The Stemkoski Research Group

Thank you for your interest in the Stemkoski Research Group! I have mentored dozens of individual and group student research projects at all levels (from first-year to senior and graduate college students) for over 15 years. This page contains basic information about student-accessible research topics, projects, and creative work opportunities. Many of the topics involve mathematics and/or computer science; I am also interested in cross-disciplinary projects incorporating technology in areas such as music, art, literature, science, and economics, and I am open to project ideas in other areas as well.

All are welcome! For many of the topics listed here, the required background knowledge is minimal (such as Calculus courses for mathematics projects, or programming courses for computer science projects). Any additional knowledge can be learned as needed; many projects begin with background readings and discussion. The most important qualities you will need to have or develop are:

  • interest in the topic itself
  • attention to detail and precision
  • ability and motivation to work independently
  • time management skills to pace your efforts steadily and meet deadlines
  • resourcefulness in locating information and references relevant to topic
  • availability to meet on a regular basis
  • ability to communicate clearly with others (verbally and in writing)
  • resiliency to continue in spite of possible challenges and difficulties
  • an enthusiastic and positive attitude!

As long as you have some of these qualities and are willing to work to develop the rest, a research project can be a worthwhile experience for you!

If you are a current Adelphi student, you have the option to sign up for a research course or independent study course with me for credit. In such a course, your time will be spent working on one of these topics and meeting with me and/or a small group of students regularly.

The final part of your research experience will be to share and communicate the results of your work. This may consist of some combination of the following:

  • presenting at Adelphi's annual Scholarship and Creative Works conference
  • presenting at an exhibition or at a local or national conference
  • writing a report, article, or thesis, for dissemination and/or publication

For more information about any of the topics listed below, information about the research process, or if you are interested in working on any of the projects described here, please contact me via e-mail. (Due to time constraints, I may not be able to accept all research mentoring requests, but I strive to accomodate as many students as possible, and if I am not available, I can help you find an alternative mentor.)

I look forward to hearing from you!

Research Topics

Some of the areas in which I mentor student research include:

  • Computer Graphics and GPU Programming

    • programming 2D and 3D cellular automata simulations (such as Conway's Game of Life)
    • documenting, writing tutorials, creating games, and developing additional features for the Basic Adaptable Game Engine Library (B.A.G.E.L.); see original codebase and instructional videos
    • designing software with consistent graphical user interfaces across Java, Python, and Javascript
    • developing and implementing algorithms to create randomly / procedurally generated content (such as 2D image textures, 3D landscapes; see here for details)
    • writing OpenGL shaders to simulate animated environmental effects (water, fire/smoke, clouds, etc.)
    • writing general shader-based particle engines/systems; see here for a live example
    • using open access geographical data (such as Open Street Map) to generate interactive 3D environments (such as these)
    • creating interactive web-based 2D and 3D function graphers using MathBox
    • writing OpenGL shaders for mathematical visualization: graphing implicit functions / multivariable functions and generating geometric fractals (Sierpinski triangle, Hilbert curve) and complex fractals (Mandlebrot and Julia sets)
    • investigating graphical representations of higher-dimensional spaces and objects (such as tesseracts) using projections in combination with color-based visual cues to convey hyper-depth data
    • rendering 3D scenes using raymarching signed distance fields instead of triangular meshes (see here for a live example)

  • Augmented and Virtual Reality

    Most of these projects are web-based, for accessibility purposes, built using A-Frame and/or Three.js and/or AR.js. Many of the projects are cross-platform compatible and run on some combination of smartphones, tablets, laptops (with webcams), and VR headsets (such as Meta Quest).
    • creating interactive AR-based experiences, using single- and multi-marker tracking; see here for examples
    • designing alternative screen-based control systems for navigating 3D environments; see here for examples
    • creating VR applications that run in the Meta Quest browser and use controllers; see here (bottom of page) for examples

  • Theoretical Computer Science

  • Theoretical Mathematics

    • knot theory: identifying and classifying polynomial-based parameterizations of (open-ended) knots
    • fractal geometry: using iterated curve hoisting and Fourier series to generate parameterizations of fractal-like curves
    • number theory: investigating accessible proofs of Fermat's Last Theorem for small prime exponents
    • group theory: determining the structure of permutation groups associated to polyhedral puzzles similar to Rubik's Cube
    • game theory: applying game theoretic concepts to models in evolutionary biology, economics, and social sciences, analyzed via differential equations or computer simulations

  • Mathematics Education

    • creating interactive graphs using Desmos and GeoGebra
    • creating physical and digital manipulatives for classroom use
    • writing historical modules for mathematics courses
    • designing and programming interactive "pedagogically telescopic" proofs

  • Interdisiciplinary Areas

    • writing interactive fiction (see Twinery for software and examples)
    • generating mathematically inspired art (2D examples based on Fractal Geometry or Hyperbolic Geometry; 3D examples made with Blender)
    • creating agent-based simulation models for the sciences and social sciences (see NetLogo for software and examples)
    • writing programs that create randomized stories, music, or art, based on a set of training examples or statistical data

Current/Former Research Students and Projects

  • "Star-Shaped Regions in Non-Euclidean Geometries", with Matthew Klepadlo, 2023-2024
  • "Philosophy of Mathematics: Provability and Truth", with Tori de la Hoz, 2023-2024
  • "Advanced 3D Game Development", with Rousseau Francois, Ralph Garcia, and Larry Moreno, 2023-2024
  • "Machine Learning and Procedurally Generated Stories", with Norah Curran (1), 2023-2024
  • "Interactive Web-Based Music Applications", with Tyler Reid, 2023-2024
  • "Procedurally Generated Music and Computer Graphics”, with Christopher Benson and Faith Mock (2), 2022-2023
  • "Interactive Computer Animations for Mathematics Education”, with Faith Mock and Jarred Navarro (2), 2022-2023
  • "Computer Graphics and GPU Programming with Java", with James Cona, 2020-2021
  • "Agent-Based Models and Genetic Algorithms", with Jennefer Maldonado, 2019-2020
  • "Parameterizations of Fractal-like Curves", with Vincent Schinina (3), 2019-2020
  • "3D Videography and Virtual Reality", with Paul Maurantonio, 2019-2020
  • "Psychological Effects of Loot Boxes in Video Games", with Thomas Dayton (1), 2019-2020
  • "Computer Graphics and GPU Programming with Python", with Michael Pascale, 2019-2020
  • "Augmented Reality: Theory and Applications", with Ryan Barrett (1)(2), 2018-2019
  • "Virtual Reality Video Game Development", with Evan Leider (2), 2018-2019
  • "Python Algorithms for Constructive Solid Geometry", with Bradon Cortes and Maxwell Guarnieri, 2018-2019
  • "Interactive Literature: Creation and Context", with Caitlin Lenhan (1), 2017-2018
  • "Adaptive Learning Technology in Mathematics Education", with Emily Harris (1), 2017-2018
  • "Adelphi University: 3D Multiplayer Simulation", with Mathew Mallory, Robert Monteleone, and Justin Pedowitz (2), 2016-2017
  • "Understanding the Fourth Spatial Dimension via Interactive Software", with Cécile Cornelus (1), 2014-2015
  • "Creating a 3D Computer Graphics Engine", with Matthew Matero, 2013-2014
  • "Hyperbolic Geometry and the Art of M.C. Escher", with Julia Huntermark (1), 2012-2013
  • "Generalized Self-Similar Curves", with Carissa Brtalik and Magdalena Mulvihill (3), 2012-2013
  • "Polynomial Knots", with Anthony Del Latto, Dayna Goeringer, and Steven Roveto (3), 2011-2012
  • "Evolution and Population Dynamics in Game Theory", with Tara Gangarossa (3), 2011-2012
  • "Efficiency of Algorithms for Solving Rubik's Cube with Abstract Algebra", with Nicolas Micelli (3), 2011-2012
  • "Hinton and the Fourth Spatial Dimension", with Samuel C. Herwood (1),(3), 2011-2012
  • "Hyperbolic Curve Cryptography", with Katherine Weiss (3), 2011-2012
  • "Polynomial Knots of Degree Seven", with Salvatore Giunta and Kavi Gupta (3), 2010-2011
  • "Generalizations of the Prisoners' Dilemma", with Rachel Sherman (3), 2010-2011
  • "Rubik Groups of Dual Polyhedra", with Corinna Venezia (3), 2010-2011
  • "Telescopic Proofs and Fermat's Last Theorem", with Christopher Kirk, 2009-2010
  • "Group Structure of Rubik-like Puzzles (Octahedra)", with Shannon Zeckzer (3), 2009-2010
  • "Agent-Based Simulations of the Anasazi Culture", with Nicole Alves (1)(3), 2008-2009
  • "Group Structure of Rubik-like Puzzles (Prisms)", with Jaclyn Bogensberger (1)(3), 2008-2009
  • "Geometry of the Parameter Space of Polynomial Knots", with Adam Schoepfin (1), 2008-2009
  • "Game-Theoretic Agent-Based Models and Evolution of Behavioral Strategies", with Edwin Chen (1), 2007-2008
  • "Many-Option Games and Genetic Algorithm-Based Simulation Models of Social Interaction", with Joseph Dilallo (1), 2007-2008
  • "A Comparative Analysis of Traditional Economic Theory and Complexity Economics", with Akhil Ketkar, 2007-2008

(1) indicates project was basis for student's Honors College thesis
(2) indicates project was presented by student(s) at a local conference
(3) indicates project was presented by student(s) at a national conference