Algebraic Geometry in Cosmology

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The talk is based on joint work with Yuri Manin (arXiv:1402.2158). Using algebro-geometric blowups it is possible to construct a family of models of gluing of aeons across a Big-Bang type singularity, which includes the case of Penrose's conformally cyclic cosmology, as well as inflationary multiverse models generalizing the "eternal symmetree", and BKLL mixmaster type cosmologies. Using the mixmaster dynamics, formulated in terms of elliptic curves and modular curves, we speculate on the geometry of cosmological time near the gluing of aeons. We show also that this type of model allows for phenomena of noncommutativity of spacetime coordinates near the Big-Bang and the crossing of aeons.