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Texas A&M University
Mathematics

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 Noncommutative Functions 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

Florent Baudier
Metric space and Banach space geometry

Gregory Berkolaiko
Spectral theory of differential operators on graphs

Michael Brannan
Functional analysis, quantum groups, quantun information

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

Ken Dykema
Operator algebras, free probability

Simon Foucart
Compressed sensing and approximation theory

Stephen Fulling
PDE, applications in theoretical physics

Boris Hanin
Probability theory, spectral asymptotics, deep learning

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

Jeffrey Kuan
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

Li Gao
Hao Guo
Richard Lynch
Robert Rahm
Jurij Volcic
Shilin Yu

Graduate Students

Jimmy Corbin
Jintao Deng
Parker Duncan
Kari Eifler
Priyanga Ganesan
John Griffin
Amanda Hoisington
Sheagan John
Amudhan Krishnaswamy-Usha
Mingyu Liu
Xin Ma
Jacob Mashburn
Wonhee Na
Tristan Pace
Xiaoyu Su
Krzysztof Swiecicki
Geng Tian
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, 2018.