# Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar

## Three 20-min Research Talks

**Yash Deshmukh **(Columbia University): Moduli Spaces of Nodal Curves from Homotopical Algebra

I will discuss how the Deligne-Mumford compactification of curves arises from the uncompactified moduli spaces of curves as a result of some algebraic operations related to (pr)operadic structures on the moduli spaces. I will describe how a variation of this naturally gives rise to another new partial compactification of moduli spaces curves. Time permitting, I will indicate how it is related to secondary operations on symplectic cohomology and discuss some ongoing work in this direction.

**Lea Kenigsberg **(Columbia University): Coproduct Structures, a Tale of Two Outputs

I will motivate the study of coproducts and describe a new coproduct structure on the symplectic cohomology of Liouville manifolds. Time permitting, I will indicate how to compute it in an example to show that it's not trivial. This is based on my thesis work, in progress.

**Thomas Massoni **(Princeton University): Non-Weinstein Liouville Domains and Three-Dimensional Anosov Flows

Weinstein domains and their symplectic invariants have been extensively studied over the last 30 years. Little is known about non-Weinstein Liouville domains, whose first instance is due to McDuff. I will describe two key examples of such domains in dimension four, and then explain how they fit into a general construction based on Anosov flows on three-manifolds. The symplectic invariants of these “Anosov Liouville domains” constitute new invariants of Anosov flows. The algebraic structure of their wrapped Fukaya categories is in stark contrast with the Weinstein case.

This is mostly based on joint work arXiv:2211.07453 with Kai Cieliebak, Oleg Lazarev and Agustin Moreno