Peter B Gilkey
Mathematics Department
College of Arts and Sciences
University of Oregon
Eugene Oregon 97403 USA
1-541-346-4717 (office phone) 1-541-346-0987 (fax)

Expository Papers of

Peter B. Gilkey , 202 Deady Hall Mathematics Department at the University of Oregon .
  • [E0] The index theorem, Lecture notes for course at I. C. T. P. (Trieste) 1988.
  • [E1] Hearing the shape of a drum, Current Contents, V30 32 (1990), p 16.
  • [E2] The index theorem and Clifford modules, Forty more years of ramifications: Spectral asymptotics and its applications, ed. S. A. Fulling and F. J. Narcowich (vol I Discourses in Mathematics and its Applications, publ Texas A\&M) (1991), 265-316.
  • [E3] Heat Equation Asymptotics. Proc. Symp. Pure and Applied Math. V54 (1993), 317-336.
  • [E4] Asymptotic expansions in spectral geometry. Geometry in partial differential equations ed. A. Prastary and T. Rassias. World Scientific (1994), p 100-113. Expository.
  • [E5] Heat content asymptotics of Riemannian manifolds, joint with M. Van den Berg and S. Desjardins. Differential Geometry and its Applications ed. O. Kowalski and D. Krupka (proceedings of 5th international conference 1992 on differential geometry and its applications at Silesian University), Silesian University at Opava (1993) ISBN 80-901581-0-2, p61-64.Differential Geometry and Its Applications, Proc. Conf. 1992, Opava (Silesian University, Opava, 1993). (electronic edition: ELibEMS,
  • [E6] Applications of spectral geometry to geometry and topology. Lecture notes series 12. Research institute of mathematics global analysis research center. Seoul National University, Seoul 151-742 Korea (1993), 78pp.
  • [E7] Heat content asymptotics of elliptic operators with non scalar leading symbol, in "Proceedings of workshops in pure mathematics, Volume 13, Part III: Differential Geometry and Related Topics" published by "Pure Mathematics Research Association, The Korean Academic Council" (1993), 127-152.
  • [E8] The Gromov Lawson Rosenberg conjecture: when do manifolds admit metrics of positive scalar curvature. Heat kernel techniques and quantum gravity, edited by S. A. Fulling, Discourses in mathematics and its applications 4. 449-460. ISBN 0-9630728-3-8
  • [E9] Heat equation and heat content asymptotics. Heat kernel techniques and quantum gravity, edited by S. A. Fulling, Discourses in mathematics and its applications 4. 1-10. ISBN 0-9630728-3-8 [E10] Asymptotic spectra for Weyl geometries. Romanian conference on geometry. Joint with Bokan and Simon. To appear ANALELE STIINTIFICE ALE UNIVERSITATII "AL.I.CUZA" DIN IASI, Tomul XLII,Supliment,s.I.a Matematica, 1996, p (59-71?)
  • [E12] Spectral geometry of Riemannian submersions. Joint with Leahy and Park. Zbornik radova, Mathematical institute of SANU, Belgrade, Yugoslavia 1997 New Series Book 6 p 36-54. Mathematical institute of SANU, Belgrade, Yugoslavia
  • [E13] Pseudo-Riemannian Osserman manifolds. With Blazic, Bokan, and Rakic. Journal of Balkan Society of Geometers, editors Udriste and Miron. vol. 2, no 2, 1997
  • [E14] The Atiyah-Singer index theorem.  Handbook of Differential Geometry} vol 1 (Elsevier), edited by Franki Dillen (2000) 709--746
  • [E15] Heat Content Asymptotics. Eds: B. Booss-Bavnbek, K. Wojciechowski Geometric Aspects of Partial Differential Equations. Proceedings of a Minisymposium on Spectral Invariants,Heat Equation Approach, September 18-19, 1998, Roskilde, Denmark. Contemporary Mathematics Vol 242, Amer. Math. Soc., Providence, R.I., 1999, pp 125-134
  • [E16] Articles for Encyclopedia of Mathematics (Kluwer academic publishers): Heat content asymptotics, Osserman conjecture, Gromov-Lawson conjecture, and Ivanov-Petrova metrics. See Encyclopedia of Mathematics, Supplement II Michiel Hazewinkel Ed ISBN 0-7923-6114-8, 2000. 620pp, Kluwer Academic Publisher
  • [E17] Curvature, Spectra, and Riemannian Submersions, acecepted for publication in Trends in Mathematics Information Center for Mathematical Sciences KIAST (Korea) Volume 2, December 1999 pp164--169/ Joint with JH Park
  • [E18] Riemannian submersions and heat content asymptotics. Proceedings of the first workshop for women mathematicians. Volume 1 (1999) ed Suk Young Lee (Institute of Mathematical Sciences, EWHA WOMANS UNIVERSITY) pp23--30. Joint with JH Park
  • [E19]  Geometric properties of the curvature operator. Proceedings of Beijing Conference ("Geometry and Topology of Submanifolds, vol. X", World Scientific, Singapore eds: W.H. Chen, A.-M. Li, U. Simon, L. Verstraelen, C.P. Wang, and M. Wiehe) ISBN 981-02-4476-2 p 62-70 (2000)
  • [E20] Asymptotics of the heat equation with `exotic' boundary conditions or with time dependent coefficients. Nucl. Phys. B. (Proc. Suppl) 104 (2002) 63--70. Joint with Kirsten, Park, Vassilevich.
  • [E21] Heat Content Asymptotics,  Joint with J. H. Park , Nucl. Phys. B. (Proc. Suppl) 104 (2002) 185--188
  • [E22] Complex IP pseudo-Riemannian algebraic curvature tensors.Joint with R. Ivanova PDES, Submanifolds and affine differential geometry, Banach center publications, vol 57, Institute of mathematics, Polish academy of sciences, Warszawa 2002, 195--202.
  • [E23] The spectral geometry of the Riemann curvature tensor, joint with Ivanova and Zhang. Trends in Mathematics, 5 (2002), 105--114
  • [E24] The spectral geometry of the Riemann curvature operator in the higher signature setting. Joint with C. Dunn, R. Ivanova, and S. Nikcevic. To appear NONLINEAR FUNCTIONAL ANALYSIS  AND APPLICATIONS, special volume dedicated to Professor Grigorios Tsagas, scheduled to appear in September,2004. math.DG/0312249
  • [E25] The Index Theorem, joint with I. Ivanova, K. Kirsten, and JH Park, Encyclopedia of Mathematical Physics (Elsevier Academic) eds. J.-P. Francoise, G.L. Naber and Tsou S.T.  Oxford: Elsevier, 2006 (ISBN 978-0-1251-2666-3), volume 3 page 23--31.
  • [E26] Characteristic Classes. Joint with R.Ivanova and S. Nikcevic. Encyclopedia of Mathematical Physics (Elsevier Academic) eds. J.-P. Francoise, G.L. Naber and Tsou S.T.  Oxford: Elsevier, 2006 (ISBN 978-0-1251-2666-3), volume 1 page 488-495.
  • [E27] The spectral geometry of operators of Dirac and Laplace type. Handbook of Global Analysis" (Demeter Krupka and David Saudners), p287-324.
  • [E28] Stanilov--Tsankov--Videv Theory, SIGMA 3 (2007), 095, 13 pages; arXiv:0708.0957, joint with M. Brozos-V\'azquez, B. Fiedler, E. Garc\'{\i}a--R\'{\i}o, S. Nik\v cevi\'c, G. Stanilov, Y. Tsankov, R. V\'azquez-Lorenzo, and V. Videv; Published as
  • [E29] Geometric realizations of curvature, M. Brozos-V{\'a}zquez, P. Gilkey, and S. Nik\v cevi\'c Nihonkai Mathematical Journal Issue 1 Volume 20 (2009) 1--24; arXiv:0904.1192 Web page spun on 12 January 2010 by Peter B Gilkey 202 Deady Hall, Department of Mathematics at the University of Oregon, Eugene OR 97403-1222, U.S.A. Phone 1-541-346-4717 of Deady Spider Enterprises