Abstract. The modern approach to algebraically approximating smoothmanifolds originated in Nash's renowned 1952 work, which Tognolisubstantially improved upon in 1973. I will discuss these historicaldevelopments alongside the subsequent work of several mathematiciansincluding Akbulut, King, Benedetti, and Tognoli. Most recently, Benoistmade significant progress in 2024. Building on Benoist's paper, I obtainedadditional results regarding this problem. My talk will conclude withthese recent results and their applications.\n\nhttps://indico.math.cnrs.fr/event/14566/
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