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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 leitmotif 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, or Numerical Analysis. In addition, there are modern day interactions with fields such as Algebraic Topology, Geometry, Probability, Signal Processing, Quantum Information, and Machine Learning.

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

Seminars affiliated with the group include the Seminar on Banach and Metric Space Geometry and the Working Seminar on Banach and Metric Spaces, the Noncommutative Geometry Seminar, the Free Probability and Operators Seminar, the Groups and Dynamics Seminar, the Mathematical Physics and Harmonic Analysis Seminar and the Stochastic Processes Seminar. The analysis and probability group also organizes the Workshop in Analysis and Probability every summer. The Douglas and Foias endowed lecture series regularly feature distinguished speakers in Functional Analysis.

Faculty

Patricia Alonso Ruiz
Stochastic processes, analysis on metric measure spaces

Michael Anshelevich
Operator algebras, free probability

Dean Baskin
PDE, microlocal analysis

Florent Baudier
Metric space and Banach space geometry

Gregory Berkolaiko
Spectral problems in mathematical physics

Simone Cecchini
Topology and analysis on manifolds, index theory, K-theory

Andrew Comech
Harmonic analysis, spectral theory, partial differential equations

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

Sherry Gong
Low dimensional topology, operator theory

Jeffrey Kuan
Probability theory

Peter Kuchment
Spectral theory, PDE, mathematical physics

David Larson
Operator algebras, frame theory, wavelets

Wencai Liu
Spectral theory, PDE

Jonas Lührmann
Partial differential equations and mathematical physics

Grigoris Paouris
High dimensional probability, asymptotic geometric analysis, convex geometry

Rob Rahm
Harmonic analysis

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

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

Hùng Việt Chu
Yuqing Lin
Qiaochu Ma
Daniel Perales Anaya
Paul Simanjuntak
Jinmin Wang
Yuliia Yershova
Bo Zhu

Emeritus Faculty

Stephen Fulling
PDE, applications in theoretical physics

William B. Johnson
Banach spaces

Dan Lewis,
Banach spaces

Carl M. Pearcy, Jr.
Operator theory

Gilles Pisier
Functional analysis

Graduate Students

Luis E. Aceves
Laura Booton
Bradley Check
Lawrence Dongilli
Valentia Fragkiadaki
Amanda Hoisington
Seth Hoisington
Xuehan Hu
Yi-Chieh Huang
Zhenyu Huang
Milan Jovanovic
Ajay Kumar Karri
Alexandros Kazantzidis
Marshall King
Yongming Li
Jose Lopez Garcia
Ting Lu
Ryan Malthaner
Daniel Mandragona
Hatice Pekmez
Xiaoyu Su
Ryo Toyota
Garrett Tresch
Alex Weygandt
Zhiyuan Yang
Junchen Zhao

Last update: July 2024.