UNC Math: met

Michael E. Taylor

Position
William R. Kenan Professor of Mathematics

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

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

Field
Partial Differential Equations

Memberships
American Academy of Arts and Sciences **
American Mathematical Society
Mathematical Association of America
Society for Industrial and Applied Mathematics

Check out the following Conference on PDE July 16-20, 2012.

Click here for pdf files related to my January 2012 AMS talk.

Click here for pdf files related to my talks at the Fabes-Riviere Symposium, April 2011.

Click here for pdf files related to my Functional Analysis course.

Click here for pdf files related to my Complex Analysis course.

Click here for pdf files related to Math 383.

Click here for pdf files related to Math 524.

Click here for pdf files related to vanishing viscosity limits for Navier-Stokes equations

Click here for pdf files related to my PDE course.

Click here for pdf files on some of my talks in our Analysis/PDE Seminar

Click here for a copy (pdf file) of
"Pseudodifferential Operators"
Four lectures at MSRI, September 2008

Click here for pdf files on related material on pseudodifferential operators, microlocal analysis, and wave propagation.

Papers Since 2000
  1. Review of "Distributions - Theory and Applications" (by J. Duistermaat and J. Kolk), SIAM Review, to appear.
  2. Nonlinear bound states on weakly homogeneous spaces (with H. Christianson, J. Metcalfe, and J. Marzuola), Preprint, 2012.
  3. Regularity of standing waves on Lipschitz domains, Canadian J. Math., to appear.
  4. Dispersive wave estimates on 3D hyperbolic space (with J. Metcalfe), Proc. AMS, to appear.
  5. Heat semigroup bounds on BV(Omega) and related estimates, Potential Analysis 35 (2011), 89-101.
  6. Random walks, random flows, and enhanced diffusivity in advection-diffusion equations, Discrete and Cont. Dyn. Sys. 17 (2012), 1261-1287.
  7. Gaussian processes associated with infinite bead-spring networks II: beads with mass and the vanishing mass limit, Commun. Math. Sci. 10 (2012), 671-692.
  8. Gaussian processes associated with infinite bead-spring networks, Commun. Math. Sci. 9 (2011), 517-534.
  9. Vanishing viscosity limits for a class of circular pipe flows (with A. Mazzucato), Commun. PDE 36 (2011), 328-361.
  10. Regularity for a class of elliptic operators with Dini continuous coefficients, J. Geometric Analysis 21 (2011), 174-194.
  11. Nonlinear waves on 3D hyperbolic space (with J. Metcalfe), Trans. AMS 363 (2011), 3489-3529.
  12. Inverse problems for obstacles in a waveguide (with T. Christiansen), Commun. PDE 35 (2010), 328-352.
  13. 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
  14. Variants of Arnold's stability results for 2D Euler equations, Canadian Math. Bull. 53 (2010), 163-170.
  15. Quadrature estimates for multidimensional integrals (with J. Rauch), Houston J. Math. 36 (2010), 727-749.
  16. 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.
  17. Functions of the Laplace operator on manifolds with lower Ricci and injectivity bounds, Commun. PDE 34 (2009), 1114-1126.
  18. Local regularity results for second order elliptic systems on Lipschitz domains (with M. Mitrea), Functiones et Approximatio 40 (2009), 175-184.
  19. Hardy spaces and bmo on manifolds with bounded geometry, J. Geometric Anal. 19 (2009), 137-190.
  20. Finsler structures and wave propagation, "Sobolev Spaces in Mathematics," International Math. Series Vol. 10, Springer-Verlag 2009, pp. 317-334.
  21. Vanishing viscosity plane parallel channel flow and related singular perturbation problems (with A. Mazzucato), Analysis and Partial Differential Equations 1 (2008), 35-93.
  22. 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.
  23. A Saint-Venant principle for Lipschitz cylinders, Proc. Symp. Pure Math., AMS, 79 (2008), 337-345.
  24. Short time behavior of solutions to Schrodinger equations (linear and nonlinear) II, Canadian J. Math. 60 (2008), 1168-1200.
  25. 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.
  26. Anderson-Cheeger limits of smooth Riemannian manifolds, and other Gromov-Hausdorff limits, Journal of Geometric Analysis 17 (2007), 365-374.
  27. Scattering length of positive potentials, Houston J. Math. 33 (2007), 979-1003.
  28. The complex Frobenius theorem for rough involutive structures (with C.D. Hill), Trans. AMS 359 (2007), 293-322.
  29. Wave equations and diffraction, Encyclopedia of Mathematical Physics, Elsevier, London, 2006, Vol. 5, pp. 401-407.
  30. The Poisson problem in weighted Sobolev spaces on Lipschitz domains (with M. Mitrea), Indiana Univ. Math. J. 55 (2006), 1063-1089.
  31. Short time behavior of solutions to nonlinear Schrodinger equations in one and two space dimensions, Comm. in PDE 31 (2006), 945-957.
  32. Existence and regularity of isometries, Trans. AMS 358 (2006), 2415-2423.
  33. Scattering length and the spectrum of -Laplacian + V, Canadian Math. Bull. 49 (2006), 144-151.
  34. Lipschitz domains, domains with corners, and the Hodge Laplacian (with M. Mitrea and A. Vasy), Comm. in PDE 30 (2005), 1445-1462.
  35. Regularity of functions smooth along foliations, and elliptic regularity (with J. Rauch), J. Funct. Anal. 225 (2005), 74-93.
  36. Regularity of loop group factorization, Proc. AMS 133 (2005), 627-631.
  37. 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.
  38. 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.
  39. 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.
  40. Group actions and singular martingales II: the recognition problem (with J. Rosenblatt), Canadian J. Math. 5 (2004), 431-448.
  41. Fourier series and lattice point estimates, Houston J. Math. 30 (2004), 117-135.
  42. 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.
  43. Maximal entropy measure for rational maps and a random iteration algorithm (with J. Hawkins), International J. of Bifurcation and Chaos 13 (2003), 1442-1447.
  44. Integrability of rough almost complex structures (with C.D. Hill), J. Geometric Anal. 13 (2003), 163-172.
  45. The Schrodinger equation on spheres, Pacific J. Math. 209 (2003), 145-155.
  46. Commutator estimates, Proc. AMS 131 (2003), 1501-1507.
  47. 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.
  48. Potential theory on Lipschitz domains in Riemannian manifolds: the case of Dini metric tensors (with M. Mitrea), Trans. AMS 355 (2003), 1961-1985.
  49. 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.
  50. Group actions and singular martingales (with J. Rosenblatt and D. Stroock), Ergodic Theory and Dyn. Sys. 23 (2003), 293-305.
  51. Differential forms and the change of variable formula for multiple integrals, J. Math. Anal. and Applications 268 (2002), 378-383.
  52. Curvature and uniformization (with R. Mazzeo), Israel J. Math. 130 (2002), 323-346.
  53. Harmonic analysis and degenerate diffusions on Euclidean groups, Annals of Global Anal. and Geom. 22 (2002), 179-196.
  54. The Gibbs phenomenon, the Pinsky phenomenon, and variants for eigenfunction expansions, Comm. PDE 27 (2002), 565-605.
  55. Navier-Stokes equations on Lipschitz domains in Riemannian manifolds (with M. Mitrea), Math. Annalen 321 (2001), 955-987.
  56. Eigenfunction expansions and the Pinsky phenomenon on compact manifolds, J. Fourier Anal. 7 (2001), 507-522.
  57. 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.
  58. Layer potentials, the Hodge Laplacian, and global boundary problems in nonsmooth Riemannian manifolds (with D. Mitrea and M. Mitrea), Memoirs AMS #713, 2001.
  59. 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.
  60. Incompressible fluid flows on rough domains, pp. 320-334 in Semigroups of Operators: Theory and Applications (A.V. Balakrishnan, ed.), Birkhauser, Boston, 2000.
  61. Pointwise Fourier inversion - an addendum, Proc. AMS 129 (2000), 2001-2003.
  62. 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.
  63. Potential theory on Lipschitz domains in Riemannian manifolds: Holder continuous metric tensors (with M. Mitrea), Comm. PDE 25 (2000), 1487-1536.
  64. 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. Propagation, reflection, and diffraction of singularities of solutions to wave equations, Bull. AMS 24 (1978), 589-611.
  19. The asymptotic behavior of the scattering peak in classical scattering (with A. Majda), Comm. Pure Appl. Math. 30 (1977), 639-669.
  20. Grazing rays and reflection of singularities of solutions to wave equations, Comm. Pure Appl. Math. 29 (1976), 1-38.
  21. Potential and scattering theory on wildly perturbed domains (with J. Rauch), J. Funct. Anal. 18 (1975), 27-59.
  22. Gelfand theory of pseudodifferential operators and hypoelliptic operators, Trans. AMS 153 (1971), 495-510.
  23. Functions of several self-adjoint operators, Proc. AMS 19 (1968), 91-98.

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

Miscellaneous Notes (Available on Request)
  1. Discrete Fourier inversion, Gibbs phenomenon, and beyond
  2. Remarks on fractional diffusion equations
  3. Regularity for a class of elliptic operators with Dini continuous coefficients
  4. Boundary Problems for Wave Equations with Grazing and Gliding Rays, with R. Melrose.
  5. Wave patterns for solutions to semilinear equations utt = uxx + f(u)
  6. Curvature, conformal mapping, and 2D stationary fluid flows
  7. Serendipitous Fourier inversion
  8. Double Fourier series of functions with simple singularities - a graphical case study
  9. Notes on integration on Lie groups
  10. Some matrix integrals related to random matrix theory
  11. Remarks on regularity of harmonic maps
  12. Propagation of oscillatory waves with small envelopes
  13. The Hopf bracket (with C. Lebrun)
  14. Averaging rotations
  15. Lattice point counts in 3D and the Pinsky phenomenon
  16. Remarks on M. Pinsky's derivation of the modulus of continuity for Brownian motion.
  17. Tidbits in harmonic analysis
    • The Schrodinger equation and Gauss sums
    • Multiple eigenvalues of operators with noncommutative symmetry groups
    • The remainder in Taylor series

Classroom Notes
  1. Difference Schemes for ODE
  2. Numbers (pdf)
  3. Outline of Calculus in Several Variables
  4. Elementary Differential Geometry
  5. Differential Geometry
  6. Introduction to Complex Analysis
  7. Lectures on Lie Groups
  8. Finite and Infinite Dimensional Lie Groups and Evolution Equations
  9. Notes on Compact Riemann Surfaces