Analysis

Faculty Members

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.

Denka Kutzarova — Functional analysis (geometry of Banach spaces), approximation theory.

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.

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.

Zhong-Jin Ruan — Operator spaces and operator algebras.

Richard Sowers — Probability theory, stochastic analysis, partial differential equations.

Anush Tserunyan — Descriptive set theory, Borel actions of countable groups, definable equivalence relations, Polish group actions, applications in ergodic theory and topological dynamics.

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

Jing Wang — Fields probability, analysis, and sub-Riemannian geometry. In particular diffusion semigroups on sub-Riemannian manifolds and the related functional inequalities with geometric contents; small time estimations of transition densities of strongly hypoelliptic diffusion processes.

Faculty Members in Related Areas

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.

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.

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.

Joseph B. Miles — Entire and meromorphic functions, complex function theory, classical analysis.

Robert G. Muncaster — Invariant manifolds, asymptotic behavior, nonlinear elasticity, gas theory.

Anthony L. Peressini — Functional analysis, math. education.

Horacio A. Porta — Analysis.

Joseph Rosenblatt — Harmonic analysis, ergodic theory, functional analysis.

Emeriti Faculty in Related Areas

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.