Almost Complex Geometry Seminar

Department of Mathematics
The Graduate Center of CUNY

some Fridays 12noon - 1:30pm
via Zoom, link below, open to public
Organizers: Luis Fernandez, Mehdi Lejmi Scott Wilson

Scope: this seminar is devoted to all topics related to almost complex manifolds, including complex manifolds, symplectic topology and geometry, (almost) Kahler geometry, and spin_c geometry, as well the tools of algebraic topology and geometric analysis that have proven useful in studying such structures. The goal is expose students and faculty to present day research and foundational material in a relaxed format that includes traditional lectures with an actively engaged audience.
Prior Semesters: Spring 2021 Fall 2020 Fall 2019 Spring 2019 Fall 2018 Spring 2018 Fall 2017

Fall 2021:

This semester we remain in remote-only meetings, and will abbreviate the schedule to one Friday of each month, until in-person meetings can be accommodated.
Join Zoom Meeting
Meeting ID: 825 6324 2686
Passcode: 999054

9/24: Prof. Fabio Paradiso (U. Torino)
Title: Generalized Kahler almost abelian Lie groups

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 left-invariant 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)
Title: Kahler-Einstein and Kahler-Ricci Soliton Metrics on Cohomogeneity-One Manifolds

Abstract: We employ shear operators to give a new interpretation of the integrability of almost-complex structures in dimension 4. In higher dimensions these operators can be used to restrict the Gray-Hervella class of an almost-Hermitian structure. We then use these notions in a construction of a Lie bracket ansatz for Kahler metrics. This ansatz includes manifolds of cohomogeneity-one, including a new complete Kahler-Einstein manifold and Kahler-Ricci solitons. The Kahler-Einstein manifold is 4-dimensional with isometry group E(2), the rigid motions of the plane. The Kahler-Ricci solitons reside on 2m-dimensional manifolds for any m>1. They are gradient, expanding, and their isometry group is the (2m-1)-dimensional Heisenberg group H_{2m-1}. 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 4-dimensional, Kahler Ricci-flat, non-cohomogeneity one metrics and discuss possible extensions to higher dimensions.

11/19: Kevin Sackel (Stony Brook University)
Title: Vignettes from the locally conformal symplectic landscape.

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:
Title: Informal discussion (students and faculty welcome)

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



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