A Differential Algebraic Closure Theory for Tilings: A Unified Constructive Framework

Key Points

• This research aims to develop a constructive framework for studying diverse tiling problems across various geometric contexts.
• Developed a unifying framework based on differential algebraic closure for tilings.
• Encoded geometric constraints into differential algebraic equations (DAE) systems.
• Included machine learning techniques like graph neural networks to enhance calculations.
• Introduced explicit recursive construction methods for different tiling cases.
• Established connections between tilings and geometric flows, facilitating dynamic analysis.
• Explored implementations of the fractional quantum Hall state within this framework.

Abstract