All Research

For more information, please see my homepage https://math.unm.edu/~schroder/index.html
Prof. Skripka has been doing research on noncommutative analysis with applications to mathematical physics and noncommutative geometry, and recently started research on quantum and high-dimensional statistics. Some of her contributions to multilinear operator integration and its applications are explained in the featured article "Untangling Noncommutativity with Operator Integrals" in the Notices of the AMS and summarized in the research monograph "Multilinear Operator Integrals: Theory and Applications". Skripka's research has been recognized with an NSF CAREER award and the Ruth I. Michler Memorial Prize.

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.

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.

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

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.
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.
Prof. Zinchenko's research is in analysis and mathematical physics with focus on problems in approximation and spectral theory. His work in spectral theory concerns spectral properties and inverse problems for Sturm-Liouville, Schrodinger, and Jacobi operators. Zinchenko's work in approximation theory focuses on properties of extremal polynomials such as Chebyshev and orthogonal polynomials.
A list of recent publications is available on Google Scholar.
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