## The upcoming talk

*At the next session of the TCS,*

*on the 19_{th} of June 2024,*

at 2:15 – 4:15 p.m. CET / 3:15 – 5:15 p.m. EET

**Cornelia Vizman (Universitatea de Vest din Timișoara)**

*shall talk about*

“Universal extensions of Lie algebras of Hamiltonian/divergence free vector fields”.

#### Abstract

*This talk is about two conjectures by Claude Roger in [2]. I will shortly recall our older work [1], where we prove the conjecture about the universal central extension of the Lie algebra of Hamiltonian vector fields. Then I will focus on the universal central extension of the Lie algebra of exact divergence free vector fields. To prove this second conjecture, one needs to make a detour in the realm of Leibniz algebras.*

Joint work with Bas Janssens (Delft University of Technology) and Leonid Ryvkin (University Claude Bernard Lyon 1)

*References:*

[1] B. Janssens, C. Vizman, Universal central extension of the Lie algebra of Hamiltonian vector fields, IMRN, 2016.16 (2016) 4996-5047.

[2] C. Roger, Extensions centrales d’algèbres et de groupes de Lie de dimension infinie, algèbre de Virasoro et généralisations, Rep. Math. Phys., 35 (1995) 225–266.

(**All seminar talks are given on the online zoom platform. The web link for every session is circulated via the TCS mailing list. In order to be enlisted, please contact the Organisers.**)

## Calendar

Date | Speaker (affiliation) | (with a link to the slides, whenever available)Title |

June 19^{th}, 2024 | Cornelia Vizman (Universitatea de Vest din Timișoara) | Universal extensions of Lie algebras of Hamiltonian/divergence free vector fields |

June 12^{th}, 2024 | Wojciech Kamiński (IFT WFUW) | Conformal Einstein’s Equations |

June 5^{th}, 2024 | Eugen Cioroianu (Universitatea din Craiova) | Jacobi-like structures: A line-bundle perspective |

May 29^{th}, 2024 | Oleksii Kotov (Univerzita Hradec Králové) | Introduction to Z-graded manifolds |

May 22^{nd}, 2024 | Maciej Dunajski (University of Cambridge) | Quasi-Einstein metrics |

May 15^{th}, 2024 | Calin I. Lazaroiu (IFIN-HH & UNED) | Weakly Abelian gauge theories |

May 8^{th}, 2024 | Javier de Lucas Araujo (KMMF WFUW) | The local classification of finite-dimensional Lie algebras of analytic Hamiltonian vector fields on the plane |

May 1^{st}, 2024 | Ø (holiday) | Ø |

April 24^{th}, 2024 | Daniel Beltiţă (IMAR) | Lie group representations and standard subspaces of Hilbert spaces |

April 17^{th}, 2024 | Rafał R. Suszek (KMMF WFUW) | 1001 Tricks with Character(s)– A Case for Simplicial Mechanics stitched by Categorified Correspondences |

April 10^{th}, 2024 | Stefan Carstea (IFIN-HH) | Discrete integrable dynamical systems:geometry of invariants and symmetries |

March 27^{th}, 2024 | Katarzyna Grabowska (KMMF WFUW) | Algebroids – a playground for geometric mechanics |

March 20^{th}, 2024 | Janusz Grabowski (IMPAN) | Homogeneity and formalisms of mechanics |

March 13^{th}, 2024 | Radu Purice (IMAR) | Some results in the spectral analysis of quantum Hamiltonians with magnetic fields |

March 6^{th}, 2024 | Vasile Brînzănescu (IMAR) | Algebraic Geometry at IMAR: past and present research |