Analysis
Graduate Courses
The document Graduate Study in Analysis outlines the general areas of analysis studied here and describes the advanced undergraduate and graduate courses that are offered regularly.
Faculty Members in Analysis
Pierre Albin — Analytic representations of topological invariants, analysis on non-compact or singular spaces, spectral geometry.
Florin Boca — Operator algebras, number theory, mathematical physics.
John P. D'Angelo — Several complex variables, complex geometry, partial differential equations.
Burak Erdogan — Harmonic analysis on Euclidean spaces and PDEs.
Aimo Hinkkanen — One complex variable, Möbius groups, quasiconformal maps, complex dynamics.
Marius Junge — Banach and operator spaces, operator algebras, noncommutative probability.
Ely Kerman — Hamiltonian dynamics and symplectic topology.
Kay Kirkpatrick — Statistical mechanics, probability, differential equations, and applications to physics and biology.
Richard Laugesen — Differential equations, mathematical physics, and complex analysis; specialty - extremal problems.
Xiaochun Li — Hilbert transform along the vector field; Multilinear oscillatory integrals; multilinear Carleson theorem.
Sergiy Merenkov — Geometric theory of conformal and quasiconformal maps, with applications to areas such as geometric group theory and analysis on fractals.
Igor Nikolaev — Quasiconformal mappings, Monge-Ampere equations, regularity problems in Riemannian geometry.
Julian I. Palmore — Dynamical systems, chaos theory, and frameworks for analysis, stability, and verification, validation and visualization of distributed interactive simulations.
Joseph Rosenblatt — Harmonic analysis, ergodic theory, functional analysis.
Zhong-Jin Ruan — Operator spaces and operator algebras.
Richard Sowers — Probability theory, stochastic analysis, partial differential equations.
Alexander E. Tumanov — Several complex variables, differential geometry, partial differenital equations.
Jeremy Tyson — Geometric function theory, quasiconformal maps, analysis in nonsmooth metric spaces, sub-Riemannian geometry.
Jang-Mei Wu — Geometric and Complex Analysis, Potential Theory and Related Problems in Probability and Partial Differential Equations.
Postdocs
Jingwei Guo — Harmonic analysis and analytic number theory.
Faculty Members in Related Areas
Robert Bauer — Stochastic analysis on manifolds.
Bruce C. Berndt — Classical analysis, in particular, as related to Ramanujan's notebooks, infinite series, elliptic and modular functions, special functions, asymptotic series, and contour integration.
Lee DeVille — Stochastic analysis, differential equations, dynamical systems.
Eduard Kirr — Existence and stability of coherent structures in equations from mathematical physics, their coupling with radiation under perturbations, theory and numerical simulation of waves in homogeneous and random media.
Robert G. Muncaster — Invariant manifolds, asymptotic behavior, nonlinear elasticity, gas theory.
Bruce Reznick — Combinatorial methods in analysis, inequalities.
Nikolaos Tzirakis — Harmonic Analysis and Dispersive Partial Differential Equations.
Emeriti Faculty
I. David Berg — Operator theory, spectral theory, almost periodic functions, manifolds with boundary, differential geometry.
Earl R. Berkson — Complex function theory, classical analysis, operator theory, real analysis.
Donald L. Burkholder — Probability theory, stochastic processes, functional analysis, Fourier analysis.
Lester L. Helms — Probability theory, diffusion equations, second-order elliptic partial differential equations, heat equation, stochastic processes.
Robert P. Kaufman — Classical analysis, complex function theory, Hausdorff measure, analytic sets.
Peter A. Loeb — Nonstandard analysis, potential theory, covering theorems, integration theory.
Heinrich P. Lotz — Banach spaces, Banach lattices, positive operators.
Joseph B. Miles — Entire and meromorphic functions, complex function theory, classical analysis.
Anthony L. Peressini — Functional analysis, math. education.
Horacio A. Porta — Analysis.
Emeriti Faculty in Related Areas
Robert Carroll — Transmutation of operators, scattering theory, special functions and integral transformations, inverse problems, symmetric spaces and Lie theory, soliton mathematics.
C. Ward Henson — Relations between analysis and mathematical logic, especially: non-standard analysis, applications of model theory in functional analysis,model theory of Banach space, decision problems and definability problems in analysis, model theoretic properties of the real exponential function.
Lynn McLinden — Convex, nonsmooth and nonlinear analysis, and their application to optimization, variational and equilibrium problems.
Kenneth B. Stolarsky — Exponential polynomials, location of zeros, inequalities.