# Faculty Research Areas

## ALGEBRA AND LOGIC

**Ralph McKenzie**, Ph.D. (University of Colorado, Boulder)

Algebra and Logic

**Michael L. Mihalik**, Ph.D. (SUNY, Binghamton)

Geometric Group Theory

**Andrew Moorhead**, Ph.D. (University of Colorado, Boulder)

Algebraic Systems, Algebra and Logic

**Alexander Yu. Ol’shanskiy**, Ph.D. (Moscow State University, Russia)

Group Theory

**Denis Osin**, Ph.D. (Moscow State University, Russia)

Geometric Group Theory

**Adam Prenosil**, Ph.D. (Charles University, Prague)

Operator Algebras, Functional Analysis

**John G. Ratcliffe**, Ph.D. (University of Michigan)

Geometric Group Theory

**Mark V. Sapir**, Ph.D. (Moscow State Pedagogical Institute, Russia)

Group Theory, Algorithmic Problems in Algebra

**Stephen G. Simpson**, Ph.D. (Massachusetts Institute of Technology)

Mathematical Logic, Foundations of Mathematics

**Steven T. Tschantz**, Ph.D. (University of California, Berkeley)

Logic, Universal Algebra, Computer Algebra

**Constantine Tsinakis**, Ph.D. (University of California, Berkeley)

Ordered Algebraic Structures, Logic

## ANALYSIS AND APPLIED ANALYSIS

See also Noncommutative Geometry and Operator Algebras Research Group

**John F. Ahner**, Ph.D. (University of Delaware)

Integral Equation Methods in Scattering and Potential Theory, Fractional Calculus and Mixed Boundary Value Problems, Elasticity Theory, Conservation Laws

**Akram Aldroubi**, Ph.D. (Carnegie Mellon University)

Harmonic Analysis, Sampling Theory, Mathematical Biology

**Scott Atkinson**, Ph.D. (University of Virginia)

Operator Algebras, Functional Analysis

**Dietmar Bisch**, Ph.D. (University of California, Los Angeles)

Operator Algebras

**Cheng Chu**, Ph.D. (Washington University, St. Louis)

Operator Theory, Complex Analysis

**Philip S. Crooke III**, Ph.D. (Cornell University)

Biomathematics

**Emmanuele DiBenedetto**, Ph.D. (University of Texas, Austin)

Partial Differential Equations, Mathematical Biology

**Marcelo Disconzi**, Ph.D. (SUNY, Stony Brook)

Partial Differential Equations, Mathematical Physics

**Cain Edie-Michell**, Ph.D. (Australian National University)

Operator Theory

**Douglas P. Hardin**, Ph.D. (Georgia Institute of Technology)

Harmonic Analysis, Potential Theory, Fractal Geometry

**Vaughan Jones**, Ph.D.(University of Geneva, Switzerland)

Von Neumann Algebras

**Chenyun Luo**, Ph.D. (Johns Hopkins University)

Partial Differential Equations

** Giusy Mazzone**, Ph.D. (University of Pittsburgh)

Partial Differential Equations, Fluid Mechanics

**Robert McRae**, Ph.D. (Rutgers University)

Vertex Operator Algebras

**Brent Nelson**, Ph.D. (University of California, Los Angeles)

Operator Algebras, Free Probability

**Jesse Peterson**, Ph.D. (University of California, Los Angeles)

Operator Algebras, Ergodic Theory

**Alexander M. Powell**, Ph.D. (University of Maryland)

Applied and Computational Harmonic Analysis, Mathematical Signal Processing

**Lauren Ruth**, Ph.D. (University of California, Riverside)

Von Neumann Algebras, Automorphic Forms, Representation Theory

**Edward B. Saff**, Ph.D. (University of Maryland)

Complex Analysis, Potential Theory, Approximation Theory

**Gieri Simonett**, Ph.D. (University of Zurich, Switzerland)

Partial Differential Equations, Free Boundary Problems

**Jared Speck**, Ph.D. (Rutgers University)

Partial Differential Equations, Mathematical Physics, Relativity

**Glenn F. Webb**, Ph.D. (Emory University)

Mathematical Biology, Population Dynamics, Models of Tumor Growth, Differential Equations

**Dechao Zheng**, Ph.D. (SUNY, Stony Brook)

Functional Analysis, Operator Theory, Complex Analysis, Harmonic Analysis

## COMPUTATIONAL MATHEMATICS

See also Center for Constructive Approximation

**Akram Aldroubi**, Ph.D. (Carnegie Mellon University)

Wavelet Theory, Image and Signal Processing

**Douglas P. Hardin**, Ph.D. (Georgia Institute of Technology)

Inverse Problems, Wavelet Theory, Fractal Geometry

**Woden Kusner**, Ph.D. (University of Pittsburgh)

Discrete Geometry, Geometric Optimization

**Mike Neamtu**, Ph.D. (University of Twente, Netherlands)

Approximation Theory, Spline Theory, Numerical Analysis, Financial Mathematics

**Alexander M. Powell**, Ph.D. (University of Maryland)

Applied and Computational Harmonic Analysis, Mathematical Signal Processing

**Edward B. Saff**, Ph.D. (University of Maryland)

Approximation Theory, Complex Analysis, Potential Theory

**Larry L. Schumaker**, Ph.D. (Stanford University)

Approximation Theory, Spline Theory, Computer-Aided Design

## GEOMETRY AND TOPOLOGY

See also Noncommutative Geometry and Operator Algebras Research Group

**Anna Marie Bohmann**, Ph.D. (University of Chicago)

Algebraic Topology, Homotopy Theory

**Jonathan Campbell**, Ph.D. (Stanford University)

Algebraic Topology

**Marcelo Disconzi**, Ph.D. (SUNY, Stony Brook)

Geometric Analysis

**Spencer D. Dowdall**, Ph.D. (University of Chicago)

Geometric Topology, Geometric Group Theory

**Matthew Haulmark**, Ph.D. (University of Wisconsin, Milwaukee)

Geometric Group Theory

**C. Bruce Hughes**, Ph.D. (University of Kentucky)

Geometric and Algebraic Topology, Manifold Theory, Controlled Topology, Stratified Spaces

**Gennadi Kasparov**, Ph.D. (Moscow State University, Russia)

K-theory, Noncommutative Geometry, Operator Algebras

**Michael L. Mihalik**, Ph.D. (SUNY Binghamton)

Algebraic Topology, Low Dimensional Topology, Geometric Group Theory

**Alexander Yu. Ol’shanskiy**, Ph.D. (Moscow State University, Russia)

Geometric Group Theory

**Denis Osin**, Ph.D. (Moscow State University, Russia)

Geometric Group Theory

**Rares Rasdeaconu**, Ph.D. (SUNY, Stony Brook)

Differential and Symplectic Geometry

**John G. Ratcliffe**, Ph.D. (University of Michigan)

Low Dimensional Topology, Hyperbolic Geometry

**Mark V. Sapir**, Ph.D. (Moscow State Pedagogical Institute, Russia)

Geometric Group Theory, Algorithmic Problems in Algebra

**Jared Speck**, Ph.D. (Rutgers University)

Geometric Analysis

**Ioana Suvaina**, Ph.D. (SUNY, Stony Brook)

Differential Geometry, Kahler Geometry, Seiberg-Witten Theory and Symplectic Topology

**Steven T. Tschantz**, Ph.D. (University of California, Berkeley)

Group Theory, Hyperbolic Geometry

**Grace Work**, Ph.D. (University of Illinois Urbana-Champaign)

Hyperbolic Geometry, Dynamics

## GRAPH THEORY AND COMBINATORICS

**Alexander Cameron**, Ph.D. (University of Illinois, Chicago)

Combinatorics, Graph Theory

**Paul H. Edelman**, Ph.D. (Massachusetts Institute of Technology)

Algebraic Combinatorics, Geometric Combinatorics, Cooperative Games

**Mark N. Ellingham**, Ph.D. (University of Waterloo, Canada)

Graph Theory, Paths and Cycles, Topological Graph Theory

**Jakayla Robbins**, Ph.D. (University of Kentucky)

Matroid Representation Theory, Oriented Matroids, Combinatorial Optimization

**Larry Rolen**, Ph.D. (Emory University)

Theory of Partitions

**Stephen G. Simpson**, Ph.D. (Massachusetts Institute of Technology)

Infinitary Combinatorics, Ramsey Theory

## MATHEMATICAL BIOLOGY

**Philip Crooke III**, Ph.D. (Cornell University)

Mathematical Biology

**Emmanuele DiBenedetto**, Ph.D. (University of Texas, Austin)

Mathematical Biology

**Glenn F. Webb**, Ph.D. (Emory University)

Mathematical Biology, Population Dynamics, Models of Tumor Growth

**William Holmes**, Ph.D. (Indiana University, Bloomington)

Mathematical Biology

**Yixiang Wu**, Ph.D. (University of Louisiana, Lafayette)

Partial Differential Equations, Mathematical Biology

## NUMBER THEORY AND ALGEBRAIC GEOMETRY

**Rares Rasdeaconu**, Ph.D. (SUNY, Stony Brook)

Algebraic Geometry

**Larry Rolen**, Ph.D. (Emory University)

Number Theory, Modular Forms, Arithmetic Geometry