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Taylor, Michael E

Michael Taylor

William R. Kenan Distinguished Professor
Phillips Hall 326

Research Interests

Partial differential equations, harmonic analysis, geometric analysis, stochastic analysis


Professional background

A.B., Princeton University, 1967; Ph.D., University of California, Berkeley, 1970; Instructor and Assistant Professor, University of Michigan, 1970-76; Associate Professor, Rice University, 1976-78; Alfred P. Sloan Fellow, 1977-78; Professor, Rice University, 1978-81; Professor, SUNY Stony Brook, 1981-87; Sherman Fairchild Distinguished Scholar, CalTech, 1986-87; William R. Kenan, Jr. Professor, UNC Chapel Hill, 1987-present


Research Synopsis

My research in Partial Differential Equations involves a variety of areas: wave equations, including diffraction, scattering, and inverse problems; nonlinear evolution equations, including nonlinear Schrodinger equations, Euler and Navier-Stokes equations for fluids, and analysis of standing and traveling waves; harmonic analysis, including spectral theory of Laplace operators, behavior of singular integral operators on uniformly rectifiable domains and applications to boundary problems on rough domains, and index theory of Toeplitz operators in rough, multidimensional domains; and stochastic analysis, bearing on phenomena ranging from enhanced diffusion in fluids to non-gaussian processes on fractal sets.


Representative Publications

Partial Differential Equations I - Basic theory Partial Differential Equations II - Qualitative Studies of Linear Equations Partial Differential Equations III - Nonlinear Equations
Michael Taylor,
Springer-Verlag, 115, 2 116, 2 117, 2, 2011

Singular integrals and Elliptic Boundary Problems on Regular Semmes-Kenig-Toro Domains
S. Hofmann, M. Mitrea, and M. Taylor,
International Mathematics Research Notices , 14, 2567-2865, 2010

Finite Propagation Speed, Kernel Estimates for Functions of the Laplace Operator, and the Geometry of Complete Riemannian Manifolds
J. Cheeger, M. Gromov, and M. Taylor,
Journal of Differential Geometry, 17, 15-53, 1982


Inaugural MPE Prize

Inaugural MPE Prize

The Society for Industrial and Applied Mathematics inaugural MPE Prize... Dissertations And Diapers

Dissertations And Diapers

Ph.D. Students Bryn Barker and DJ Passey featured in Campaign for Carolina article