Dennis Sweeney

I'm a fifth-year Ph.D. student in the Department of Mathematics at The Ohio State University.

I'm interested in algebraic topology, semigroup theory, and computer science.

My advisor is Sanjeevi Krishnan.

Github

My OSU page

Google Scholar

Mastodon

ORCiD

Research

• Homotopy Types of Small Semigroups [arXiv]
  by Dennis Sweeney.
  Submitted February 2025.
• Regular isotopy classes of link diagrams from Thompson’s groups. [Journal, arXiv]
  by Rushil Raghavan and Dennis Sweeney.
  Published 2023 in Journal of Knot Theory and Its Ramifications.
• Graphical Optimization of Spectral Shift Reconstructions for Optical Backscatter Reflectometry. [Journal]
  by Daniel C. Sweeney, Dennis M. Sweeney, and Christian M. Petrie.
  Published 2021 in Sensors.

Media

• A Sphere is a Loop of Loops
  An animated explainer on homotopy groups. Discusses geometric intuition for π₁/π₂/π₃ using loopspaces of metric spaces. Includes an original, nonstandard visualization of the Hopf map.
  • Ranked #1 in "peer review" of over 400 entries in the 2025 Summer of Math Exposition (SoME4) competition

Software

• I've contributed as a Core Developer to the Python programming language and its standard implementation CPython.
• homology-js, an interactive homology calculator for the browser.
• mutable_lattice, a fast integer linear algebra package for Python, written in C.
• fast_semigroup_homology, a Python package for computing homology of finite semigroups/monoids.
• abelian.py, a Künneth Theorem/Universal Coefficients calculator python script.
• monoid_homology.py a script for computing homology of a monoid presented by a complete rewriting system.
• multimerge, a Python package implementing a multi-way merge algorithm.
• bitalign, a Python package for finding how two bitstrings best line up.
• Data and programs for computing with knots from Thompson's group (unpolished).