3620 South Vermont Avenue, Los Angeles, CA 90089

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Yash Deshmukh, University of Columbia

Abstract: A result of G. Drummond-Cole relates the framed little disks operad to the genus zero Deligne-Mumford operad. In this talk, I will discuss the higher genus, multiple input-output analog of this result. I will explain how the extension of an action of the properad of Riemann surfaces having parameterized boundaries to an action of the properad of nodal Riemann surfaces is equivalent, homotopically, to the data of trivializations of certain operations coming from the moduli spaces of annuli. In the process, I will also introduce a new partial compactification of the moduli spaces of Riemann surfaces which is relevant to the study of symplectic cohomology, and describe a version of the above statement concerning the extension of action to these moduli spaces.

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