We describe some recent and ongoing developments in the study of highest weight representations of affine W-algebras, with an emphasis on new techniques and intuitions coming from the local geometric Langlands program. We will describe what is known in the principal case, including the geometric representation theory (Steinberg--Whittaker sheaves), and some related conjectures of Aganagic--Frenkel--Okounkov,Feigin--Gainutdinov--Semikhatov--Tipunin, Frenkel--Kac--Wakimoto, and Gaitsgory--Lurie. We will also outline some related expectations and conjectures for the non-principal cases.

Room:
RIMS 402 (November 14 (Mon), November 15 (Tue), November 21 (Mon), November 22 (Tue))
RIMS 006 (November 16 (Wed))