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Vaughan, Mary

Mary C Vaughan

Department of Mathematics

PDEs & Harmonic Analysis: nonlocal equations, fractional operators, regularity theory


Office Location

Academic Positions

  • RTG Postdoctoral Scholar
    The University of Texas at Austin, Austin, TX, 2020-present


  • Ph.D. in Mathematics
    Iowa State University, Ames, IA, 2015-2020
  • B.S. in Mathematics
    University of Wisconsin - La Crosse, La Crosse, WI, 2011-2015

Partial Differential Equations & Harmonic Analysis

  • Nonlocal equations
  • Fractional derivatives
  • Regularity theory
  • Harnack inequalities
  • Monge-Ampère equations
  • Materials modeling
  • Peridynamics

You can find My papers and preprints on the ArXiv.

  1. Fractional elliptic equations in nondivergence form: definition, applications and Harnack inequality 
    preprint, 2021 (with P. R. Stinga)

  2. One-sided fractional derivatives, fractional Laplacians, and weighted Sobolev spaces
    Nonlinear Anal., 2020 (with P. R. Stinga)

  3. The dual Kaczmarz algorithm
    Acta Appl Math., 2020 (with A. Aboud, E. Curl, S. N. Harding, and E. S. Weber)

Current Course

  • Spring 2021: M 427L - Advanced Calculus for Applications II

Previous courses at the University of Texas at Austin

  • Fall 2020: M 408L - Integral Calculus

Previous courses at Iowa State University

Instructor of Record

  • Summer 2019: Math 266/7 - Elementary Differential Equations & Laplacs Transforms
  • Spring 2018: Math 166 - Calculus II
  • Summer 2017: Math 166 - Calculus II

Teaching Assistant

  • Fall 2017: Math 165 - Calculus I (Team-Based Learning)
  • Fall 2016: Math 160 - Survey of Calculus
  • Spring 2016: Math 265 - Calculus III
  • Fall 2015: Math 166 - Calculus II