EPFL Retrieved from https en wikipedia org w index php title Jurg Peter Buser amp oldid 1188025462, wikipedia, wiki, book, books, library,

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