## 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.

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

Michael Brannan — Operator algebras, free probability, non-commutative,

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.

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.

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.

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.