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We present a periodic infinite chain of finite generalisations of the exceptional structures, including e 8 , the exceptional Jordan algebra (and pair), and the octonions. We demonstrate that the exceptional Jordan algebra is part of an infinite family of finite-dimensional matrix algebras (corresponding to a particular class of cubic Vinberg's T-algebras). Correspondingly, we prove that e 8 is part of an infinite family of algebras (dubbed "Magic Star" algebras) that resemble lattice vertex algebras. Seminar delivered by MR at the 4th Mile High Conference on Nonassociative Mathematics

We introduce a quantum model for the universe at its early stages, formulating a mechanism for the expansion of space and matter from a quantum initial condition, with particle interactions and creation driven by algebraic extensions of the Kac–Moody Lie algebra e9. We investigate Kac–Moody and Borcherds algebras, and we propose a generalization that meets further requirements that we regard as fundamental in quantum gravity.

We present a periodic infinite chain of finite generalisations of the exceptional structures, including the exceptional Lie algebra e 8 , the exceptional Jordan algebra (and pair) and the octonions. We will also argue on the nature of space-time and indicate how these algebraic structures may inspire a new way of going beyond the current knowledge of fundamental physics.

In neighborhoods throughout major American cities, grassroots efforts in community revitalization are reshaping the public processes and institutional framework involving the design and development of public space. Treating the public realm as both a physical space and an expression of relationships between multiple institutions, organizations, and individuals, this study examines the social and political epistemologies and processes behind the creation of a waterfront park in Oakland, California. It also presents a framework of community‐driven practice in the making of the public realm, based on converging theories of social movements and planning and a critique of the current participatory design model.