Research

Overview

My research is in low-dimensional topology, with an emphasis on 3-manifolds and links. My thesis work lies in quantum topology: I study how quantum invariants, in particular the Turaev–Viro invariants, reflect the geometry of 3-manifolds through the generalized Turaev–Viro volume conjecture. My thesis establishes the conjecture for several large classes of 3-manifolds using analytic estimates, TQFT methods, and Ohtsuki’s saddle-point method, supported by computer experiments in Python. Looking ahead, I aim to connect this work to topological quantum computing.
Quantum topology3-manifoldsTuraev–Viro invariantsVolume conjectureTQFTQuantum computing
Core participant and volume conjecture working group spokesperson, IPAM Long Program on Quantum Topology, Character Varieties, and Low-Dimensional Geometry (UCLA, Fall 2026).

Publications & Preprints

Topology

  • Seifert fibered 3-manifolds and Turaev–Viro invariants volume conjecture
    S. Marasinghe (2025)
    Submitted to the International Journal of Mathematics
    arXivPDF
  • Seifert cobordisms and the Chen–Yang volume conjecture
    R. Detcherry, E. Kalfagianni, S. Marasinghe (2025)
    Submitted to the Journal of the London Mathematical Society
    arXivPDF
  • Gluing of two hyperbolic 3-manifolds and the generalized Turaev–Viro invariants volume conjecture
    S. Marasinghe, K. H. Wong, E. Kalfagianni
    In preparation

Mathematics Education

  • Patterns Emerge in Students’ Use of AI in Mathematics
    S. Marasinghe (2026)
    FAST Fellowship classroom research project; presented at the FAST Fellowship Symposium, Michigan State University (April 2026)

Talks

Conference & Invited Talks

  • Introduction to the Turaev–Viro invariants volume conjecture
    IPAM Long Program: Quantum Topology, Character Varieties, and Low-Dimensional Geometry, UCLA
    October 2026
  • Seifert cobordisms and the Chen–Yang volume conjecture
    Advances in Geometric and Quantum Topology, Temple University, Philadelphia
    Slides
    July 13–16, 2026
  • Seifert cobordisms and the Chen–Yang volume conjecture
    Pitt AWM Student Seminar, University of Pittsburgh
    SlidesYouTube
    March 2026 Video: Seifert cobordisms and the Chen–Yang volume conjecture
  • Seifert fibered 3-manifolds and Turaev–Viro invariants volume conjecture
    Midwest Panorama of Geometry and Topology Conference, University of Iowa
    Slides
    June 2025
  • Seifert fibered 3-manifolds and Turaev–Viro invariants volume conjecture
    10th Annual Graduate Student Conference in Algebra, Geometry, and Topology, Temple University
    Slides
    May 2025 Seifert fibered 3-manifolds and Turaev–Viro invariants volume conjecture

Seminar Talks

  • Witten–Reshetikhin–Turaev invariants of Seifert fibered 3-manifolds
    MSU Graduate Geometry and Topology Seminar
    Spring 2025
  • Introduction to the volume conjecture
    MSU Graduate Geometry and Topology Seminar
    Spring 2025
  • Turaev–Viro invariants and Witten–Reshetikhin–Turaev invariants
    Michigan State University
    Fall 2024
  • Ribbon categories
    Michigan State University
    2024
  • 6j-symbols
    MSU Graduate Geometry and Topology Seminar
    2024