A Homotopical Description of Deligne-Mumford Compactifications

Explore a homotopical approach to Deligne-Mumford compactifications in this one-hour lecture from the Western Hemisphere Virtual Symplectic Seminar. Delve into how moduli spaces of curves across all genera emerge from framed curve moduli spaces through the homotopic trivialization of specific circle actions. Examine the relevance of this description to connecting Gromov-Witten invariants with Fukaya categories. Compare the presented findings to existing literature in the field. If time allows, investigate a variation of the result leading to a partial compactification of curve moduli spaces, with implications for symplectic cohomology studies.