Constraints and Aperiodicity in Physics - Hamiltonian Cycles and Quantum Dimer Models

Explore the intersection of local constraints and aperiodic tilings in this lecture from the DIAS Mini Symposium. Discover how correlations emerge from local constraints in physics through examination of constrained models on aperiodic tilings. Learn about proven results for Hamiltonian cycles on the Ammann Beenker tiling, including solutions to the three-colouring problem and travelling salesperson problem. Examine the exact solution of the interacting quantum dimer model on the recently discovered 'Spectre' aperiodic monotiling. Understand ongoing research generalizing these results to random graphs and the development of a new machine learning approach (RSMI-NE) for studying constrained models in large networks without periodicity. Gain insights into cutting-edge research connecting mathematical physics, graph theory, and machine learning applications in non-periodic systems.