Analysis Research Group

at the University of Houston

Group Leaders

Dr. David Blecher

Non-Selfadjoint Operator Algebras and Operator Spaces

Dr. Bernhard Bodmann

Wavelets, Frames, and Image Analysis

Dr. Mehrdad Kalantar

Operator Algebras, Topological Groups, and Quantum Groups

Dr. Anna Vershynina

Quantum information theory and science, quantum many-body physics

Research Areas

Functional Analysis is a broad area of modern mathematics that has grown out of, and maintains connections with, multiple diverse topics in science, engineering, and technology. Our group pursues several lines of investigation, including basic research in pure mathematics to improve general understanding of the subject, as well as development of mathematical results that lay the groundwork for applications. A common theme among our group members' work is the study of operators on Hilbert spaces, which may be though of as infinite-dimensional generalizations of Euclidean space.

Operator Algebras

Many important collections of operators have algebraic structure that can be exploited to study all the operators simultaneously. Among other benefits, this algebraic viewpoint allows for the spectral theory of a single operator to be extended to a collection, and it provides a way to generalize the study of continuous functions on a topological space to noncommutative algebras, earning the subject the name "noncommutative topology".

Wavelets and Frames

Wavelets may be visualized as brief wave-like oscillations that can be combined to produce more complicated waves. Decomposing signals into wavelets is useful for both analysis and transmission of the signals, and techniques from Harmonic Analysis and Fourier Analysis are often applied. As a mathematical tool, wavelets can be used to extract information from many different kinds of data, including audio signals, images, and video.

Quantum Groups

Quantum groups include several kinds of noncommutative algebras (or the spaces they act on) that arise in quantum mechanics and theoretical physics. Quantum groups are often viewed as depending on an auxiliary parameter, such as h or q. As this parameter varies, it deforms a commutative algebra of functions into an algebra of functions on a "noncommutative space" (in the spirit of the noncommutative geometry of Alain Connes).

Quantum Information

While classical information is stored in bits of 0 or 1, quantum information is stored in "qubits" operating under two key principles of quantum physics: superposition (meaning each qubit simultaneously represents a 0 and 1 with different probabilities for each), and entanglement (meaning one qubit's state affects the state of another). Using these principles, qubits can process information in ways that are difficult or impossible with classical methods.

Bios of Group Leaders


            Dr. David Blecher
Ph.D., University of Edinburgh in Scotland, 1988
M.Sc., Cambridge University in England, 1985
B.Sc., University of the Witwatersrand, 1983


Dr. Blecher is a professor at the University of Houston. He has published more than 80 research papers in his field and has been the recipient of the UH Award for Excellence in Research and Scholarship. He serves on the editorial boards of the Houston Journal of Mathematics and the Journal of Mathematical Analysis and Applications, and he has also been the recipient of several NSF grants. Dr. Blecher's research interests include Operator Algebras, Operator Spaces, Operator Theory, and Functional Analysis. He is the author of the the following books and monographs:

  • Operator algebras and their modules---an operator space approach by David Blecher and Christian Le Merdy, London Mathematical Society Monographs. New Series, 30. Oxford Science Publications. The Clarendon Press, Oxford University Press, Oxford, 2004. x+387 pp.
  • Categories of operator modules (Morita equivalence and projective modules) by David Blecher, Paul Muhly, and Vern Paulsen, Mem. Amer. Math. Soc. 143 (2000), no. 681, viii+94 pp.
  • The calculus of one-sided M-ideals and multipliers in operator spaces by David Blecher and Vrej Zarikian, Mem. Amer. Math. Soc. 179 (2006), no. 842, viii+85 pp


            Dr. Bernhard Bodmann
Ph.D., University of Florida, 2001
Masters (Diplom), Universität Erlangen, 1997


Dr. Bodmann is a professor at the University of Houston. He has been the recipient of grants from NSF and NSERC. His research interests include uncertainty principles in harmonic analysis, the design of frames for the coding of analog signals, wavelet and filter design, and mathematical physics. Selected papers:

  • Bernhard G. Bodmann and Peter G. Casazza, The road to equal-norm Parseval frames, J. Funct. Anal. 258, 397-420 (2010).
  • Bernhard G. Bodmann, David W. Kribs and Vern I. Paulsen, Decoherence-Insensitive Quantum Communication by Optimal C*-Encoding, IEEE Trans. Inform. Theory 53, 4738-4749 (2007).
  • Bernhard G. Bodmann, Optimal linear transmission by loss-insensitive packet encoding, Appl. Comput. Harmon. Anal. 22, 274-285, (2007).
  • Bernhard G. Bodmann, Manos Papadakis, and Qiyu Sun, An inhomogeneous uncertainty principle for digital low-pass filters, J. Fourier Anal. Appl. 12, 181-211, (2006).
  • Bernhard G. Bodmann, A lower bound for the Wehrl entropy of quantum spin with sharp high-spin asymptotics, Commun. Math. Phys. 250, 287-300, (2004).


            Dr. Mehrdad Kalantar
Ph.D., Carleton University, Canada, 2011
M.Sc., Sharif University, Iran, 2006
B.Sc., Chamran University, Iran, 2004


Dr. Kalantar is an assistant professor at the University of Houston. His research interests include operator algebras, topological quantum groups, noncommutative harmonic analysis, and noncommutative ergodic theory. Selected papers:

  • M. Kalantar and M. Kennedy, Boundaries of Reduced C*-algebras of Discrete Groups, J. Reine Angew. Math. (Crelle's Journal), to appear.
  • M. Kalantar, M. Neufang and Z.-J. Ruan, Realization of Quantum Group Poisson Boundaries as Crossed Products, Bull. Lond. Math. Soc. 46 (2014), no. 6, 1267-1275.
  • J. Crann and M. Kalantar, An Uncertainty Principle for Unimodular Quantum Groups , J. Math. Phys. 55 (2014), 081704.
  • M. Kalantar, A Limit Theorem for Discrete Quantum Groups, J. Funct. Anal. 265 (2013), no. 3, 469-473.


            Dr. Anna Vershynina
Ph.D. University of California, Davis 2012
M.A. University of California, Davis 2012


Dr. Vershynina is an assistant professor at the University of Houston. Her primary research interests lie in the area of quantum information theory. Additionally she does work on quantum computation and quantum many-body physics. Selected papers:

  • E. A. Carlen, A. Vershynina, "Recovery map stability for the Data Processing Inequality", arxiv:1710.02409, 2017 (to appear)
  • A. Vershynina, "Entanglement rates for bipartite open systems", Physical Review A, 92(2):022311, (2015)
  • E. H. Lieb, A. Vershynina, "Upper bound on mixing rates", Quantum Information and Computation, 13(11&12):0986, (2013)
  • B. Nachtergaele, A. Vershynina, V. A. Zagrebnov, "Lieb-Robinson bound and the existence of the thermodynamic limit for the class of irreversible dynamics", AMS Contemporary Mathematics, 552:161, (2011)



            Ahmed Abouserie

      Advisor: Undecided


            Tattwamasi Amrutam

      Advisor: Dr. Mehrdad Kalantar


            Sarah Chehade

      Advisor: Dr. Anna Vershynina


            Dylan Domel-White

      Advisor: Dr. Bernhard Bodmann


            Robert Mendez

      Advisor: Dr. Bernhard Bodmann


            Worawit Tepsan

      Advisor: Dr. David Blecher


            Zhenhua Wang

      Advisor: Dr. David Blecher

Analysis Seminar

                        The Analysis Research Group runs a weekly seminar hosting talks by both internal and external speakers:

Analysis Seminar Webpage

The seminar is open to anyone who wishes to attend.

Theses of Former Students

  • Soha Abdulbaki, Advisor: Vern Paulsen, Thesis: Generalized Sigma-Delta Quantization.
  • Damon Hay, Advisor: David Blecher, Thesis: Non-Commutative Topology and Peak Interpolation for Operator Algebras.
  • Deepti Kalra, Advisor: Vern Paulsen, Thesis: Equiangular Cyclic Frames.

  • Roderick Holmes, Advisor: Vern Paulsen, Thesis: Optimal Frames.
  • Masayoshi Kaneda, Advisor: Vern Paulsen, Thesis: Multipliers and Algebrizations of Operator Spaces.

  • James Solazzo, Advisor: Vern Paulsen, Thesis: Interpolation and Computability.

  • Rajia Khoury, Advisor: Vern Paulsen, Thesis: Closest Matrices in the Space of Doubly Stochastic Matrices.

  • Sarah H. Ferguson, Advisor: Vern Paulsen, Thesis: Ext, Analytic Kernels and Operator Ranges.

  • Chun Zhang, Advisor: Vern Paulsen, Thesis: Representation and Geometry of Operator Spaces.

  • Che-Chen "Peter" Chu, Advisor: Vern Paulsen, Thesis: Finite Dimensional Representations of Function Algebras.

  • Terry Richard Tiballi, Advisor: Vern Paulsen, Thesis: Symmetric Orthogonalization of Vectors in Hilbert Space.

  • Ching-yun Suen, Advisor: Vern Paulsen, Thesis: The Representation Theory of Completely Bounded Maps on C*-algebras.

Contact Information

Department of Mathematics

University of Houston

Mailing Address
3551 Cullen Blvd., Room 641
Philip Guthrie Hoffman Hall
Houston, TX 77204-3008

We are located on the 6th floor of Philip Guthrie Hoffman Hall,
listed as PGH on the UH Campus map.

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