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Functional Analysis at 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, Engeneering, 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 convex geometry, dynamical systems, free probability theory, mathematical finance, mathematical physics, probability theory and wavelets.

Our Linear Analysis Seminar is devoted to the study of several topics in functional analysis, including normed spaces and operators on them, noncommutative theory, and probabilistic methods. Related seminars include the Banach Spaces Seminar, the Free Probabiltiy Seminar, the Groups and Dynamics Seminar, the Probabiltiy Seminar and the Several Complex Variables Seminar. The analysis and probability group also organizes a workshop every summer.

Faculty

Michael Anshelevich
Operator algebras, free probability

Gregory Berkolaiko
Spectral theory of differential operators on graphs

Michael Brannan
Functional analysis, Quantum groups

Ron DeVore
Walter E. Koss Professor of Mathematics
Approximation theory, numerical analysis

Ron Douglas
Operator algebras, operator theory

Ken Dykema
Operator algebras, free probability

Simon Foucart
Compressed sensing and approximation theory

Stephen Fulling
PDE, applications in theoretical physics

William B. Johnson
A.G. & M.E. Owen Chair of Mathematics
Banach spaces, nonlinear functional analysis,
probability theory

David Kerr
Operator algebras, dynamical systems

Peter Kuchment
Spectral theory, PDE

David Larson
Operator algebras, wavelets

Grigoris Paouris
Convex geometry

Gilles Pisier
A.G. & M.E. Owen Chair of Mathematics
Probability theory, harmonic analysis,
operator theory, C*-algebras

Alex Poltoratski
Harmonic and complex analysis

Eviatar Procaccia
Probability theory

Kamran Reihani
C*-algebras, dynamics, noncommutative geometry

Thomas Schlumprecht
Banach spaces, probability theory, convex geometry,
mathematics in finance

Roger Smith
von Neumann algebras, C*-algebras, operator theory

Robin Tucker-Drob
Dynamical systems and group theory

Zhizhang Xie
K-theory of operator algebras, index theory, noncommutative geometry

Guoliang Yu
Thomas W. Powell Chair in Mathematics
Noncommutative geometry, K-theory, index theory,
topology and analysis of manifolds,

Visiting Faculty

Florent Baudier
Benben Liao
Richard Lynch
Pavlos Motakis
Robert Rahm
Kun Wang
Yuan Zhang

Graduate Students

David Buzinksi
Jimmy Corbin
Jintao Deng
Kari Eifler
Priyanga Ganesan
John Griffen
Amudhan Krishnaswamy-Usha
Xin Ma
Mehrzad Monzavi
Wonhee Na
Jospeh Noles
Suleyman Kagan Samurkas
Krzysztof Swiecicki
Andrew Swift
Yi Wang
Konrad Wrobel
Jiayan Ye

Emeritus Faculty

Dan Lewis,
Banach spaces

Ciprian Foias
Operator theory, PDE

Carl M. Pearcy, Jr.
Operator theory

Joel Zinn
Probability limit theorems, probability inequalities, convex geometry

Last update: Sept. 1, 2017.