#### Alladi Ramakrishnan Hall

#### Homotopically extending actions of moduli spaces of Riemann surfaces

#### Yash Deshmukh

##### Columbia University

*A proposal of Kontsevich for recovering enumerative mirror symmetry from homological mirror symmetry involves the construction of categorical enumerative invariants associated with suitable (smooth, proper, Calabi-Yau) categories. Defining these invariants involves constructing 'actions' of uncompactified moduli spaces of Riemann surfaces and extending these to actions of compactified moduli spaces. In this talk, I will discuss the homotopy theoretic aspects of this extension problem. After a general overview of mirror symmetry, I will explain what the 'actions' of moduli spaces mentioned above refer to. I will then describe the extension statements which are motivated by looking at what happens on the A-side (the symplectic side) of mirror symmetry and sketch a proof. I will not assume any specialized knowledge of mirror symmetry or symplectic topology.*

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