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Konrad Aguilar

  • Expertise

    Expertise

    Konrad Aguilar works in the area of noncommutative/quantum metric geometry, which lies at the intersection of functional analysis, operator algebras, noncommutative geometry and metric geometry. The purpose of this combination is to use tools from all these areas to build a notion of convergence of certain operator algebras that arise as limits. One of the main goals of this area is to then provide new finite-dimensional approximations to infinite-dimensional spaces. However, as a byproduct, this equips certain matrices with new structures, and thus, produces new objects to study in matrix analysis. Aguilar has contributed to noncommutative metric geometry, in part, by studying the operator algebras called approximately finite-dimensional (AF) algebras and enjoys working with undergraduates on the finite-dimensional and matrix aspects of the algebras, which leads to a deeper understanding of these spaces and the area.

    Research Interests

    • Compact quantum metric spaces
    • Quantum Gromov-Hausdorff convergence
    • Finite-dimensional approximations
    • Compact quantum groups

    Areas of Expertise

    • C*-algebras
    • Noncommutative Metric Geometry
    • Functional Analysis
  • Work

    Work

    With Frédéric Latrémolière, Quantum Ultrametrics on AF algebras and the Gromov-Hausdorff propinquity. Studia Mathematica 231 (2015) 2, pp. 149-193, ArXiv: 1511.07114.

    Fell topologies for AF-algebras and the quantum propinquity. Journal of Operator Theory 82 (2019), no. 2, 469--514, ArXiv: 1608.07016.

    With Frédéric Latrémolière, Some applications of conditional expectations to convergence for the quantum Gromov-Hausdorff propinquity. 12 pages, (Accepted 2018) to appear in Banach Center Publications, ArXiv: 1708.00595.

    With Tristan Bice, Standard Homogeneous C*-algebras as compact quantum metric spaces. 32 pages, (Accepted 2018) to appear in Banach Center Publications, ArXiv: 1711.08846.

    With Samantha Brooker, Quantum metrics from traces on full matrix algebras. Involve 12 (2019), no.2, 329--342, ArXiv: 1906.09728.

    With Jens Kaad, The Podleś sphere as a spectral metric space.  Journal of Geometry and Physics 133 (2018), 260--278. ArXiv: 1803.03027.

    Inductive limits of C*-algebras and compact quantum metric spaces. 24 pages, (Accepted 2019) to appear in Journal of The Australian Mathematical Society, ArXiv: 1807.10424.

    With Alejandra López, A quantum metric on the Cantor space. 22 pages, submitted, ArXiv: 1907.05835.

    Quantum metrics on the tensor product of a commutative C*-algebra and an AF C*-algebra. 31 pages, submitted, ArXiv: 1907.07357.

    With Frédéric Latrémolière and Timothy Rainone. Bunce-Deddens algebras as quantum Gromov-Hausdorff distance limits of circle algebras. 37 pages, submitted, ArXiv: 2008.07676.

  • Education

    Education

    Ph.D. in Mathematics
    University of Denver

    M.S. in Mathematics
    University of Denver

    B.S. in Applied Mathematics
    California State Polytechnic University, Pomona

  • Awards & Honors

    Awards & Honors

    Mathematical Association of America (MAA) Project NExT fellow, 2021-2022

    American Mathematical Society and Simons Foundation (AMS-Simons) Travel Grant recipient, 2019-2022