Analysis
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.
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 , bioProfessor Elgart primary research area is mathematical physics. The mathematical tools he uses mostly come from analysis and probability.
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Peter Haskell , bioProfessor Haskell conducts research in index theory, which is the study of the connections between analysis and topological or geometric structures.
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José Ramón Madrid Padilla , bioProfessor 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 Ari Palsson , bioAssociate Professor Palsson conducts research in harmonic analysis, geometric measure theory, combinatorics, number theory and partial differential equations.
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Wenbo Sun , bioAssistant Professor Wenbo Sun works on the problems lying at the interaction of ergodic theory, combinatorics, and number theory.
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Yun Yang , bioAssistant professor Yang conducts research in ergodic theory and dynamical systems.
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Guher Camliyurt , bioDr. 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 , bioMy 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 , bioProfessor Reznikoff is Department Chair and Professor. Her research in analysis currently focuses on groupoid representations of C*-algebras.
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Shu-Ming Sun , bioProfessor 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 , bioDr. 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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Chengcheng Yang , bioI am interested in Geometric Measure Theory.
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Fangchi Yan , bioDr. 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 , bioDr. 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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Nilton Garcia Hilares , bioDr. Hilares' research interests lie in computational and applied linear algebra.
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Samantha Brooker , bioI am a Postdoctoral Associate studying operator algebras and noncommutative geometry.
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Xin Yang , bioI am an instructor whose main research area is Partial Differential Equations.
Recently Retired Faculty
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Joseph Ball , bioProfessor 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 , bioProfessor 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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Terry Herdman , bioDr. Herdman’s research focuses on modeling, analysis, parameter identification and approximations for systems governed by Volterra Integral and Functional Differential Equations.
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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 , bioProfessor Renardy's research is in partial differential equations and applications to fluid mechanics, in particular viscoelastic flows.
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Bob Rogers , bioProfessor Rogers studies continuum mechanics and nonconvex problems in partial differential equations. He also studies models of acoustics.
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John Rossi , bioProfessor Rossi conducts research in complex function theory with specialties in value distribution theory and potential theory.