Scholars@Duke

• Background
• 

  Education, Training, & Certifications

  • Ph.D., University of Florida 2020
• 

  Previous Appointments & Affiliations

  • Phillip Griffiths Assistant Research Professor, Mathematics, Trinity College of Arts & Sciences 2020 - 2022
• Expertise
• 

  Subject Headings

  • Applied Topology
• Research
• 

  Fellowships, Supported Research, & Other Grants

  • Summer Graduate Research Fellowship awarded by University of Florida Center for Applied Mathematics 2019
  • Graduate Student Fellowship awarded by University of Florida Informatics Institute 2018 - 2019
  • Special Hausdorff Program awarded by Hausdorff Institute for Mathematics 2017
• Publications & Artistic Works
• 

  Selected Publications

  • Academic Articles

    • Wagner, Alexander, Elchanan Solomon, and Paul Bendich. “Improving Metric Dimensionality Reduction with Distributed Topology,” June 14, 2021.
       Link to Item
    • Wagner, Alexander. “Nonembeddability of persistence diagrams with $p>2$ Wasserstein metric.” Proceedings of the American Mathematical Society 149, no. 6 (March 29, 2021): 2673–77. https://doi.org/10.1090/proc/15451.
       Full Text
    • Solomon, Elchanan, Alexander Wagner, and Paul Bendich. “From Geometry to Topology: Inverse Theorems for Distributed Persistence,” January 28, 2021.
       Link to Item
    • Solomon, Elchanan, Alexander Wagner, and Paul Bendich. “A Fast and Robust Method for Global Topological Functional Optimization.” 24th International Conference on Artificial Intelligence and Statistics (Aistats) 130 (2021): 109-+.
       Link to Item
    • Bubenik, P., and A. Wagner. “Embeddings of persistence diagrams into Hilbert spaces.” Journal of Applied and Computational Topology 4, no. 3 (September 1, 2020): 339–51. https://doi.org/10.1007/s41468-020-00056-w.
       Full Text
    • Bendich, Paul, Peter Bubenik, and Alexander Wagner. “Stabilizing the unstable output of persistent homology computations.” Journal of Applied and Computational Topology, November 9, 2019, 1–30.
       Link to Item

  • Conference Papers

    • Solomon, E., A. Wagner, and P. Bendich. “From Geometry to Topology: Inverse Theorems for Distributed Persistence.” In Leibniz International Proceedings in Informatics, Lipics, Vol. 224, 2022. https://doi.org/10.4230/LIPIcs.SoCG.2022.61.
       Full Text
    • Wagner, Alexander, and Stan Uryasev. “Portfolio Optimization with Expectile and Omega Functions,” n.d.
• Teaching & Mentoring
• 

  Recent Courses

  • MATH 494: Research Independent Study 2023
  • COMPSCI 445: Introduction to High Dimensional Data Analysis 2022
  • MATH 218D-1: Matrices and Vector Spaces 2022
  • MATH 221: Linear Algebra and Applications 2022
  • MATH 393: Research Independent Study 2022
  • MATH 465: Introduction to High Dimensional Data Analysis 2022
  • MATH 493: Research Independent Study 2022
  • MATH 721: Linear Algebra and Applications 2022
  • MATH 765: Introduction to High Dimensional Data Analysis 2022
  • STA 465: Introduction to High Dimensional Data Analysis 2022
  • COMPSCI 434: Topological Data Analysis 2021
  • MATH 411: Topology 2021
  • MATH 412: Topological Data Analysis 2021
  • MATH 711: Topology 2021
  • MATH 713: Topological Data Analysis 2021
• 

  Advising & Mentoring

  • Mentoring undergraduate student Jesse Zhang at Duke University, 2022-
    Mentored undergraduate students David Freeman, Gianfranco Cortes-Arroyo, and Jose Bouza at the University of Florida, 2018-2019.
• Scholarly, Clinical, & Service Activities
• 

  Presentations & Appearances

  • Distributed Persistent Homology: Inverse Theorems and Dimensionality Reduction. ATMCS 10. University of Oxford. June 2022  2022
  • Distributed Persistent Homology: Inverse Theorems and Dimensionality Reduction. ANT-CoG Seminar. UNC Greensboro. February 2022  2022
  • A Topological Heatmap for the Shape of Biological Images. AMS Fall Southeastern Virtual Sectional Meeting. November 2021  2021
  • Learning with Approximate or Distributed Topology. Topological Data Analysis Workshop. April 2021  2021
  • From Geometry to Topology: Inverse Theorems for Distributed Persistence. ACMS Applied Math Seminar. March 2021  2021
  • Nonembeddability of Persistence Diagrams into Hilbert Spaces. ATMCS / AATRN 2020. Applied Algebraic Topology Research Network. August 2020  2020
  • Portfolio Optimization with Expectile and Omega Functions. Winter Simulation Conference. December 2019  2019
  • Embeddings of Persistence Diagrams into Hilbert Spaces. AMS Sectional Meeting. November 2019  2019
  • The Generic Nature of Morse Functions. AMS Spring Southeastern Sectional Meeting. March 2019  2019
  • A Persistent Homology Measure for Morse Functions. Joint Mathematics Meetings. January 2019  2019
  • Stabilizing the location of persistent homology. Algebraic Topology: Methods, Computation and Science. Institute of Science and Technology Austria. June 2018  2018
• 

  Outreach & Engaged Scholarship

  • Facilitator. Julia Robinson Mathematics Festival. September 14, 2019  2019
• 

  Service to the Profession

  • Participant. Faculty Curriculum on Anti-Racism. Duke Office of Faculty Advancement. January 11, 2021 - January 14, 2021  2021

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