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Kevin R. Vixie
Interests and Expertise
- Geometric Analysis, broadly defined
- High Dimensional Geometry
- Data analysis methods using geometric insights
Research
The threads of my research program lie along 3 harmonious directions. The first is geometric analysis broadly defined to be geometric measure theory together with significant parts of variational and harmonic analysis, nonlinear functional analysis, PDEs and hard analysis. The second is the geometry of sets, measures and functions in high or infinite dimensions. Concentration of measure phenomena and the Johnson-Lindenstrauss lemma are important examples. Finally, the third area is the development of prototype (often Matlab) algorithms for data analysis using insights from the first two areas of research.
Examples of research projects past and present include the development of image metrics which ignore unimportant differences, the sharp characterization of minimizers to variational functionals like the L1TV and ROF functionals, sparse dynamic tomography, the flat norm for images and shapes, and the propagation of uncertainty through image and shape analysis methods. The projects range from pure geometric measure theory questions to very applied data analysis problems.
Links
Geometric Measure Theory Course
Contact
- email: vixie@speakeasy.net
- phone: 310 740 2835