​Abstracts and notes:

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Talk 1: Hochschild (co-)homology, closed-open and open-closed maps.

Speaker: Boxi Hao
Abstract: After reviewing some basics of Hochschild (co)homology, we will introduce another chain complex computing Hochild (co)homology, called two-pointed Hochschild (co)chains. We will sketch the construction of open-closed and closed-open maps between the Hochschild (co)homology of the wrapped Fukaya category of a Liouville domain and its symplectic cohomology. Then a similar pair of maps for the two-pointed version will be developed.
Notes for the Talk 1
 

Talk 2: Operations from glued pairs of disks.

Speaker: Kenneth Blakey
Abstract: We begin by discussing the Deligne-Mumford compactification of the moduli space of pairs of disks via appealing to the moduli space of tricolored disks. We then continue by discussing moduli spaces arising from gluing pairs of disks together along identified boundary components. Finally, we construct Floer data and operations associated to these abstract moduli spaces and discuss examples of such operations. The main applications, discussed later in the learning seminar, will be to Floer theory in the product and pseudoholomorphic quilts. 

Notes for the Talk 2

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Talk 3: Floer theory in the product.

Speaker: Siyang Liu
Abstract: In this talk, I'll present the construction of product Fukaya category W^2, a technical replacement of wrapped Fukaya categories of product Liouville manifolds. Via the theory of pseudo-holomorphic quilts developed by Ma'u, Wehrheim and Woodward, we will construct an A_\infty-bifunctor M: W^2\to W-mod-W, and compute M on product Lagrangians and diagonals. This allows us to interpret symplectic cohomology SH^*(M)  of a Liouville manifold M as endomorphisms of diagonal bimodules.

Notes for the Talk 3

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Talk 4:  Moduli spaces with forgotten points and homotopy units.

Speaker: Siyang Liu
Abstract: In this talk, I will briefly explain the construction of units and homotopy units in wrapped Floer theory. The construction requires some new moduli space constructions, the moduli space of discs with forgotten points and homotopy units.

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Talk 5: Split-generating the diagonal.

Speaker: Yonghwan Kim
Abstract: We explain how the diagonal is split-generated by product Lagrangians. We first review the material introduced in Siyang's talks. The proof will then essentially be an application of the proof of Abouzaid's generation criterion.

Notes for the Talk 5
 

Talk 6: Weak Calabi-Yau structure and Cardy condition.

Speaker: Roman Krutowski
Abstract: I will first introduce the inverse dualizing bimodule and show that its tensor product with the diagonal bimodule is quasi-isomorphic to the 2-pointed cochain complex computing Hochschild cohomology. Then I will discuss the construction of the weak Calabi-Yau structure on the wrapped Fukaya category of a Liouville domain. Finally, we will use the above multiplication map and the weak Calabi-Yau structure to show that both open-closed and closed-open maps are isomorphism by constructing a homotopy between the two compositions of the above-mentioned pairs of maps. 
Notes for the Talk 6