Analysis and Partial Differential Equations
Faculty | |
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James Brennan | Professor (Potential Theory and Complex Analysis), Ph.D., Brown University, 1968 |
Russell Brown | Professor (Harmonic Analysis, Inverse Problems, Partial Differential Equations), Ph.D., University of Minnesota, 1987 |
Francis Chung | Associate Professor (Inverse Problems, Mathematical Physics, Partial Differential Equations, Harmonic Analysis), Ph.D., University of Chicago, 2012 |
Peter Hislop | Professor (Mathematical Physics and Geometric Analysis), Ph.D., University of California-Berkeley, 1984 |
Peter Perry | Professor (Mathematical Physics, Geometric Analysis, Dispersive Nonlinear PDE), Ph.D., Princeton University, 1981 |
Zhongwei Shen | Professor (Partial Differential Equations, Harmonic Analysis, and Mathematical Physics), Ph.D., University of Chicago, 1989 |
Mihai Tohaneanu | Associate Professor (Analysis and Partial Differential Equations), Ph.D., University of California-Berkeley, 2009 |
Current Ph.D Students |
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Chase Ashby (Hislop) |
Shi-Zhuo Looi (Tohaneanu) |
Robert Righi (Shen) |
Camille Schuetz (Perry) |
Jamison Wallace (Shen) |
Emeritus Faculty | |
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Richard Carey | Functional Analysis |
Ray Cox | Analysis |
Ronald Gariepy | Partial Differential Equations |
Lawrence Harris | Functional Analysis, Infinite-Dimensional Holomorphy, Polynomials |
John Lewis | Partial Differential Equations |
Ted Suffridge | Complex Analysis |
James Wells | Analysis, Numerical Analysis |
Sad News
During 2021, we lost two of our Emeritus Faculty members. Ray Rishel passed away on 10 July 2021 at the age of 91. An obituary tells about his life and career. David Adams passed away on 30 July 2021. Suzanne Lenhart (a doctoral graduate of Kentucky) prepared an obituary summarizing his life and describing some of his contributions to mathematics.
Analysis and Partial Differential Equations Seminar
Tuesdays at 11:00 A.M.; Coordinator: Peter Hislop .
Ohio River Analysis Meeting (ORAM)
The Ohio River Analysis Meeting is an annual meeting sponsored by the University of Kentucky and the University of Cincinnati. Each meeting brings leading experts in analysis to the region and also provides an opportunity for students and recent graduates to present their work. The 12th edition of this conference is tentatively scheduled for 18-19 March 2023 at the University of Cincinnati. Information about the series can be found at list of ORAM conference websites at the University of Cincinnati.
Ph.D. Dissertations Since 1989
- Landon Gauthier (2022) Inverse Boundary Value Problems for Polyharmonic Operators with Non-smooth Coefficients (advisor: R.Brown)
- Sam Herschenfeld (2021), Some Proofs Regarding Minami Estimates and Local Eigenvalue Statistics for some Random Schrödinger Operator Models (advisor: P. Hislop)
- Joel Klipfel (2020), The Direct Scattering Map for the Intermediate Long Wave Equation (advisor: P. Perry)
- Ben Brodie (2020), Eigenvalue Statistics and Localization for Random Band Matrices with Fixed Width and Wegner Orbital Model (advisor: P. Hislop)
- Maryam al Ghafli (2019), An Inverse Eigenvalue Problem for the Schrödinger Equation on the Unit Ball of R^{3} (advisor: P. Hislop)
- Jinping Zhuge (2019), Boundary Layers in Periodic Homogenization (advisor: Z. Shen)
- George Lytle (2019), Approximations in Reconstructing Discontinuous Conductivities in the Calderón Problem (advisor: P. Perry)
- Stephen Deterding (2018), Bounded Point Derivations on Certain Function Spaces (advisor: J. Brennan)
- B. Chase Russell (2018), Homogenization in Perforated Domains and with Soft Inclusions (advisor: Z. Shen)
- Joseph Lindgren (2017), Orbital Stability of Solitons Solving Non-Linear Schrödinger Equations in an External Potential (advisor: P. Hislop)
- Jiaqi Liu (2017), Global Well-Posedness for the Derivative Nonlinear Schrödinger Equation Through Inverse Scattering (advisor: P. Perry)
- Morgan Schreffler (2017), Approximation of Solutions to the Mixed Dirichlet-Neumann Boundary Value Problem on Lipschitz Domains (advisor: R. Brown)
- Robert Wolf (2017), Compactness of Isoresonant Potentials (advisor: P. Hislop)
- Laura Croyle (2016), Solutions to the L^{p} Mixed Boundary Value Problem in C^{1,1} Domains (Advisor: R. Brown)
- Shu Gu (2016), Homogenization of Stokes Systems with Periodic Coefficients (Advisor: Z. Shen)
- Michael Music (2016), Inverse Scattering for the Zero-Energy Novikov-Veselov Equation (Advisor: P. Perry)
- Yaowei Zhang (2016), The Bourgain Spaces and Recovery of Magnetic and Electric Potentials of Schrödinger Operators (Advisor: R. Brown)
- Aaron Saxton (2014), Decay estimates on trace norms of locaized functions of Schrödinger operators (Advisor: P. Hislop)
- Murat Akman (2014), On The Dimension of a Certain Measure Arising From a Quasilinear Elliptic PDE (Advisor: J. Lewis)
- Megan Gier (2014), Eigenvalue Multiplicities of the Hodge Laplacian on Coexact 2-forms for Generic Metrics on 5-Manifolds (Advisor: P. Hislop)
- Tao Huang (2013), Regularity and Uniqueness of Harmonic and Biharmonic Map Heat Flows (Advisor: C. Wang).
- Ryan Walker (2013), On a Paley-Wiener Theorem for the ZS-AKNS Scattering Transform (Advisor: P. Perry).
- Jay Hineman (2012), The Hydrodynamic Flow of Nematic Liquid Crystals in Three Dimensions (Advisor: C. Wang)
- Chris Mattingly (2012), Rational Approximation on Compact Nowhere Dense Sets (Advisor: J. Brennan).
- Jun Geng (2011), Elliptic Boundary Value Problems on Non-smooth Domains (Advisor: Z. Shen).
- Erin Militzer (2011), L^{p} Polynomial Approximation and Uniform Rational Approximation (Advisor: J. Brennan).
- Justin Taylor (2011), Convergence of Eigenvalues for Elliptic Systems on Domains with Thin Tubes and the Green Function for the Mixed Problem (Advisor: R. Brown).
- Phuoc Ho (2010), Upper Bounds on the Splitting of Eigenvalues (Advisor: P. Hislop).
- Joel Kilty (2009), L^{p} Boundary Value Problems on Lipschitz Domains (Advisor: Z. Shen).
- Julie Miker (2009), Eigenvalue Inequalities for a Family of Spherically Symmetric Riemannian Manifolds (Advisor: P. Hislop).
- Zhongyi Nie (2009), Estimates for a Class of Multi-linear forms (Advisor: R. Brown).
- Teng Jiang (2008), Absolute Minimizers of L^{∞} Functional under the Dirichlet Energy Constraint (Advisor: C. Wang).
- Christopher Frayer (2008), Scattering Theory on the Line with Singular Miura Potentials (Advisor: P. Perry).
- Aekyoung Shin Kim (2007), The L^{p} Neumann Problem for Laplace Equation in Convex Domains (Advisor: Z. Shen).
- Yuho Shin (2006), Geodesics of a Two-Step Nilpotent Lie Group (Advisor: P. Perry).
- Bjorn Bennewitz (2006), Nonuniqueness in a Free Boundary Problem (Advisor: J. L. Lewis).
- Mike Dobranski (2004), Construction of Exponentially Growing Solutions to First-Order Systems with Non-Local Potentials (Advisor: R. Brown).
- Mary Goodloe (2004), Hadamard Products of Convex Harmonic Mappings (Advisor: T. Suffridge).
- Steve Kovacs (2004), Invertibility Preserving maps of C^{*}-Algebras (Advisor: L. Harris).
- Stacey Mueller (2004), Harmonic Mappings and Solutions of a Differential Equation Related to de la Vallee Poussin Means (Advisor: T. Suffridge).
- Wataru Ishizuka (2003), The Weak Compactness and Regularity of Weakly Harmonic Maps (Advisors: C. Wang and L. Harris).
- Christopher Morgan (2001), On Univalent Harmonic Mappings (Advisor: T. Suffridge).
- Carl Lutzer (2000), On the extraction of topological and geometric information from the spectrum of the Dirichlet to Neumann operator (Advisor: P. Hislop).
- Jeffery D. Sykes (1999), Regularity of Solutions of the Mixed Boundary Problem for Laplace's Equation on a Lipschitz Graph Domain (Advisor: R. Brown).
- Jerry R. Muir, Jr. (1999), Linear and Holomorphic Idempotents and Retracts in the Open Unit Ball of a Commutative C*-algebra with Identity (Advisor: T. Suffridge ).
- Michael D. Galloy (1998), Harmonic Univalent Mappings on the Unit Disk and the Punctured Unit Disk (Advisor: T. Suffridge ).
- John T. Thompson (1998), A Study of Harmonic Mappings on Punctured Domains: An Argument Principle and Some Coefficient Results (Advisor: T. Suffridge).
- Wei Hu (1997), The Initial-boundary Value Problem for Higher Order Differential Operators on Lipschitz Cylinders (Advisor: R. Brown).
- John Prather (1997), Geometric Properties of the Hadamard Product (Advisor: T. Suffridge).
- Michael Dorff (1997), The Inner Mapping Radius and Construction of Harmonic, Univalent Mappings of the Unit Disk (Advisor: T. Suffridge).
- Robert Robertson (1996), An inverse boundary value problem in linear elasticity (Advisor: P. Hislop).
- John Tolle (1996), Location of Inhomogeneities in Elastic Media (Advisor: R. Gariepy).
- Ron Vandenhouten (1996), Stability for the Biharmonic and Polyharmonic Obstacle Problems (Advisor: D. R. Adams).
- Kevin Roper (1995), Convexity Properties of Holomorphic Mappings in C (Advisor: T. Suffridge).
- Evelyn Pupplo-Cody (1992), A Structural Formula for a Class of Typically Real Functions and Some Consequences (Advisor: T. Suffridge).
- Barbara Hatfield (1991), Gradient Estimates for Capillary Problems (Advisor: R. Gariepy).
- Hi Jun Choe (1989), Regularity for Minimizers of Certain Singular Functionals (Advisor: R. Gariepy).