In my Ph.D. thesis, I argue that lattice-based multi-agent systems constitute a broad class of networked multi-agent systems in which relational data is passed between nodes. Mathematically modeled as lattice-valued sheaves, I initiate a discrete Hodge theory with a Laplace operator, analogous to the graph Laplacian and the graph connection Laplacian, acting on assignments of data to the nodes of a lattice-valued sheaf.

Link: “Lattice Theory in Multi-Agent Systems”

Research Video

I made a 10 minute video that provides a brief summary of my thesis.

Behind the Scences

I used a combination of the following software tools to make my 10 minute reserarch statment:

  • MS PowerPoint, for text, equation, and 2D animations;
  • Cinema4D and Houdini, for 3D animations;
  • Premiere for composting;
  • After Effects for green screen effects;
  • Photoshop for making the chalkboard background;
  • Media Encoder for exporting animations and the final product to various file formats.

At the time, I paid for the Adobe Creative Cloud, but I don’t continue to pay for the costly monthly subscription. There are open-source “alternatives,” as I understand. Cinema4D and Houdini have education liscences that make using these products virtually free.