Melody Molander

UC Santa Barbara


melodymolander(at)math(dot)ucsb(dot)edu

Home Research Teaching Quantum Algebra & Topology Seminar Talks Outreach

Invited Talks

  1. Joint Mathematics Meetings, “Knots, Skein Modules, and Categorification” Special Session, San Francisco, CA, January 2024, "Skein Theory of Index 4 Subfactor Planar Algebras"
  2. Claremont Topology Seminar, Claremont McKenna College, November 2023, "Skein Theory for Affine ADE Subfactor Planar Algebras"
  3. Twinned Conference on C*-Algebras and Tensor Categories, Fields Institute (in person) and ICMS (streamed live), November 2023, "Skein Theory for Affine ADE Subfactor Planar Algebras"
  4. QGS: Quantum Groups Seminar (Zoom), Université de Lille & University of Oslo, March 2023, "Skein Theory for Affine ADE Subfactor Planar Algebras" (Slides, Video)
    Abstract Subfactor planar algebras first were constructed by Vaughan Jones as a diagrammatic axiomatization of the standard invariant of a subfactor. These planar algebras also encode two other invariants of the subfactors: the index and the principal graph. The Kuperberg Program asks to find all diagrammatic presentations of subfactor planar algebras. This program has been completed for index less than 4. In this talk, I will introduce subfactor planar algebras and give some presentations of subfactor planar algebras of index 4 which have affine ADE Dynkin diagrams as their principal graphs.

Conferences

  1. Young Mathematicians in C*-Algebras (YMC*A), KU Leuven, August 2023, "Skein Theory of Subfactor Planar Algebras"
  2. Great Plains Operator Theory Symposium (GPOTS), The Ohio State University, May 2023, "Skein Theory for Index 4 Subfactor Planar Algebras"
  3. AMS Spring Western Sectional, "Algebraic Structures in Knot Theory" Special Session, Fresno State, May 2023, "Diagrammatic Presentations of Affine Type A Subfactor Planar Algebras of Index 4"
  4. Moab Topology Conference, Utah State - Moab, May 2023, "Skein Theory for Affine ADE Subfactor Planar Algebras"
  5. Redbud Topology Conference, University of Oklahoma, March 2023, "Skein Theory of Affine Type A Subfactor Planar Algebras"
  6. Underrepresented Students in Topology and Algebra Symposium (USTARS), University of Washington, March 2023, Diagrammatic Presentations of Index 4 Planar Algebras
  7. Tech Topology Conference, Georgia Tech, December 2022, "Diagrammatic Presentations of Index 4 Subfactor Planar Algebras"
  8. Topology Students Workshop, Georgia Tech, July 2022, "Diagrammatic Presentations of Affine Type A Subfactor Planar Algebras of Index 4"
  9. BRIDGES: Building Relationships for an Inclusive and Diverse Group of Emerging Students, University of Utah, June 2022, "Diagrammatic Presentations of Affine Type A Subfactor Planar Algebras of Index 4" (Poster)
  10. TORAS: Texas-Oklahoma Representation Theory and Automorphic Forms for Students, University of Oklahoma, March 2015 (Co-Organizer)
  11. Undergraduate Research Conference, UC Davis, April 2014 Comparing Voting Systems Using Kemeny Rankings (Poster)
  12. MAA Golden Section Meeting, Sonoma State University, February 2014, Comparing Voting Systems Using Kemeny Rankings (Poster)

Talks given at the UCSB Hypatian Seminar

  1. "Katherine Johnson: The pioneer whose research got us to outer space!", November 2021
  2. "The Total Beginner's Guide to Creating your Graduate Student Webpage", January 2021
  3. "Creating your Graduate Student Website", January 2020
  4. "Ada Lovelace: Victorian Computer Programming Visionary", November 2019

Talks given for special events

  1. "Pascal's Triangle", Association for Women in Mathematics Math Circle, UC Santa Barbara, February 2020
  2. "My Career in Web Development (and Teaching!)"", Mathematics Career Day, UC Davis, May 2018
  3. "Fractals and the World Around Us" (with Dr. Jeffrey Meyer), Math Day Fun Session, University of Oklahoma, November 2015