Statistical mechanics, Algebra, and Geometry

The conference “Statistical mechanics, Algebra, and Geometry” aims to unite researchers interested in quantum gravity and its rich relations to von-Neumann algebras on the hand, and statistical mechanics approaches, such as Eigenstate Thermalization (ETH), as well as other manifestations of quantum chaos, on the other. The main goal of this conference is to assemble a critical number of top researchers able to engage in discussion and productive collaboration on the relation between von-Neumann algebras, emergent geometry, and recent advances in gravity based in statistical descriptions of quantum chaotic field theories. The aim is to give a compte rendu of the current state of play in the rapidly emerging research line aiming to formalize the conceptual lessons of the quantum informational approach to spacetime geometry, as well as the successes and challenges of using the conceptual and technical insights of quantum chaos to address the same problem. The striking commonalities of these two approaches, for example their close connection to the theory of free probability, which appears both in the classification of von Neumann algebras, as well as in the modern statistical description of the so-called ’eigenstate thermalization hypothesis’, will then hopefully help participants to forge a way forward in addressing deep open problems, for example on the consistent formulation of pure gravity in three dimensions, as well as the role of topology in gravity in three dimensions and above.

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