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Explore a comprehensive mathematical framework for understanding interacting particle systems with conservation laws in this 52-minute conference talk. Learn about a unified approach that encompasses various discrete particle systems including exclusion processes, generalized exclusion processes, misanthrope processes, and multi-species exclusion processes. Discover how this framework addresses two fundamental questions: the formulation of conserved quantities and the conditions required for scaling limits to hold. Examine the co-homological justification for conserved quantities and investigate the combinatorial structures that emerge from these considerations. Understand the geometric formulation of diffusion and mobility matrices for systems with product reversible measures, regardless of gradient type. Review the conjectured universal forms of hydrodynamic limits and equilibrium fluctuations, while discussing current gaps in mathematical proofs. Gain insights into cutting-edge research that bridges specific model studies with general theoretical frameworks in mathematical physics and probability theory.
