Almost Complex Geometry Seminar
Department of Mathematics

Fall 2021:This semester we remain in remoteonly meetings, and will abbreviate the schedule to one Friday of each month, until inperson meetings can be accommodated.Join Zoom Meeting Meeting ID: 825 6324 2686 Passcode: 999054 
9/24: Prof. Fabio Paradiso (U. Torino)
Abstract: Generalized Kahler structures were introduced by M. Gualtieri as a generalization of Kahler structures in the broader setting of generalized geometry.
In this talk, I will present some recent results concerning leftinvariant generalized Kahler structures on almost abelian Lie groups and their compact quotients. This is joint work with Anna Fino.

10/29: Prof.Robert Ream (Clark University)
Abstract: We employ shear operators to give a new interpretation of the integrability of almostcomplex structures in dimension 4. In higher dimensions these operators can be used to restrict the GrayHervella class of an almostHermitian structure. We then use these notions in a construction of a Lie bracket ansatz for Kahler metrics. This ansatz includes manifolds of cohomogeneityone, including a new complete KahlerEinstein manifold and KahlerRicci solitons. The KahlerEinstein manifold is 4dimensional with isometry group E(2), the rigid motions of the plane. The KahlerRicci solitons reside on 2mdimensional manifolds for any m>1. They are gradient, expanding, and their isometry group is the (2m1)dimensional Heisenberg group H_{2m1}. We discuss the curvature asymptotics and geometric properties of these manifolds and compare them to known examples. If time permits we will briefly describe a local result concerning 4dimensional, Kahler Ricciflat, noncohomogeneity one metrics and discuss possible extensions to higher dimensions.

11/19: Kevin Sackel (Stony Brook University)
Abstract: In the first half of the talk, we will present a cohesive topological picture for locally conformal symplectic (LCS) geometry and their automorphisms. In the second half, we will explore a variety of less elementary theorems in the field. Some of these results bring LCS geometry closer to symplectic geometry; others push it farther away. An example of the latter is the fact that every almost complex manifold admits an LCS structure, a result due originally to Eliashberg and Murphy and more recently refined by Bertelson and Meigniez. Although most of the talk is expository, parts of the perspective I will present have not appeared in the literature.

12/10:
Abstract: We invite graduate students especially to talk math as well as
plans for next semester.
