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Analysis is one of the fundamental branches of mathematics, with powerful applications throughout mathematics as well as in the natural sciences and industry. Here at Virginia Tech we have faculty working on various topics within analysis or using the tools of analysis to study applications. Areas covered include dynamical systems, erogdic theory, geometry, harmonic analysis, mathematical physics and partial differential equations.

picture for analysis research group

In the picture above, professor Malabika Pramanik (Univrsity of Brittish Columbia) gives a talk at the Mid-Atlantic Analysis Meeting (2018) hosted by Virginia Tech.

Research Advisors for Analysis

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    Alex Elgart profile picture
    Alex Elgart , bio

    Professor Elgart primary research area is mathematical physics. The mathematical tools he uses mostly come from analysis and probability.

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    Peter Haskell profile picture
    Peter Haskell , bio

    Professor Haskell conducts research in index theory, which is the study of the connections between analysis and topological or geometric structures.

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    Jose Ramon Madrid Padilla profile picture
    José Ramón Madrid Padilla , bio

    Professor Madrid works in harmonic analysis and its connections to related fields such as number theory, combinatorics, ergodic theory and PDE.

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    Eyvindur Paisson profile picture
    Eyvindur Ari Palsson , bio

    Associate Professor Palsson conducts research in harmonic analysis, geometric measure theory, combinatorics, number theory and partial differential equations.

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    Went Sun profile picture
    Wenbo Sun , bio

    Assistant Professor Wenbo Sun works on the problems lying at the interaction of ergodic theory, combinatorics, and number theory.

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    Yun Yang profile picture
    Yun Yang , bio

    Assistant professor Yang conducts research in ergodic theory and dynamical systems.

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    Guher Camliyurt profile picture
    Guher Camliyurt , bio

    Dr. Camliyurt's research interests include mathematical fluid dynamics, nonlinear waves, and unique continuation problems for general elliptic and parabolic PDEs.

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    Andreas Deuchert's profile picture
    Andreas Deuchert (starting Fall 2024) , bio

    My main research interests are mathematical quantum mechanics and quantum statistical mechanics. In my work, I develop analytic, functional analytic, and probabilistic methods with a focus on variational techniques to study mathematical problems originating from solid-state physics.

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    Sarah Reznikoff profile picture
    Sarah Reznikoff , bio

    Professor Reznikoff is Department Chair and Professor. Her research in analysis currently focuses on groupoid representations of C*-algebras.

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    Sho-Ming Sun profile picture
    Shu-Ming Sun , bio

    Professor Sun's research interests include the mathematical theory of fluid mechanics, the theory of partial differential equations, and applied nonlinear analysis.

Researchers in Analysis

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    Artem Hulko profile picture
    Artem Hulko , bio

    Dr. Hulko conducts research in mathematical analysis, particularly in the area of non-self-adjoint operators on Hilbert spaces. He is also interested in Game Theory.

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    Brian Cook profile picture
    Brian Cook , bio

    Visiting Assistant Professor Cook's research focuses on arithmetic harmonic analysis, extremal combinatorics & additive/analytic number Theory.

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    Diego Calle profile picture
    Diego Calle , bio

    Professor Calle conducts research in the structure of closed algebraic ideals in the algebra L(X) where X is a Banach space.

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    Fanfchi Yan's profile picture
    Fangchi Yan , bio

    Dr. Yan studies partial differential equations (PDEs) that are motivated from the modeling of physical phenomena and real-world problems in general. His research focuses on the problem of well-posedness for nonlinear dispersive equations, including the Korteweg-de Vries (KdV) equation and the nonlinear Schrödinger (NLS) equation.

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    Josh Clemons profile picture
    Josh Clemons , bio

    Dr. Clemons does research in the overlapping ares of complex dynamical systems, ergodic theory, and topology and teaches a wide variety of traditional courses in differential equations and combinatorics.

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    Stanca Ciupe profile picture
    Nilton Garcia Hilares , bio

    Dr. Hilares' research interests lie in computational and applied linear algebra.

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    Numann Malik profile picture
    Numann Malik , bio

    Dr. Malik's interests lie in nonlinear partial differential equations; specifically the asymptotic behavior, orbital stability, and effective dynamics, of dark solitons that arise from defocusing nonlinear Schrodinger equations.

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    Ziqiang Li , bio

    Visiting Assistant Professor Dr. Li researches algorithms on the 2-sphere for the use of computational geometry, numerical methods, and analytical cartography. On the side, he studies flows in microfluidic systems.

Recently Retired Faculty

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    Joseph Ball profile picture
    Joseph Ball , bio

    Professor Ball conducts research in Hilbert-space operator theory and operator algebras, exploring connections with multivariable function theory and engineering systems theory.

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    Martin Day profile picture
    Martin Day , bio

    Professor Day's research focused on applications of the large deviations analysis of stochastic processes, specifically the classical exit problem for diffusions. Later work involved fluid limit analysis of queueing processes.

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    Jong Uhn Kim , bio

    Professor Kim's research has been in analysis of partial differential equations which arise in fluid mechanics and elasticity.

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    Michael Renardy profile picture
    Michael Renardy , bio

    Professor Renardy's research is in partial differential equations and applications to fluid mechanics, in particular viscoelastic flows.

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    Robert Rogers profile picture
    Bob Rogers , bio

    Professor Rogers studies continuum mechanics and nonconvex problems in partial differential equations. He also studies models of acoustics.

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    John Rossi profile picture
    John Rossi , bio

    Professor Rossi conducts research in complex function theory with specialties in value distribution theory and potential theory.