### Yangians and Cohomological Hall algebras of curves

Project Type: JSPS Grant-in-Aid for Scientific Research (C)

Funded by: Japan Society for the Promotion of Science

Period: Apr 01, 2021 – Mar 31, 2026

Budget: ¥ 4290000

Website: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21K03197/

Principal Investigator: Francesco Sala (Università di Pisa)

##### Description

The project stands at the crossroads between representation theory and geometry. It aims at discovering new algebraic structures (Lie algebras associated with curves) which should encode geometric properties of (moduli) spaces appearing in the so-called Riemann-Hilbert and the non-abelian Hodge correspondences for curves. We expect that this theory of Lie algebras associated with curves will unlock a new striking connection between geometry, algebra, and physics, which needs to be investigated further.