### GRT at home Seminar

Andrea Maffei, University of Pisa, Italy

Local opers with two singularities in the case of $$\mathsf{PSL}(2)$$

Organizer's time: 2021-02-23 17:00 Europe/Rome

Duration: 1 hour 15 minutes

Abstract: Let $G$ be an adjoint simple algebraic group over the complex numbers with Lie algebra $\mathfrak{g}$. Opers are particular families of $G$-connections on an algebraic curve. Feigin and Frenkel proved that in the case of the punctured disc, the ring of functions on the space of opers is isomorphic to the center of the enveloping algebra of the affine Lie algebra of $\mathfrak{g}^L$ at the critical level. Gaitsgory and Frenkel studied the geometry of the space of opers and its relations with the representation theory of the affine Lie algebra of $\mathfrak{g}^L$. In the case of unramified connections and spherical representations their results are more complete and precise. Together with Giorgia Fortuna, Davide Lombardo and Valerio Melani, we have studied local opers with two singularities in the case of $\mathsf{PSL}(2)$, proving analogues of some of the results of Feigin and Frenkel and of Frenkel and Gaitsgory.