Title：Construction of nilpotent Lie algebras with complex structures

Reporter：Adela Latorre

Work Unit：Universidad Politécnica de Madrid

Time：2023/09/21 17:00-19:00

Address：Zoom id：904 645 6677 Password:2023

**Summary of the report: **

Complex manifolds can be characterized as pairs (M,J), where M is an even-dimensional differentiable manifold and J is a complex structure on it. Although the explicit construction of these J's is a difficult task, the problem can be slightly simplified when M is a nilmanifold and one restricts to the study of invariant complex structures on M. In this case, the problem of finding the pairs (M,J) is related to the classification of real nilpotent Lie algebras with complex structures. Such classification has been completed in real dimensions 4 and 6. However, the same techniques are difficult to apply when the dimension of the nilpotent Lie algebra is equal to or higher than 8. In this talk, we will present a new approach to the problem that will allow us to find every 8-dimensional real nilpotent Lie algebra having one-dimensional center and admitting complex structures.

**Introduction of the Reporter: **

Adela Latorre works at the Department of Applied Mathematics of the Polytechnic University of Madrid (Spain). Her main research area is complex non-Kähler geometry, although she is also interested in topics related to Lie algebras and Lie groups.