Functional Analysis
Texas A&M University

While it is impossible to give an exact definition of such a vital area as functional analysis, its leitmotiv is the amalgamation of algebraic and topological structures: vector spaces endowed with topologies, operators between these vector spaces, and algebras of operators. These structures are found at the core of many fields inside and outside of mathematics, for example quantum physics, engineering, differential equations, numerical analysis. In addition, there are modern day interactions with fields such as algebraic topology, finance, geometry, probability, and signal processing.

Our functional analysis group has diverse interests: Banach spaces, operator spaces, C*-algebras, von Neumann algebras, nonlinear functional analysis. Furthermore, members of our group are interested in applications to probability theory, free probability theory, wavelets, mathematical finance, dynamical systems, and convex geometry.

Our weekly seminar is devoted to the study of several topics in functional analysis, including normed spaces and operators on them, noncommutative theory, and probabilistic methods.

The functional analysis and probability group also organizes a workshop every summer.

Faculty
Michael Anshelevich
Operator algebras, free probability
Lewis Bowen
Ergodic theory, geometry, dynamics
Ron Douglas
Operator algebras, operator theory
Ken Dykema
Operator algebras, free probability
Ciprian Foias
Operator theory, PDE
William B. Johnson
A.G. & M.E. Owen Chair of Mathematics Banach spaces, nonlinear functional analysis, probability theory
David Kerr
Operator algebras, dynamical systems
David Larson
Operator algebras, wavelets
Dan Lewis
Banach spaces
Dmitry Panchenko
Probability theory
Grigoris Paouris
Convex geometry
Carl M. Pearcy, Jr.
Operator theory
Gilles Pisier
A.G. & M.E. Owen Chair of Mathematics
Probability theory, harmonic analysis, operator theory, C*-algebras
Alex Poltoratski
Harmonic and complex analysis
Thomas Schlumprecht
Banach spaces, probability theory, convex geometry, mathematics in finance
Roger Smith
von Neumann algebras, C*-algebras, operator theory
Joel Zinn
Probability limit theorems, probability inequalities, convex geometry
Visiting Faculty
Graduate Students
Aaron Bailey
Javier Alejandro Chavez Dominguez
Mitch Hitchcock
Kate Jushenko
Misko Mitkovski
Thanh-Hao Nguyen
Sofia Ortega-Castillo
Timothy Rainone
Daniel Redelmeier
Francisco Torres-Ayala