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All Research

My research interests are in the areas of noncommutative analysis, operator theory, mathematical physics, probability and statistics. For more details see my personal homepage and the featured article "Untangling Noncommutativity with Operator Integrals" in the Notices of the AMS, 2020 or the short note "Operator Integrals in Theory and Applications" in the Notices of the AMS, 2019.

My research is supported by the National Science Foundation CAREER award.

 

Deborah Sulsky
Applied Mathematics

My research is in biomathematics, continuum mechanics and scientific computation. Over the years, I have developed numerical algorithms for studying problems in embryology, population ecology,  suspension flow, fluid mechanics, and solid mechanics. My recent work involves development of the Material-Point Method (MPM) for solving large-deformation continuum mechanics problems.

Applied Mathematics

My research focuses on developing high-performance parallel algorithms for solving challenging applied mechanics and engineering problems. The methods are scalable on modern heterogeneous architectures, which are used to solve large-scale engineering problems. List of publications is on Google Scholar.

Pure Mathematics

My research is in the areas of partial differential equations, analysis and geometry.  I am interested in problems concerning local and non-local differential equations, calculus of variations and unique continuation, geometric analysis (special holonomy geometries, conformal geometry, contact, CR and quaternionic contact structures). I also have used harmonic and complex analysis in questions related to fluid dynamics, local zeta functions and unique continuation. See https://www.unm.edu/~vassilev/ for further details.

Janet Vassilev
Pure Mathematics

My primary research interests are in Commutative Algebra and in particular:

  • Closure/Interior operations and structures induced on rings and modules via these operations
  • Chariacteristic p methods in commutative algebra
  • Local Cohomology
  • Differential operators on affine semigroup rings

 

Helen Wearing
Applied Mathematics

Mathematical biology: I'm broadly interested in using mathematical models to understand the biological processes that shape population and community dynamics, with a particular interest in the ecology and evolution of infectious diseases. My research uses a combination of analytical, statistical and computational tools that are drawn from the fields of dynamical systems and stochastic processes.

Statistics

My primary research interests are in statistical computing, nonparametric function estimation, data mining, time series and mixed models. I am interested in developing new statistical theory and methods and in applying statistical tools to real life problems.

My research interests are in the areas of spectral theory for Schrodinger type operators, Extremal polynomials (e.g., Chebyshev and orthogonal polynomials), approximation theory, and more broadly in analysis and mathematical physics.

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