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