UNC Math: met

Michael E. Taylor

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William R. Kenan Professor of Mathematics

Mathematics Dept.
Univ. of North Carolina
Chapel Hill NC 27599-3250
e-mail: met@math.unc.edu

A.B., Princeton Univ., 1967
Ph.D., Univ. of California, Berkeley, 1970

Partial Differential Equations

American Academy of Arts and Sciences
American Mathematical Society
Society for Industrial and Applied Mathematics

Downloadable Lecture Notes and Assorted Papers, by Subject Area

  1. Pseudodifferential operators, Fourier integral operators, and microlocal analysis.
  2. Singular integral operators and PDE on rough domains.
  3. Wave propagation.
  4. Spectral theory and harmonic analysis of the Laplacian and other elliptic operators, including Fourier inversion.
  5. Elliptic equations, Dirichlet problems, Green functions, etc.
  6. Diffusion processes and other random processes.
  7. Quantum chaos and other connections with quantum theory.
  8. Seminar talks and various AMS talks.
  9. Linear algebra notes.
  10. Functional Analysis course.
  11. Classical Fourier Analysis, sometimes with a modern perspective.
  12. Complex Analysis course.
  13. Math 521-522, basic undergraduate analysis (advanced calculus).
  14. Math 524, second semester ODE.
  15. Math 653, beginning graduate analysis.
  16. Differential Geometry, Riemann surfaces, CR-manifolds, index theory.
  17. Elementary Geometry notes.
  18. Lie Groups and representation theory.
  19. Special Functions.
  20. Euler and Navier-Stokes equations.
  21. PDE course.
  22. Computer notes: numerics and graphics.

Some of these notes are also available on AMS Open Math Notes.

Papers Since 2000
  1. The Dirichlet-to-Neumann map, Preprint, 2017.
  2. Maximal entropy measures of Fatou boundaries (with J. Hawkins), Discrete and Cont. Dynamical Systems, to appear.
  3. Multidimensional Toeplitz operators with locally sectorial symbols, Comm. PDE 22 (2017), 1322-1334.
  4. The Weierstrass P-function as a distribution on a complex torus, and its Fourier series, Houston J. Math., to appear.
  5. Variations on the Donoho-Stark uncertainty principle estimate, J. Geometric Analysis 28 (2018), 492-509.
  6. Asymptotics for some non-classical conormal distributions whose symbols contain negative powers of log |xi|, Jour. of Fourier Analysis and Appl., to appear.
  7. Euler equation on a rotating surface (containing an appendix with J. Marzuola), J. Funct. Anal. 270 (2016), 3884-3945.
  8. Multidimensional Riemann-Hilbert problems on domains with uniformly rectifiable interfaces (with I. Mitrea and M. Mitrea), Preprint, 2015.
  9. Higher dimensional vortex standing waves for nonlinear Schrodinger equations (with J. Marzuola), Comm. in PDE 41 (2016), 398-446.
  10. Traveling wave solutions to NLS and NLKG equations in non-euclidean settings, Houston J. Math. 42 (2016), 143-165.
  11. Variations on quantum ergodic theorems, Potential Analysis 43 (2015), 625-651.
  12. Commutator estimates for Holder continuous and bmo-Sobolev multipliers, Proc. AMS 143 (2015), 5265-5274.
  13. Symbol calculus for operators of layer potential type on Lipschitz surfaces with vmo normals, and related pseudodifferential operator calculus (with S. Hofmann and M. Mitrea), Anal. and PDE 8 (2015), 115-181.
  14. Poisson equations, uniformization, and geometrical optics, Contemporary Math. 644 (2015), 241-260.
  15. Cauchy integrals, Calderon projectors, and Toeplitz operators on uniformly rectifiable domains (with I. Mitrea and M. Mitrea), Advances in Math. 268 (2015), 666-757.
  16. Wave decay on manifolds with bounded Ricci tensor, and related estimates, J. Geometric Analysis 25 (2015), 1018-1044.
  17. Nonlinear bound states on weakly homogeneous spaces (with H. Christianson, J. Metcalfe, and J. Marzuola), Commun. PDE 39 (2014), 34-97.
  18. Random walks and approximate integration on compact homogeneous spaces, Illinois J. Math. 57 (2013), 559-576.
  19. Regularity of standing waves on Lipschitz domains, Canadian J. Math. 65 (2013), 702-720.
  20. Review of "Distributions - Theory and Applications" (by J. Duistermaat and J. Kolk), SIAM Review 54 (2012), 617-621.
  21. Dispersive wave estimates on 3D hyperbolic space (with J. Metcalfe), Proc. AMS 140 (2012), 3861-3866.
  22. Random walks, random flows, and enhanced diffusivity in advection-diffusion equations, Discrete and Cont. Dyn. Sys. 17 (2012), 1261-1287.
  23. Gaussian processes associated with infinite bead-spring networks II: beads with mass and the vanishing mass limit, Commun. Math. Sci. 10 (2012), 671-692.
  24. Heat semigroup bounds on BV(Omega) and related estimates, Potential Analysis 35 (2011), 89-101.
  25. Gaussian processes associated with infinite bead-spring networks, Commun. Math. Sci. 9 (2011), 517-534.
  26. Vanishing viscosity limits for a class of circular pipe flows (with A. Mazzucato), Commun. PDE 36 (2011), 328-361.
  27. Regularity for a class of elliptic operators with Dini continuous coefficients, J. Geometric Analysis 21 (2011), 174-194.
  28. Nonlinear waves on 3D hyperbolic space (with J. Metcalfe), Trans. AMS 363 (2011), 3489-3529.
  29. Inverse problems for obstacles in a waveguide (with T. Christiansen), Commun. PDE 35 (2010), 328-352.
  30. Singular integrals and elliptic boundary problems on regular Semmes-Kenig-Toro domains (with S. Hofmann and M. Mitrea), International Math. Research Notices 2010 (2010), 2567-2865, doi: 10.1093/imrn/rnp214
  31. Variants of Arnold's stability results for 2D Euler equations, Canadian Math. Bull. 53 (2010), 163-170.
  32. Quadrature estimates for multidimensional integrals (with J. Rauch), Houston J. Math. 36 (2010), 727-749.
  33. Hardy spaces, singular integrals, and the geometry of Euclidean domains of locally finite perimeter (with S. Hofmann, E. Marmolejo Olea, M. Mitrea, and S. Perez Esteva), Geom. and Funct. Anal. 19 (2009), 842-882.
  34. Functions of the Laplace operator on manifolds with lower Ricci and injectivity bounds, Commun. PDE 34 (2009), 1114-1126.
  35. Local regularity results for second order elliptic systems on Lipschitz domains (with M. Mitrea), Functiones et Approximatio 40 (2009), 175-184.
  36. Hardy spaces and bmo on manifolds with bounded geometry, J. Geometric Anal. 19 (2009), 137-190.
  37. Finsler structures and wave propagation, "Sobolev Spaces in Mathematics," International Math. Series Vol. 10, Springer-Verlag 2009, pp. 317-334.
  38. Vanishing viscosity plane parallel channel flow and related singular perturbation problems (with A. Mazzucato), Analysis and Partial Differential Equations 1 (2008), 35-93.
  39. Vanishing viscosity limits and boundary layers for circularly symmetric 2D flows (with M. Lopes Filho, A. Mazzucato, and H. Nussenzveig Lopes), Bull. Brazilian Math. Soc. 39 (2008), 471-513.
  40. A Saint-Venant principle for Lipschitz cylinders, Proc. Symp. Pure Math., AMS, 79 (2008), 337-345.
  41. Short time behavior of solutions to Schrodinger equations (linear and nonlinear) II, Canadian J. Math. 60 (2008), 1168-1200.
  42. Geometric and transformational properties of Lipschitz domains, Semmes-Kenig-Toro domains, and other classes of finite perimeter domains (with S. Hofmann and M. Mitrea), J. Geometric Anal. 17 (2007), 593-648.
  43. Anderson-Cheeger limits of smooth Riemannian manifolds, and other Gromov-Hausdorff limits, Journal of Geometric Analysis 17 (2007), 365-374.
  44. Scattering length of positive potentials, Houston J. Math. 33 (2007), 979-1003.
  45. The complex Frobenius theorem for rough involutive structures (with C.D. Hill), Trans. AMS 359 (2007), 293-322.
  46. Wave equations and diffraction, Encyclopedia of Mathematical Physics, Elsevier, London, 2006, Vol. 5, pp. 401-407.
  47. The Poisson problem in weighted Sobolev spaces on Lipschitz domains (with M. Mitrea), Indiana Univ. Math. J. 55 (2006), 1063-1089.
  48. Short time behavior of solutions to nonlinear Schrodinger equations in one and two space dimensions, Comm. in PDE 31 (2006), 945-957.
  49. Existence and regularity of isometries, Trans. AMS 358 (2006), 2415-2423.
  50. Scattering length and the spectrum of -Laplacian + V, Canadian Math. Bull. 49 (2006), 144-151.
  51. Lipschitz domains, domains with corners, and the Hodge Laplacian (with M. Mitrea and A. Vasy), Comm. in PDE 30 (2005), 1445-1462.
  52. Regularity of functions smooth along foliations, and elliptic regularity (with J. Rauch), J. Funct. Anal. 225 (2005), 74-93.
  53. Regularity of loop group factorization, Proc. AMS 133 (2005), 627-631.
  54. Sobolev and Besov space estimates for solutions to second order PDE on Lipschitz domains in manifolds with Dini or Holder continuous metric tensors (with M. Mitrea), Comm. PDE 30 (2005), 1-37.
  55. Boundary regularity for the Ricci equation, geometric convergence, and Gel'fand's inverse boundary problem (with M. Anderson, A. Katsuda, Y. Kurylev, and M. Lassas), Invent. Math. 158 (2004), 261-321.
  56. The Dirichlet-to-Neumann map, viscosity solutions to eikonal equations, and the self-dual equations of pattern formation (with N. Ercolani), Physica D 196 (2004), 205-223.
  57. Group actions and singular martingales II: the recognition problem (with J. Rosenblatt), Canadian J. Math. 5 (2004), 431-448.
  58. Fourier series and lattice point estimates, Houston J. Math. 30 (2004), 117-135.
  59. Remarks on Fourier integral operators, pp. 257-262 in Geometric Methods in Inverse Problems and PDE Control (C. Croke, I. Lasiecka, G. Uhlmann and M. Vogelius, eds.), IMA Vol. 137, Springer-Verlag, New York, 2003.
  60. Maximal entropy measure for rational maps and a random iteration algorithm (with J. Hawkins), International J. of Bifurcation and Chaos 13 (2003), 1442-1447.
  61. Integrability of rough almost complex structures (with C.D. Hill), J. Geometric Anal. 13 (2003), 163-172.
  62. The Schrodinger equation on spheres, Pacific J. Math. 209 (2003), 145-155.
  63. Commutator estimates, Proc. AMS 131 (2003), 1501-1507.
  64. Multidimensional Fejer Kernel Asymptotics, Proc. Summer Res. Conf. in Harmonic Analysis, W. Beckner et al., eds., Contemporary Math. 320, AMS, Providence, R.I., 2003, pp. 411-434.
  65. Potential theory on Lipschitz domains in Riemannian manifolds: the case of Dini metric tensors (with M. Mitrea), Trans. AMS 355 (2003), 1961-1985.
  66. The Dirichlet-to-Neumann map for complete Riemannian manifolds with boundary (with M. Lassas and G. Uhlmann), Commun. in Analysis and Geometry 11 (2003), 207-221.
  67. Group actions and singular martingales (with J. Rosenblatt and D. Stroock), Ergodic Theory and Dyn. Sys. 23 (2003), 293-305.
  68. Differential forms and the change of variable formula for multiple integrals, J. Math. Anal. and Applications 268 (2002), 378-383.
  69. Curvature and uniformization (with R. Mazzeo), Israel J. Math. 130 (2002), 323-346.
  70. Harmonic analysis and degenerate diffusions on Euclidean groups, Annals of Global Anal. and Geom. 22 (2002), 179-196.
  71. The Gibbs phenomenon, the Pinsky phenomenon, and variants for eigenfunction expansions, Comm. PDE 27 (2002), 565-605.
  72. Navier-Stokes equations on Lipschitz domains in Riemannian manifolds (with M. Mitrea), Math. Annalen 321 (2001), 955-987.
  73. Eigenfunction expansions and the Pinsky phenomenon on compact manifolds, J. Fourier Anal. 7 (2001), 507-522.
  74. Potential theory on Lipschitz domains in Riemannian manifolds: Lp, Hardy, and Holder space results (with M. Mitrea), Commun. in Analysis and Geometry 9 (2001), 369-421.
  75. Layer potentials, the Hodge Laplacian, and global boundary problems in nonsmooth Riemannian manifolds (with D. Mitrea and M. Mitrea), Memoirs AMS #713, 2001.
  76. Extension and representation of divergence-free vector fields on bounded domains (with T. Kato, M. Mitrea, and G. Ponce), Math. Res. Letters 7 (2000), 643-650.
  77. Incompressible fluid flows on rough domains, pp. 320-334 in Semigroups of Operators: Theory and Applications (A.V. Balakrishnan, ed.), Birkhauser, Boston, 2000.
  78. Pointwise Fourier inversion - an addendum, Proc. AMS 129 (2000), 2001-2003.
  79. Potential theory on Lipschitz domains in Riemannian manifolds: Sobolev-Besov space results and the Poisson problem (with M. Mitrea), J. Funct. Anal. 176 (2000), 1-79.
  80. Potential theory on Lipschitz domains in Riemannian manifolds: Holder continuous metric tensors (with M. Mitrea), Comm. PDE 25 (2000), 1487-1536.
  81. The Dirichlet-Jordan test and multidimensional extensions, Proc. AMS 129 (2000), 1031-1035.

Selected Older Papers
  1. Pointwise Fourier inversion on tori and other compact manifolds, J. Fourier Anal. 5 (1999), 449-463.
  2. Boundary layer methods for Lipschitz domains in Riemannian manifolds (with M. Mitrea), J. Funct. Anal. 163 (1999), 181-251.
  3. Pointwise Fourier inversion: a wave equation approach (with M. Pinsky), J. Fourier Anal. 3 (1997), 647-703.
  4. Estimates for approximate solutions to acoustic inverse scattering problems, pp. 463-499 in "Inverse Problems in Wave Propagation," (G. Chavent et al., eds.) IMA Vol. 90, Springer-Verlag, New York, 1997.
  5. Microlocal analysis and nonlinear PDE, Proc. Symp. Pure Math. 59 (1996), 211-223.
  6. Paradifferential operators and commutator estimates (with P. Auscher), Comm. PDE 20 (1995), 1743-1775.
  7. Analysis on Morrey spaces and applications to Navier-Stokes and other evolution equations, Commun. PDE 17 (1992), 1407-1456.
  8. Semiclassical spectra of gauge fields (with A. Uribe), J. Funct. Anal. 110 (1992), 1-46.
  9. Microlocal analysis in spectral and scattering theory and index theory, Proc. International Congr. Math. 1990, 1225-1234.
  10. Semiclassical asymptotics, gauge fields, and quantum chaos (with R. Schrader), J. Funct. Anal. 83 (1989), 258-316.
  11. Cycles and relative cycles in analytic K-homology (with P. Baum and R. Douglas), J. Diff. Geom. 30 (1989), 761-804.
  12. Lp spectral theory of Kleinian groups (with E. B. Davies and B. Simon), J. Funct. Anal. 78 (1988), 116-136.
  13. Near peak scattering and the corrected Kirchhoff approximation for convex obstacles (with R. Melrose), Advances in Math. 55 (1985), 242-315.
  14. Noncommutative microlocal analysis, Part I, Memoirs AMS #313, 1984.
  15. Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds (with J. Cheeger and M. Gromov), J. Diff. Geom. 17 (1982), 15-53.
  16. A model for harmonics on stringed instruments (with A. Bamberger and J. Rauch), Arch. Rat. Mech. Anal. 79 (1982), 267-290.
  17. Diffraction of waves by conical singularities (with J. Cheeger), Comm. Pure Appl. Math. 35 (1982), 275-331, 487-529.
  18. Fourier integral operators and harmonic analysis on compact manifolds, Proc. Symp. Pure Math. 35 (Part 2) (1979), 115-136.
  19. Propagation, reflection, and diffraction of singularities of solutions to wave equations, Bull. AMS 24 (1978), 589-611.
  20. The asymptotic behavior of the scattering peak in classical scattering (with A. Majda), Comm. Pure Appl. Math. 30 (1977), 639-669.
  21. Grazing rays and reflection of singularities of solutions to wave equations, Comm. Pure Appl. Math. 29 (1976), 1-38.
  22. Electrostatic screening (with J. Rauch), J. Math. Phys. 16 (1975), 284-288.
  23. Potential and scattering theory on wildly perturbed domains (with J. Rauch), J. Funct. Anal. 18 (1975), 27-59.
  24. Exponential decay of solutions to hyperbolic equations in bounded domains (with J. Rauch), Indiana Univ. Math. J. 24 (1974), 79-86.
  25. Gelfand theory of pseudodifferential operators and hypoelliptic operators, Trans. AMS 153 (1971), 495-510.
  26. Functions of several self-adjoint operators, Proc. AMS 19 (1968), 91-98.

Books and Monographs
  1. The Hodge Laplacian: Boundary Value Problems on Riemannian Manifolds, with D. Mitrea, I. Mitrea, and M. Mitrea, W. de Gruyter, 2016.
  2. Introduction to Differential Equations, Undergraduate Texts Series, American Math. Society, Providence, R.I., 2011.
  3. Measure Theory and Integration, Graduate Studies in Math. No. 76, American Math. Society, Providence, R.I., 2006.
  4. Tools for PDE: Pseudodifferential Operators, Paradifferential Operators, and Layer Potentials, Math. Surveys and Monogr, No. 81, American Math. Society, Providence, R.I., 2000.
  5. Singularities and Oscillations (ed., with J. Rauch), IMA Vol. 91, Springer-Verlag, New York, 1997.
  6. Partial Differential Equations, Vols. 1-3, Applied Math. Sciences, 115-117, Springer-Verlag, New York, 1996. (Second Edition, Springer, New York, 2011.)
  7. Pseudodifferential Operators and Nonlinear PDE, Progress in Math. 100, Birkhauser, Boston, 1991.
  8. Noncommutative Harmonic Analysis, Math. Surveys and Monogr., No. 22, American Math. Society, Providence, R.I., 1986.
  9. Pseudodifferential Operators, Princeton Univ. Press, Princeton, N.J., 1981.