University of Illinois at Urbana-ChampaignDepartment of Mathematics
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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
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, Teichmüller theory, quasiconformal maps, complex dynamics.
Dirk Hundertmark Analytic, probabilistic problems in math physics; eigenvalue moments for Schrödinger operators; spectral theory of random Schrödinger operators and statistical mechanics.
Marius Junge Banach and operator spaces, operator algebras, noncommutative probability.
Ely Kerman Hamiltonian dynamics and symplectic topology
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.
Joseph B. Miles Entire and meromorphic functions, complex function theory, classical analysis.
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

Pierre Fima

Operator algebras and quantum groups

Jiri Lebl

Several complex variables, real and complex geometry

John Mackay

Metric geometry, analysis on metric spaces, geometric group theory, hyperbolic groups.

Tao Mei

Harmonic analysis for operator(matrix) valued functions, noncommutative martingales, operator space
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
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.
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.
Kenneth B. Stolarsky Exponential polynomials, location of zeros, 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.
Anthony L. Peressini Functional analysis, math. education.
Horacio A. Porta Analysis.
J. Jerry Uhl Jr. Vector measures, Banach spaces, functional analysis, measure theory.
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.

Lynn McLinden Convex, nonsmooth and nonlinear analysis, and their application to optimization, variational and equilibrium problems.

 

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