Oliver Lindström: Log Geometric Models for Little Disks Operads

Abstract: The operads of little disks and framed little disks are arguably the most well known and important examples of topological operads. For various different reasons, at least the dimension 2 versions of these operads have long been expected to have some form of algebro-geometric or motivic origin. This expectation was shown to be true by Dmitry Vaintrob who constructed a log-geometric model of the framed little 2-dimensional disks operad in 2019. In this talk I will review the main ideas of Vaintrob's construction and explain how they can be generalized to give a similar result for little disks in arbitrary even dimension using the ``moduli space´´ of stable pointed trees of projective spaces. If time allows it, I will also review how models of the unframed little disks operads can be constructed using virtual logarithmic geometry.