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Home » Conrad Plaut

Conrad Plaut

Conrad Plaut

November 3, 2023 by

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ADDRESS
320 Ayres Hall
Email
cplaut@utk.edu
Elements Profile

Conrad Plaut

Professor

I am a Professor and former Head of the Mathematics Department at the University of Tennessee. My current research is mostly related to “topology at scale”, which seeks to apply metric measurements to classical algebraic topology. One method to do so is discrete homotopy theory, which replaces curves and homotopies in standard algebraic topology with discrete chains and homotopies. One obtains covering spaces and fundamental groups “at a scale”. Applications include explicit fundamental group finiteness theorems and generalizations of the Covering Spectrum, which is a significant subset of the Length Spectrum. Recently I have found that these ideas are related applied topology, specifically persistent homology in data analysis. My most recent work also includes applying these ideas to resistance metrics on fractals, for which there is a well-defined notion of Laplace operator but generally no non-constant rectifiable curves. The relationship between the Laplace spectrum and Length Spectrum has been a subject of research for over fifty years, and there remain some interesting open questions. The generalized spectra in my recent work provide proxies for the Length Spectrum in such spaces when there is no actual length to work with. In my career I have taught more than 25 different courses at all levels from freshman to honors undergraduate, graduate, and advanced graduate, including: calculus , matrix algebra, geometry, topology, algebra, analysis, and one of my favorites, Introduction to Abstract Math. Over the past 20 years I have served our department as Undergraduate Associate Head, Director of UTK Math Honors, and Department Head (2012-2022). My career total of grants (principally from the National Science Foundation) is more than $1.5 Million.

Education

PhD, The University of Maryland

Research

  • Differential Geometry
    • Riemannian Geometry
    • Metric Geometry/Alexandrov Spaces
    • Geometry of Fractals
  • Topology
    • Discrete Homotopy Theory
    • Topological Groups
    • Generalized Covering Spaces

Department of Math

College of Arts and Sciences

227 Ayres Hall
1403 Circle Drive
Knoxville TN 37996-1320

Email: math_info@utk.edu

Phone: 865-974-2461

The University of Tennessee, Knoxville
Knoxville, Tennessee 37996
865-974-1000

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