Laura Scull
Research Interests

My research encompasses equviariant algebraic topology, category theory and graph theory.

  • Topology is a kind of geometry that looks at how shapes can stretch and bend into one another. Algebraic topology uses algebra to describe these shapes.
  • Equivariant topology studies spaces which are symmetric in some way. They might be mirror symmetric, or maybe they can rotate around and end up looking the same, like a circle.
  • Category theory is the language mathematicians use to talk about structures which are common to different branches of mathematics. Originally developed to discuss connections between algebra and geometry, categorical structures are now spreading into other areas of mathematics.
  • Graph theory studies discrete structures created by vertices and attached edges.

    I am currently working on applying equivariant techniques to the study of orbifolds. This involves understanding categorical structures such as bicategories of fractions, and also studying geometric groupoids.
    I supervised an undergraduate research project (funded by CURM) during the 2020-21 academic year studying applying ideas from homotopy and category theory to graphs. You can watch their presentation of their work on YouTube.

  • Undergraduate Research with FLC Student Co-Authors:

  • C. Kane, D. Novoa, L. Scull and J. Thompson
    Defining a Zeroth Homotopy Invariant for Graphs
    PUMP Journal of Undergraduate Research vol 3 pp 37--51
    Published Article or Preprint

  • D. Lewis, L. Scull
    Webs of Complete Graphs
    submitted to Minnesota Journal of Undergraduate Mathematics

  • C. Hobbs, K. Martino, L. Scull
    Spider Web Graphs
    submitted to PUMP Journal of Undergraduate Research

  • Other Research

    Under Review

  • C. Farsi, L. Scull, J. Watts
    Bicategories of Action Groupoids
    submitted to Applied Categorical Structures
    arXiv version or preprint

  • Published Articles

  • D. Pronk, L. Scull
    Bicategories of Fractions Revisited: towards small homs and canonical 2-cells
    Theory and Application of Categories, vol 38 pp 913-1014 (2022)
    Published article or arXiv version or preprint

  • T. Chih, L. Scull
    Fundamental Groupoid for Graphs
    Categories and General Algebraic Structures with Applications, vol 16 pp 221-248 (2021)
    Published article or arXiv version or preprint

  • D. Pronk, L. Scull
    The Equivariant Fundamental Groupoid as an Orbifold Invariant
    Homology, Homotopy and Applications, vol 23 pp. 25-47 (2021)
    Published article or arXiv version or preprint

  • T. Chih, L. Scull
    A Homotopy Category for Graphs
    Journal of Algebraic Combinatorics, vol 53(4), pp 1231-1251 (2021)
    Published article or arXiv version or preprint

  • C. Farsi, L. Scull, J. Watts
    Classifying Spaces and Bredon (Co)Homology for Transitive Groupoids
    Proceedings of the AMS vol 148 pp. 2717-2737 (2020)
    Published article or arXiv version or preprint

  • E. Ellis, C. Roitzheim, L. Scull, C. Yarnall
    Endomorphisms of Exotic Models
    Glasgow Mathematical Journal, Volume 61, Issue 2 pp. 321-348 (2019)
    Published article or arXiv version or preprint

  • V. Coufal, D. Pronk, C. Rovi, L. Scull, C. Thatcher
    Orbispaces and their Mapping Spaces via Groupoids: A Categorical Approach,
    Contemporary Mathematics vol 641: Women in Topology: Collaborations in Homotopy Theory, editors: Maria Basterra, Kristine Bauer, Kathryn Hess, Brenda Johnson, pp 135-166 (2015)
    arXiv version or preprint

  • D. Pronk and L. Scull
    Translation Groupoids and Orbifold Bredon Cohomology
    Canadian J. Math Vol 62 (3), pp 614-645 (2010)
    Published article or preprint and a correction

  • J. MacDonald and L. Scull
    Amalgamations of categories
    Canad. Math. Bull. 52 pp 273-284 (2009)
    Published article or preprint

  • M. Bullejos and L. Scull
    A van Kampen theorem for equivariant fundamental groupoids
    JPAA Vol 212 pp 2059 - 2068 (2008)
    Published article or preprint

  • L. Scull
    A model category structure for equivariant algebraic models
    Trans AMS vol 360 pp 2505-2525 (2008)
    Published article or preprint

  • L. Scull
    On the equivariant formality of Kahler manifolds with torus group actions
    Math Z. vol 257 pp 547 - 562 (2007)
    Published Article or preprint

  • L. Scull
    Equivariant formality for actions of Torus groups
    Can. J. Math. Vol 56(06) pp 1290-1307 (2004)
    Published article or preprint

  • L. Scull
    Formality and S^1-Equivariant Algebraic Models
    Homotopy Theory: Relations with Algebraic Geometry, Group Cohomology, and Algebraic K-theory
    Contemp. Math. AMS 346 pp 463-471 (2004)

  • M. A. Mandell and L. Scull
    Algebraic Models for Equivariant Homotopy Theory over Abelian Groups
    Math Z. vol 240 pp 261-287 (2002)
    Published article or preprint

  • L. Scull
    Rational S^1-Equivariant Homotopy Theory
    Trans. AMS, vol 354 pp 1-45 (2002)
    Published article or preprint