Faculty Research Areas in the Field of Mathematics

(Home departments are indicated in parentheses for faculty who are not in the Department of Mathematics.)

Algebra

• Yuri Berest - Mathematical physics and algebraic geometry
• Louis Billera - Geometric and algebraic combinatorics
• Kenneth S. Brown - Algebra, topology, group theory
• R. Keith Dennis - Commutative and non-commutative algebra, algebraic K-theory, group theory, mathematical bibliography
• Martin Kassabov - Combinatorial group theory
• Allen Knutson - Algebraic geometry, algebraic combinatorics, algebraic groups
• Irena Peeva - Commutative algebra and algebraic geometry
• Ravi Ramakrishna - Algebraic number theory
• Timothy Riley - Geometric group theory
• Shankar Sen - Algebraic number theory
• Birgit E. Speh - Lie groups, automorphic forms, representation theory
• Michael E. Stillman - Algebraic geometry, computational algebra
• Karen Vogtmann - Topology, geometric group theory

Analysis

• Xiaodong Cao - Differential geometry and geometric analysis
• Leonard Gross - Functional analysis, constructive quantum field theory
• Timothy Healey - Nonlinear elasticity, nonlinear analysis, partial differential equations
• John H. Hubbard - Analysis, differential equations, differential geometry
• Camil Muscalu - Analysis and partial differential equations
• Laurent Saloff-Coste - Analysis, potential theory, stochastic processes
• Robert S. Strichartz - Harmonic analysis, partial differential equations, analysis on fractals

Combinatorics

• Louis Billera - Geometric and algebraic combinatorics
• Allen Knutson - Algebraic geometry, algebraic combinatorics, algebraic groups
• Lionel Levine - Probability and combinatorics
• Edward Swartz - Combinatorics and discrete geometry

Differential Equations / Dynamical Systems

• John M. Guckenheimer - Dynamical systems
• John H. Hubbard - Analysis, differential equations, differential geometry
• Yulij Ilyashenko - Dynamical systems and complex foliations
• Richard Rand - Nonlinear dynamics
• John Smillie - Dynamical systems
• Steven Strogatz - Nonlinear dynamics applied to physics, biology, and social science
• Alexander Vladimirsky - Numerical methods, dynamical systems, nonlinear PDEs, control theory

Differential Geometry

• Xiaodong Cao - Differential geometry and geometric analysis
• Tara Holm - Symplectic geometry
• John H. Hubbard - Analysis, differential equations, differential geometry
• Reyer Sjamaar - Symplectic geometry

Geometry

• Robert Connelly - Discrete geometry, computational geometry and the rigidity of discrete structures
• Edward Swartz - Combinatorics and discrete geometry

Interdisciplinary

• R. Keith Dennis - Commutative and non-commutative algebra, algebraic K-theory, group theory, mathematical bibliography
• Timothy Healey - Nonlinear elasticity, nonlinear analysis, partial differential equations
• Dexter Kozen (Computer Science) - Computational theory, computational algebra and logic, logics and semantics of programming languages
• Anil Nerode - Mathematical logic, computability theory, computer science, mathematics of AI, control engineering, quantum control of macroscopic systems
• Richard Rand - Nonlinear dynamics
• James Renegar (OR&IE) - Optimization algorithms
• Steven Strogatz - Nonlinear dynamics applied to physics, biology, and social science
• Alexander Vladimirsky - Numerical methods, dynamical systems, nonlinear PDEs, control theory

Lie Groups

• Dan M. Barbasch - Representation theory of reductive Lie groups
• Allen Knutson - Algebraic geometry, algebraic combinatorics, algebraic groups
• Reyer Sjamaar - Symplectic geometry
• Birgit E. Speh - Lie groups, automorphic forms, representation theory

Logic

• Dexter Kozen (Computer Science) - Computational theory, computational algebra and logic, logics and semantics of programming languages
• Justin Moore - Set theory, mathematical logic, and set theoretic topology
• Anil Nerode - Mathematical logic, computability theory, computer science, mathematics of AI, control engineering, quantum control of macroscopic systems
• Richard A. Shore - Mathematical logic, recursion theory, effective and reverse mathematics, set theory

Mathematical Physics

• Yuri Berest - Mathematical physics and algebraic geometry
• Leonard Gross - Functional analysis, constructive quantum field theory

PDE / Numerical Analysis

• Timothy Healey - Nonlinear elasticity, nonlinear analysis, partial differential equations
• Camil Muscalu - Analysis and partial differential equations
• Alfred H. Schatz - Numerical solutions of partial differential equations
• Alexander Vladimirsky - Numerical methods, dynamical systems, nonlinear PDEs, control theory
• Lars B. Wahlbin - Numerical solutions of partial differential equations

Probability

• Lionel Levine - Probability and combinatorics
• Laurent Saloff-Coste - Analysis, potential theory, stochastic processes

Statistics

• J.T. Gene Hwang - Statistics, confidence set theory
• Michael Nussbaum - Mathematical statistics

Topology

• Kenneth S. Brown - Algebra, topology, group theory
• Allen Hatcher - Geometric topology
• Tara Holm - Symplectic geometry
• Peter J. Kahn - Symplectic topology/geometry
• Martin Kassabov - Combinatorial group theory
• Timothy Riley - Geometric group theory
• Karen Vogtmann - Topology, geometric group theory
• James E. West - Geometric topology, infinite-dimensional topology

Last modified:January 15, 2013