## graduate student symplectic geometry seminar

This seminar is an informal, discussion-style seminar for those interested in symplectic geometry.
Some possible topics:
• Weinstein's symplectic category, Lagrangian correspondences
• Microlocal analysis, geometric quantization
• Poisson geometry, symplectic groupoids, AMM moment maps
• Chern-Simons theory, AdPW geometric quantization, configuration space integrals
• shifted symplectic structures, Lagrangian intersections, derived Poisson geometry
• symplectic geometry of moduli of local systems
• BV formalism, odd symplectic super-/graded- geometry, AKSZ & TQFTs
• Floer theory, Fukaya categories

schedule: F 1 - 2:15 @ Lunt 107

June 21, 2019 — Mike Geis — Weinstein's symplectic "category"
• Weinstein defined a morphism between symplectic manifolds as a lagrangian submanifold of the product equipped with a half density. I will describe the algebra of composition and where this concept came from. Essentially, in the case of cotangent bundles it is a geometric version of the composition algebra of Fourier integral operators on the base manifolds. I will assume no familiarity with FIOs and microlocal analysis.

• References:

June 28, 2019 — Nilay Kumar — Derived Lagrangian correspondences
• Last time Mike introduced canonical relations (aka Lagrangian correspondences) as a generalization of symplectomorphisms and described why certain types of transversality are necessary for composing them. In this talk we will work in the setting of derived (algebraic) geometry, where intersections are automatically transverse. For the first half, we will get comfortable with differential forms on derived schemes and introduce shifted symplectic structures on derived (Artin) stacks (Pantev-Toen-Vaquie-Vezzosi, 2013). We will describe the derived notion of Lagrangians and Lagrangian correspondences, and then follow Calaque (2015) in the construction of a semiclassical TFT from the data of a $$k$$-shifted symplectic derived stack $$X$$: the monoidal functor $$\text{Map}( -,X): \mathsf{Cob}_d \to \mathsf{LagCorr}_{k-d}$$.

• References: