付 佳奇 FU, Jiaqi

Talks

• 2023 Summer at SUSTech: A derived bridge between Lie algebroids and foliations. slides

  Introducing the duality between partition Lie algebroids and "foliation-like algebras".

• 2023 Summer at Wuhan university: A derived bridge between Lie algebroids and foliations.

  Introducing the duality between partition Lie algebroids and "foliation-like algebras".

• 2023-2024 Working group at Toulouse: Prismatic cohomology. homepage,

  We principally followed Bhatt's note on prismatization.

  my talk notes: 1, 2, 3, 4
• 2024 Octorber at Angers: Formal geometry of algebraic foliations. note

  The holomorphic Frobenius theorem states that every smooth holomorphic foliation is locally a fibration. However, its analogue in algebraic geometry fails manifoldly. This problem motivates infinitesimal derived foliations (in the sense of Toën and Vezzosi). In this talk, we will show that they are essentially equivalent to partition Lie algebroids, and discuss the application to the formal geometry of foliations over general bases.

• 2024 November at Texas Tech (online): A Koszul duality of partition Lie algebras. note

  Partition Lie algebras are sophisticated algebraic objects introduced by Brantner--Mathew to control infinitesimal deformations in positive characteristics. This talk will present a Koszul duality between partition Lie algebras and specific complete filtered derived rings. This duality helps to understand the homotopy operations on partition Lie algebras. Additionally, a “many-object” version of this duality connects partition Lie algebroids with infinitesimal derived foliations in the sense of Toën--Vezzosi.

• 2024 November at Göttingen: A Koszul duality of partition Lie algebras(-oids).

  Partition Lie algebras are sophisticated algebraic objects introduced by Brantner--Mathew to control infinitesimal deformations in positive characteristics. This talk will present a Koszul duality between partition Lie algebras and specific complete filtered derived rings. This duality helps to understand the homotopy operations on partition Lie algebras. Additionally, a “many-object” version of this duality connects partition Lie algebroids with infinitesimal derived foliations in the sense of Toën--Vezzosi.