O. Schiffmann - KLR algebras associated tocurves

The Khovanov–Lauda–Rouquier algebras associated to quivers play a central role in the theory of categorification of integrable highest weight representations of Kac–Moody algebras; thanks to a theorem of Varagnolo–Vasserot and Rouquier, the KLR algebras compute the Ext algebras of the so-called Lusztig perverse sheaves on the moduli stacks of representations of quivers. It is natural from several points of view to study the analogous question in the context of stacks of coherent sheaves on smooth projective curves (the corresponding perverse sheaves were introduced by Laumon). We will present some results, obtained in ongoing joint work with Fang Yang, describing bases of the KLR algebras associated to the projective line, as well as a relation to (a variant of) the Dyck path algebras introduced and studied by Carlsson, Gorsky, Mellit,... https://if-summer-2026.sciencesconf.org/